Today in Jewish History:
• Hashmonean Holiday (2nd century BCE)
On Shevat 28 (134 BCE?), Antiochus V abandoned his siege of Jerusalem and his plans for the city's destruction. This day was observed as a holiday in Hashmonean times. (Megilat Taanit)
Daily Quote:
One who does not see G-d everywhere does not see him anywhere[The Rebbe of Kotzk]
Daily Study:
Chitas and Rambam for today:
Chumash: with Rashi
• Chapter 25
31And you shall make a menorah of pure gold. The menorah shall be made of hammered work; its base and its stem, its goblets, its knobs, and its flowers shall [all] be [one piece] with it. לאוְעָשִׂיתָ מְנֹרַת זָהָב טָהוֹר מִקְשָׁה תֵּיעָשֶׂה הַמְּנוֹרָה יְרֵכָהּ וְקָנָהּ גְּבִיעֶיהָ כַּפְתֹּרֶיהָ וּפְרָחֶיהָ מִמֶּנָּה יִהְיוּ:
The menorah shall be made of hammered work: [meaning] that it must not be made in sections, [which can be removed]. Its branches and its lamps should not be made individually and then attached, as is the custom of the smiths [through a process] called solderez [in French], soldering, but it [the menorah] must come [be constructed] entirely from one piece [of gold]-beaten with a hammer and cut with a tool, and the branches separated on both sides. — [from Baraitha Melecheth HaMishkan.] מקשה תעשה המנורה: שלא יעשנה חוליות, ולא יעשה קניה ונרותיה איברים איברים, ואחר כך ידביקם כדרך הצורפין, שקורין שולדי"ר בלעז [להלחים] אלא כולה באה מחתיכה אחת, ומקיש בקורנס וחותך בכלי האומנות ומפריד הקנים אילך ואילך:
of hammered work: Heb. מִקְשָׁה. Its Aramaic translation is נְגִיד, an expression of drawing out, [meaning] that he draws the parts out of the block of gold on either side by beating [it] with a hammer. The word מִקְשָׁה means the blow of a hammer, batediz in Old French, hammered, like “knocked (נָקְשָׁן) one against the other” (Dan. 5:6). מקשה: תרגומו נגיד, לשון המשכה שממשיך את האיברים מן העשת לכאן ולכאן בהקשת הקורנס, ולשון מקשה מכת קורנס, בטידי"ץ בלעז [עשוי בהכאה] כמו (דניאל ה ו) דא לדא נקשן):
the menorah shall be made: By itself. Since Moses found difficulty with it [i.e., figuring out how to form the menorah], the Holy One, blessed is He, said to him, “Cast the talent [equivalent to sixty-four pounds of gold] into the fire, and it will be made by itself.” Therefore, it is not written: ךְתֵּעָשֶׂה but ךְתֵּיעָשֶׂה. -[from Tan. Beha’alothecha 3] תיעשה המנורה: מאליה, לפי שהיה משה מתקשה בה, אמר לו הקב"ה השלך את הככר לאור והיא נעשית מאליה, לכך לא נכתב תעשה:
its base: This refers to the foot on the bottom [of the menorah], which was made like a box with three legs coming out of it [protruding] downwards. ירכה: הוא הרגל של מטה העשוי כמין תיבה, ושלשה רגלים יוצאין הימנה ולמטה:
and its stem: [This refers to] its central stem rising from the middle of the base, erected upward. At the top of it was the middle lamp, made like a spoon, into which the oil was poured and the wick inserted. וקנה: הקנה האמצעי שלה העולה באמצע הירך זקוף כלפי מעלה, ועליו נר האמצעי עשוי כמין בזך לצוק השמן לתוכו ולתת הפתילה:
its goblets: They are a sort of cups made of glass, long and narrow, which are called maderins [in Old French], long, slender glass goblets. These, however, were made of gold, and they protruded from every branch according to the number prescribed by the text. They were [placed] on it [the menorah] only for beauty. גביעיה: הן כמין כוסות שעושין מזכוכית ארוכים וקצרים, וקורין להם מדרינ"ש בלעז [גביעים], ואלו עשויין מזהב ובולטין ויוצאין מכל קנה וקנה כמנין שנתן בהם הכתוב, ולא היו בה אלא לנוי:
its knobs: [They were] like sort of round apples all around [the branch], protruding [outward] around the middle branch, in the style of the menoroth that are made for princes. They are called pomeles [in French], apple-shaped knobs (Men. 28b). Their number is prescribed in this parsha, [i.e.,] how many knobs protruded from it and how much [space] was [left] unadorned between one knob and another knob. כפתריה: כמין תפוחים עגולין סביב, בולטין סביבות הקנה האמצעי, כדרך שעושין למנורות שלפני השרים וקורין להם פומיל"ש בלעז [כפתורים], ומנין שלהם כתוב בפרשה, כמה כפתורים בולטין ממנה, וכמה חלק בין כפתור לכפתור:
and its flowers: Engravings made on it like a sort of flowers. ופרחיה: ציורין עשויין בה כמין פרחים:
shall [all] be [one piece] with it: Everything shall be of hammered work, out of the solid block [of gold], and not made separately and then attached [to the main stem]. ממנה יהיו: הכל מקשה יוצא מתוך חתיכת העשת, ולא יעשם לבדם וידביקם:
32And six branches coming out of its sides: three menorah branches from its one side and three menorah branches from its second side. לבוְשִׁשָּׁה קָנִים יֹצְאִים מִצִּדֶּיהָ שְׁלשָׁה | קְנֵי מְנֹרָה מִצִּדָּהּ הָאֶחָד וּשְׁלשָׁה קְנֵי מְנֹרָה מִצִּדָּהּ הַשֵּׁנִי:
coming out of its sides: from here and there [in each direction] diagonally, drawn upwards until [they reached] the height of the menorah, which is the middle stem. They came out of the middle stem, one higher than the others: the bottom one was longest, the one above it was shorter than it, and the highest one shorter than that, because the height of their ends [at their tops] was equal to the height of the seventh, middle stem, out of which the six branches extended. יצאים מצדיה: לכאן ולכאן באלכסון, נמשכים ועולין עד כנגד גובהה של מנורה, שהוא קנה האמצעי, ויוצאין מתוך קנה האמצעי זה למעלה מזה, התחתון ארוך, ושל מעלה קצר הימנו והעליון קצר הימנו, לפי שהיה גובה ראשיהן שוה לגובהו של קנה האמצעי השביעי, שממנו יוצאים ששת הקנים:
33Three decorated goblets on one branch, a knob and a flower, and three decorated goblets on one branch, a knob and a flower; so for the six branches that come out of the menorah. לגשְׁלשָׁה גְבִעִים מְשֻׁקָּדִים בַּקָּנֶה הָאֶחָד כַּפְתֹּר וָפֶרַח וּשְׁלשָׁה גְבִעִים מְשֻׁקָּדִים בַּקָּנֶה הָאֶחָד כַּפְתֹּר וָפָרַח כֵּן לְשֵׁשֶׁת הַקָּנִים הַיֹּצְאִים מִן הַמְּנֹרָה:
decorated: Heb. מְשֻׁקָּדִים, as the Targum [Onkelos] renders מְצַיְירִין. They were decorated in the manner that silver and gold vessels are made, which is called nieler [in Old French, nieller in modern French, niello in English]. משקדים: כתרגומו, מצויירים היו כדרך שעושין לכלי כסף וזהב שקורין ניילי"ר [לגפר]:
and three decorated goblets: protruding from each branch. ושלשה גבעים: בולטין מכל קנה וקנה:
a knob and a flower: were on each branch. כפתר ופרח: היה לכל קנה וקנה:
34And on [the stem of] the menorah [shall be] four decorated goblets, its knobs and its flowers. לדוּבַמְּנֹרָה אַרְבָּעָה גְבִעִים מְשֻׁקָּדִים כַּפְתֹּרֶיהָ וּפְרָחֶיהָ:
And on [the stem of] the menorah [shall be] four… goblets: On the main stem of the menorah were four goblets: one protruding on it below the branches and three above the exit of the three branches that extended outwards from its sides. ובמנרה ארבעה גבעים: בגופה של מנורה היו ארבעה גביעים אחד בולט בה למטה מן הקנים, והשלשה למעלה מן יציאת הקנים היוצאים מצדיה:
decorated…its knobs and its flowers: This is one of the five verses whose meaning cannot be determined. It is unknown whether [to read] “decorated goblets” or “decorated its knobs and its flowers."-[from Yoma 52b] משקדים כפתריה ופרחיה: זה אחד מחמשה מקראות שאין להם הכרע, שאין ידוע אם גביעים משוקדים או משוקדים כפתוריה ופרחיה:
35And a knob under the two branches from it, and a knob under the two branches from it, and a knob under the two branches from it; so for the six branches that come out of the menorah. להוְכַפְתֹּר תַּחַת שְׁנֵי הַקָּנִים מִמֶּנָּה וְכַפְתֹּר תַּחַת שְׁנֵי הַקָּנִים מִמֶּנָּה וְכַפְתֹּר תַּחַת שְׁנֵי הַקָּנִים מִמֶּנָּה לְשֵׁשֶׁת הַקָּנִים הַיֹּצְאִים מִן הַמְּנֹרָה:
And a knob under the two branches: From the knob, the branches extended from its two sides in either direction. This is what we learned in the [Baraitha] Melecheth HaMishkan [ch. 10, Men. 28b, 29a]: The height of the menorah was eighteen handbreadths. [This total is arrived at as follows:] The feet [of the menorah] and the [lowest] flower were three handbreadths. That is the flower mentioned in connection with the base, as it is said: “to its base, to its flower” (Num. 8:4). Then two handbreadths [above this were] unadorned, and a handbreadth [above that] in which [there] was a goblet-[namely one] of the four goblets [mentioned in verse 34]-and a knob and a flower of the two knobs and the two flowers mentioned in connection with the menorah itself, as it is said [on verse 34]: “decorated…its knobs and its flowers.” We learn that on the main stem there were two knobs and two flowers, in addition to the three knobs from which the branches extended, as it is said [here]: “And a knob under the two branches.” And [above the lowest branches were] two handbreadths unadorned, and a handbreadth with a knob and two branches coming out of it on either side, extending upward, opposite the height of the menorah, and one handbreadth unadorned, and a handbreadth with a knob and two branches coming out of it, and one handbreadth unadorned, and a handbreadth with a knob and two branches coming out of it, extending upward, opposite the height of the menorah, and two handbreadths unadorned. [Hence,] three handbreadths remain, in which there were three goblets, a knob, and a flower. The goblets were found to number twenty-two: eighteen for the six branches [of the menorah]-three for each one-and four on the menorah itself, totaling twenty-two. And [there were] eleven knobs-six on the six branches [one on each branch], three on the menorah itself, from which the branches extended, and two more on the menorah, as it is said [in verse 34]: “decorated…its knobs,” [which means two knobs] since the minimum of [the plural] “knobs” is two. One [knob was] below, next to the base, and one in the top three handbreadths [together] with the three goblets. And it [the menorah] had nine flowers: six on the six branches [one on each branch] as it is said [in verse 33]: “on one branch, [there was] a knob and a flower,” and three [flowers] on the menorah [itself], as it is said [here], "decorated…its knobs and its flowers"-the minimum of [the plural] “flowers” is two, and one [additional flower is] mentioned in the parsha Beha’alothecha: “to its base to its flower” (Num. 8:4). If you carefully study this Mishnah that is written above, you will find them [the decorations of the menorah] according to their number, each one in its place. — [from Men. 28b] וכפתר תחת שני הקנים: מתוך הכפתור היו הקנים נמשכים משני צדיה אילך ואילך. כך שנינו במלאכת המשכן (פרק י) גובהה של מנורה שמונה עשר טפחים, הרגלים והפרח שלשה טפחים, הוא הפרח האמור בירך, שנאמר (במדבר ח ד) עד ירכה עד פרחה, וטפחיים חלק, וטפח שבו גביע מהארבעה גביעים, וכפתור ופרח משני כפתורים ושני פרחים האמורים במנורה עצמה, שנאמר משוקדים כפתוריה ופרחיה, למדנו שהיו בקנה שני כפתורים ושני פרחים לבד מן השלשה כפתורים, שהקנים נמשכין מתוכן, שנאמר וכפתור תחת שני הקנים, וגו' וטפחים חלק, וטפח כפתור ושני קנים יוצאים ממנו אילך ואילך נמשכים ועולים כנגד גובהה של מנורה, וטפחיים חלק, וטפח כפתור ושני קנים יוצאים ממנו, וטפחיים חלק וטפח כפתור ושני קנים יוצאים ממנו ונמשכים ועולין כנגד גובהה של מנורה וטפחיים חלק, נשתיירו שם שלשה טפחים, שבהם שלשה גביעים וכפתור ופרח. נמצאו גביעים עשרים ושנים שמונה עשר לששה קנים, שלשה לכל אחד ואחד, וארבעה בגופה של מנורה, הרי עשרים ושנים, ואחד עשר כפתורים ששה בששת הקנים, ושלשה בגופה של מנורה, שהקנים יוצאים מהם, ושניים עוד במנורה, שנאמר משוקדים כפתוריה, מיעוט כפתורים שנים האחד למטה אצל הירך, והאחד בשלשת טפחים העליונים עם שלשת הגביעים, ותשעה פרחים היו לה ששה לששת הקנים, שנאמר (פסוק לג) בקנה האחד כפתור ופרח, ושלשה למנורה, שנאמר משוקדים כפתוריה ופרחיה, ומיעוט פרחים שנים, ואחד האמור בפרשת בהעלותך (במדבר ח ד) עד ירכה עד פרחה. ואם תדקדק במשנה זו הכתובה למעלה, תמצאם כמנינם איש איש במקומו:
36Their knobs and their branches shall [all] be [one piece] with it; all of it [shall be] one hammered mass of pure gold. לוכַּפְתֹּרֵיהֶם וּקְנֹתָם מִמֶּנָּה יִהְיוּ כֻּלָּהּ מִקְשָׁה אַחַת זָהָב טָהוֹר:
37And you shall make its lamps seven, and he shall kindle its lamps [so that they] shed light toward its face. לזוְעָשִׂיתָ אֶת נֵרֹתֶיהָ שִׁבְעָה וְהֶעֱלָה אֶת נֵרֹתֶיהָ וְהֵאִיר עַל עֵבֶר פָּנֶיהָ:
its lamps: [They were] sort of cups into which the oil and the wicks were put. את נרתיה: כמין בזיכין שנותנין בתוכם השמן והפתילות:
[so that they] shed light toward its face: [Namely,] make the openings of the six lamps [which were] at the top of the branches that extend from of its [the menorah’s] sides, turned toward the middle one, so that when the lamps were lit they would shed light עֵבֶר פָּנֶיהָ, towards [or in the direction of] its face. Their light should be turned towards the face of the middle branch, which is the body of the menorah. והאיר על עבר פניה: עשה ששת הנרות שבראשי הקנים, היוצאים מצדיה, מסובים כלפי האמצעי, כדי שיהיו הנרות כשתדליקם מאירים אל עבר פניה, מוסב אורם אל צד פני הקנה האמצעי, שהוא גוף המנורה:
38And its tongs and its scoops [shall be] of pure gold. לחוּמַלְקָחֶיהָ וּמַחְתֹּתֶיהָ זָהָב טָהוֹר:
And its tongs: Heb. וּמַלְקָחֶיהָ. They are the tongs made to take the wicks from the oil, to set them in place and to draw them into the mouths of the lamps. Since they [are used for] taking (לוֹקְחִים) [the wicks] with them, they are called מֶלְקָחַיִם, a pair of “takers.” [The Aramaic word] וְצִבְיָתָהָא, which Onkelos renders [for וּמַלְקָחֶיהָ], is a term related to צְבַת, tenailles in French, tongs. ומלקחיה: הם הצבתים העשויין ליקח בהם הפתילה מתוך השמן לישבן ולמושכן בפי הנרות, ועל שם שלוקחים בהם קרויים מלקחים. וצביתהא שתרגם אונקלוס, לשון צבת, טינליי"א בלעז [צבת]:
and its scoops: Heb. וּמַחְךְתֹּתֶיהָ. They are a kind of small cup with which he [the kohen] would scoop the ashes that are in the lamp every morning when he [the kohen] cleaned the lamps from the ashes of the wicks that burned during the night and were [now] extinguished. The word מַחְךְתָּה is [the equivalent of] poseydure [or poysedure] in Old French, a little shovel [or] ash pan, like “to scoop (לַחְךְתּוֹת) fire from a hearth” (Isa. 30:14). ומחתתיה: הם כמין בזיכין קטנים, שחותה בהן את האפר שבנר בבקר בבקר, כשהוא מטיב את הנרות מאפר הפתילות, שדלקו הלילה וכבו, ולשון מחתה פוישידויר"א בלעז [יעה], כמו (ישעיה ל יד) לחתות אש מיקוד:
39He shall make it of a talent of pure gold, with all these implements. לטכִּכַּר זָהָב טָהוֹר יַעֲשֶׂה אֹתָהּ אֵת כָּל הַכֵּלִים הָאֵלֶּה:
a talent pure gold: Heb. כִּכַּר.[This means] that its weight along with all its implements shall be nothing but a talent, no less and no more. The talent used for mundane matters was sixty maneh, and the one used for holy matters was double, thus one hundred twenty maneh (Bech. 5a). The maneh is the litra with which silver is weighed according to the weight used in Cologne, which is the equivalent of one hundred gold pieces [or] twenty-five selas, for the sela is equivalent to four gold pieces. [This is the equivalent of sixty-four pounds.] ככר זהב טהור: שלא יהיה משקלה עם כל כליה אלא ככר, לא פחות ולא יותר, והככר של חול ששים מנה ושל קדש היה כפול, מאה עשרים מנה, והמנה הוא ליטרא ששוקלין בה כסף למשקל קולוני"א והם מאה זהובים, עשרים וחמשה סלעים והסלע ארבעה זהובים:
40Now see and make according to their pattern, which you are shown on the mountain. מוּרְאֵה וַעֲשֵׂה בְּתַבְנִיתָם אֲשֶׁר אַתָּה מָרְאֶה בָּהָר:
Now see and make: See here on the mountain the pattern that I am showing you. [This] informs us that Moses had difficulties with the construction of the menorah, until the Holy One, blessed is He, showed him a [model] menorah of fire. -[from Men. 29a] וראה ועשה: ראה כאן בהר תבנית שאני מראה אותך, מגיד שנתקשה משה במעשה המנורה, עד שהראה לו הקב"ה מנורה של אש:
which you are shown: Heb. אִשֶׁר-אַךְתָּה מָרְאֶה, as the Targum [Onkelos] renders: דִי אַךְתְּ מִתְחַזֵי, which you are shown. If it were punctuated מַרְאֶה with a “pattach,” it would mean that you show others. Now that it is punctuated with a short “kamatz,” it means that you are shown, that others show you, (for the punctuation distinguishes between the active and the passive). אשר אתה מראה: כתרגומו דאת מתחזי בטורא, אלו היה נקוד מראה בפת"ח, היה פתרונו אתה מראה לאחרים, עכשיו שנקוד חטף קמ"ץ, פתרונו דאת מתחזי, שאחרים מראים לך, שהנקוד מפריד בין עושה לנעשה:
Chapter 26
1"And the Mishkan you shall make out of ten curtains [consisting] of twisted fine linen, and blue, purple, and crimson wool. A cherubim design of the work of a master weaver you shall make them. אוְאֶת הַמִּשְׁכָּן תַּעֲשֶׂה עֶשֶׂר יְרִיעֹת שֵׁשׁ מָשְׁזָר וּתְכֵלֶת וְאַרְגָּמָן וְתֹלַעַת שָׁנִי כְּרֻבִים מַעֲשֵׂה חשֵׁב תַּעֲשֶׂה אֹתָם:
And the Mishkan you shall make out of ten curtains: to be its roof and [cover its] walls outside the planks, for the curtains are hung behind them to cover them. ואת המשכן תעשה עשר יריעות: להיות לו לגג ולמחיצות מחוץ לקרשים שהיריעות תלויות מאחוריהן לכסותן:
of twisted fine linen, and blue, purple, and crimson wool: Thus there are four kinds [of material] together in each thread, one of linen and three of wool, and each thread was doubled six times. Thus, four kinds [of material], when they are twisted together, yield twenty-four strands to a thread. — [from Baraitha Melecheth HaMishkan, ch. 2, Yoma 71b] שש משזר ותכלת וארגמן ותולעת שני: הרי ארבע מינין יחד בכל חוט וחוט אחד של פשתים ושלשה של צמר, וכל חוט וחוט כפול ששה הרי ארבעה מינין, כשהן שזורין יחד, עשרים וארבע כפלים לחוט:
A cherubim design of the work of a master weaver: Cherubim were drawn on them [the curtains] in their weave; not with embroidery, which is needlework, but with weaving on both sides, one face from here [one side] and one face from there [the other side]: a lion from this side and an eagle from that side, as silk girdles, called feysses in Old French, are woven. — [from Yoma 72b] כרבים מעשה חשב: כרובים היו מצויירין בהם באריגתן, ולא ברקימה שהוא מעשה מחט, אלא באריגה בשני כותלים, פרצוף אחד מכאן ופרצוף אחד מכאן, ארי מצד זה ונשר מצד זה, וכמו שאורגין חגורות של משי, שקורין בלעז פיישי"ש [רצועות]:
2"The length of one curtain [shall be] twenty eight cubits, and the width of one curtain [shall be] four cubits; the same measure for all the curtains. באֹרֶךְ | הַיְרִיעָה הָאַחַת שְׁמֹנֶה וְעֶשְׂרִים בָּאַמָּה וְרֹחַב אַרְבַּע בָּאַמָּה הַיְרִיעָה הָאֶחָת מִדָּה אַחַת לְכָל הַיְרִיעֹת:
3"Five of these curtains shall be joined to one another, and [the other] five curtains shall [also] be joined to one another. גחֲמֵשׁ הַיְרִיעֹת תִּהְיֶיןָ חֹבְרֹת אִשָּׁה אֶל אֲחֹתָהּ וְחָמֵשׁ יְרִיעֹת חֹבְרֹת אִשָּׁה אֶל אֲחֹתָהּ:
shall be joined: He [Bezalel] would sew them with a needle, one [curtain] alongside the other, five separately and [the other] five separately. תהיין חוברות: תופרן במחט זו בצד זו, חמש לבד וחמש לבד:
to one another: Heb. אִשָׁה אֶל-אִחֹתָהּ, lit., a woman to her sister. It is customary for Scripture to speak this way concerning a noun in the feminine gender, and concerning a noun in the masculine gender, אִישׁ אֶל-אָחִיו [lit., a man to his brother], as it is said concerning the cherubim: אִישׁ אֶל-אָחִיו (Exod. 25:20). אשה אל אחותה: כך דרך המקרא לדבר בדבר שהוא לשון נקבה. ובדבר שהוא לשון זכר אומר איש אל אחיו, כמו שנאמר בכרובים (שמות כה כ) ופניהם איש אל אחיו:
4"And you shall make loops of blue wool on the edge of one curtain [that is] at the edge of the [first] set, and so shall you do on the edge of the outermost curtain of the second set. דוְעָשִׂיתָ לֻלְאֹת תְּכֵלֶת עַל שְׂפַת הַיְרִיעָה הָאֶחָת מִקָּצָה בַּחֹבָרֶת וְכֵן תַּעֲשֶׂה בִּשְׂפַת הַיְרִיעָה הַקִּיצוֹנָה בַּמַּחְבֶּרֶת הַשֵּׁנִית:
loops: Heb. לֻלָאֹת, lazoles in Old French, loops. So did Onkelos render [it]: עִנוּבִין, a term meaning a bow. ללאת: לצול"ש בלעז [שרוכים] וכן תרגם אונקלוס ענובין, לשון עניבה:
curtain [that is] at the edge of the [first] set: Heb. בַּחֹבָרֶת. On the curtain that is the outermost of the set. The group of five curtains is called חוֹבֶרֶת. מקצה בחברת: באותה יריעה שבסוף החבור, קבוצת חמשת היריעות קרויה חוברת:
and so shall you do on the edge of the outermost curtain of the second set: On that curtain that is the outermost (הַקִּצוֹנָה), an expression derived from קָצֶה, end, meaning at the end of the set [of curtains]. וכן תעשה בשפת היריעה הקיצונה במחברת השנית:באותה יריעה שהיא קיצונה, לשון קצה, כלומר לסוף החוברת:
5"You shall make fifty loops on [the edge of] one curtain, and you shall make fifty loops on the edge of the curtain in the second set; the loops shall correspond to one another. החֲמִשִּׁים לֻלָאֹת תַּעֲשֶׂה בַּיְרִיעָה הָאֶחָת וַחֲמִשִּׁים לֻלָאֹת תַּעֲשֶׂה בִּקְצֵה הַיְרִיעָה אֲשֶׁר בַּמַּחְבֶּרֶת הַשֵּׁנִית מַקְבִּילֹת הַלֻּלָאֹת אִשָּׁה אֶל אֲחֹתָהּ:
the loops shall correspond to one another: Heb. מַקְבִּילֹתהַלֻּלָאֹת. Make sure that you make the loops exactly equidistant from one another. Their measure on this curtain should be the same for its mate. When you spread one set [of curtains] next to the other set, the loops of this curtain shall line up exactly opposite the loops of the other [curtain]. This is the [meaning of the] word מַקְבִּילֹת, [i.e.,] this one opposite that one. The Aramaic translation of נֶגֶד, opposite, is לָקֳבֵל. [Each] curtain was twenty-eight [cubits] long and four [cubits] wide. When five curtains were joined together, it was found that [altogether] they were twenty [cubits] wide, and so [too] with the second set. The length of the Mishkan was thirty [cubits] from east to west, as it is said: “twenty planks for the southern side” (verse 18), and so for the north, [with] every plank a cubit and a half [wide]. Thus, [we have altogether] thirty [cubits] from east to west. The width of the Mishkan from north to south was ten cubits, as it is said: “And for the western end of the Mishkan [you shall make six planks]” (verse 22), and [thus with] two planks at the corners [i.e., one plank at each end of the western wall], we have ten. [I.e., the interior of the Mishkan was ten cubits wide, not counting the northern and southern walls, which were each one cubit thick. Hence, the remainder of the two corner planks that do not fit against the side planks is a half cubit each, equaling one cubit. The six planks along the western side total nine cubits, thus we have altogether ten cubits on the western side.] In their [respective] places, I will explain these verses. The curtains were placed [so that] their length [was across] the [interior] width of the Mishkan, ten [of the curtains’] middle cubits as the roof of the space of the width of the Mishkan. [Another] cubit from here and a cubit from there covered the thickness of the tops of the planks, whose width was a cubit thick. Thus remained sixteen cubits: eight on the north[ern side] and eight on the south[ern side], covering the height of the planks, which were ten [cubits] high. [Thus] the bottom two cubits were exposed. The curtains were forty cubits wide when they were joined-twenty cubits for each set. Thirty of them [of the forty cubits] were for the roof of the Mishkan’s [interior] space lengthwise; one cubit corresponded to the thickness of the ends of the planks on the [Mishkan’s] west[ern side] and one cubit [was meant] to cover the thickness of the pillars on the east[ern side]-for there were no planks on the [Mishkan’s] east[ern side], only four (Old Rashi-five) pillars upon whose hooks the screen was spread and hung, like a curtain. [Aside from the above two cubits,] there remained eight cubits that hung in the back of the Mishkan on the west[ern side], with the bottom two cubits uncovered. I found this in the Baraitha of Forty-Nine Middoth. However, in Tractate Shabbath (98b) [it is stated]: The curtains did not cover the eastern pillars, and nine cubits hung in the back of the Mishkan. The text supports us [in our quotation of the Talmud, for the Torah states]: “And you shall place the dividing curtain beneath the clasps” (verse 33), but if [the truth is] like the words of this Baraitha, [it would mean that] the dividing curtain would be found to be drawn back one cubit to the west of the clasps. מקבילות הלולאות אשה אל אחותה: שמור שתעשה הלולאות במדה אחת מכוונות הבדלתן זו מזו, וכמדתן ביריעה זו כן יהא בחברתה, כשתפרוש חוברת אצל חוברת, יהיו הלולאות של יריעה זו מכוונות כנגד לולאות של זו. וזהו לשון מקבילות זו כנגד זו. תרגומו של נגד, קביל. היריעות ארכן עשרים ושמונה ורחבן ארבע, וכשחבר חמש יריעות יחד, נמצא רחבן עשרים, וכן החוברת השנית. והמשכן ארכו שלשים מן המזרח למערב, שנאמר עשרים קרש לפאת נגב תימנה (פסוק יח) וכן לצפון, וכל קרש אמה וחצי האמה, הרי שלשים מן המזרח למערב. רוחב המשכן מן הצפון לדרום עשר אמות. שנאמר (כו כב - כג) ולירכתי המשכן ימה וגו', ושני קרשים למקצעות, הרי עשר. ובמקומם אפרשם למקראות הללו. נותן היריעות אורכן לרוחבו של משכן, עשר אמות אמצעיות לגג חלל רוחב המשכן, ואמה מכאן ואמה מכאן לעובי ראשי הקרשים שעוביין אמה, נשתיירו שש עשרה אמה, שמונה לצפון ושמונה לדרום מכסות קומת הקרשים שגבהן עשר, נמצאו שתי אמות התחתונות מגולות. רחבן של יריעות ארבעים אמה, כשהן מחוברות עשרים אמה לחוברת, שלשים מהן לגג חלל המשכן לארכו ואמה כנגד עובי ראשי הקרשים שבמערב, ואמה לכסות עובי העמודים שבמזרח, שלא היו קרשים במזרח אלא ארבעה עמודים, שהמסך פרוש ותלוי בווין שבהן כמין וילון. נשתיירו שמונה אמות התלויין על אחורי הקרשים שבמערב ושתי אמות התחתונות מגולות. זו מצאתי בברייתא דארבעים ותשע מדות. אבל במסכת שבת (צח ב) אין היריעות מכסות את עמודי המזרח, ותשע אמות תלויות אחורי המשכן, והכתוב מסייענו ונתת את הפרוכת תחת הקרסים, ואם כדברי הברייתא הזאת, נמצאת פרוכת משוכה מן הקרסים ולמערב אמה:
6"And you shall make fifty golden clasps, and you shall fasten the curtains to one another with the clasps; so shall the Mishkan become one. ווְעָשִׂיתָ חֲמִשִּׁים קַרְסֵי זָהָב וְחִבַּרְתָּ אֶת הַיְרִיעֹת אִשָּׁה אֶל אֲחֹתָהּ בַּקְּרָסִים וְהָיָה הַמִּשְׁכָּן אֶחָד:
golden clasps: Heb. קַרְסֵי, fermeylz, fermels, fermails in Old French, [meaning] hooks, clasps. One of its ends is inserted into [one of] the loops of this [one] set [of curtains] and the other end into the loops of the [second] set [of curtains, thus] fastening them [the loops] with them [the clasps]. קרסי זהב: פירמייל"ץ בלעז [סגרים] ומכניסין ראשן אחד בלולאות שבחוברת זו וראשן אחד בלולאות שבחוברת זו ומחברן בהן:
7"And [then] you shall make curtains of goat hair for a tent over the Mishkan; you shall make eleven curtains. זוְעָשִׂיתָ יְרִיעֹת עִזִּים לְאֹהֶל עַל הַמִּשְׁכָּן עַשְׁתֵּי עֶשְׂרֵה יְרִיעֹת תַּעֲשֶׂה אֹתָם:
curtains of goat hair: Heb. עִזִים, goats, from the hair of goats. — [from Baraitha Melecheth HaMishkan, ch. 3] יריעות עזים: מנוצה של עזים:
for a tent over the Mishkan: To spread them over the lower curtains. לאהל על המשכן: לפרוש אותן על היריעות התחתונות:
8"The length of one curtain [shall be] thirty cubits, and the width of one curtain four cubits; the same measure for the eleven curtains. חאֹרֶךְ | הַיְרִיעָה הָאַחַת שְׁלשִׁים בָּאַמָּה וְרֹחַב אַרְבַּע בָּאַמָּה הַיְרִיעָה הָאֶחָת מִדָּה אַחַת לְעַשְׁתֵּי עֶשְׂרֵה יְרִיעֹת:
thirty cubits: For when [Moses] placed their [the curtains’] length across the width of the Mishkan, as he did with the first [set of curtains], these were found to exceed [and overhang them] by a cubit from here [on one side] and a cubit from there [on the other side] to cover one of the two cubits of the planks that remained exposed. The bottom cubit of the plank, which the curtain did not cover, was the cubit [that was] inserted into the socket hole, for the sockets were a cubit deep. — [from Shab. 98b] שלשים באמה: שכשנותן ארכן לרוחב המשכן, כמו שנתן את הראשונות, נמצאו אלו עודפות אמה מכאן ואמה מכאן לכסות אחת מהשתי אמות, שנשארו מגולות מן הקרשים, והאמה התחתונה של קרש, שאין היריעה מכסה אותו היא האמה התחובה בנקב האדן, שהא-דנים גבהן אמה:
9"And you shall join the five curtains by themselves, and the [other] six curtains by themselves; and you shall fold the sixth curtain before the front of the tent. טוְחִבַּרְתָּ אֶת חֲמֵשׁ הַיְרִיעֹת לְבָד וְאֶת שֵׁשׁ הַיְרִיעֹת לְבָד וְכָפַלְתָּ אֶת הַיְרִיעָה הַשִּׁשִּׁית אֶל מוּל פְּנֵי הָאֹהֶל:
and you shall fold the sixth curtain: [I.e.,] of these upper curtains, which exceeds [overhangs] the lower ones. וכפלת את היריעה הששית: העודפת באלו העליונות יותר מן התחתונות:
before the front of the tent: Half its width [of the sixth curtain] was hanging and folded over the screen on the east[ern side of the Mishkan], before the entrance, resembling a modest bride whose face is covered with a veil. אל מול פני האהל: חצי רחבה היה תלוי וכפול על המסך שבמזרח כנגד הפתח, דומה לכלה צנועה המכוסה בצעיף על פניה:
10"And you shall make fifty loops on the edge of one curtain, [which is] at the edge of the [first] set, and fifty loops on the edge of the [outermost] curtain of the second set. יוְעָשִׂיתָ חֲמִשִּׁים לֻלָאֹת עַל שְׂפַת הַיְרִיעָה הָאֶחָת הַקִּיצֹנָה בַּחֹבָרֶת וַחֲמִשִּׁים לֻלָאֹת עַל שְׂפַת הַיְרִיעָה הַחֹבֶרֶת הַשֵּׁנִית:
11"And you shall make fifty copper clasps; you shall bring the clasps into the loops, and you shall fasten the tent together so that it will become one. יאוְעָשִׂיתָ קַרְסֵי נְחשֶׁת חֲמִשִּׁים וְהֵבֵאתָ אֶת הַקְּרָסִים בַּלֻּלָאֹת וְחִבַּרְתָּ אֶת הָאֹהֶל וְהָיָה אֶחָד:
12"And the overhanging excess in the curtains of the tent half of the extra curtain shall hang over the rear of the Mishkan. יבוְסֶרַח הָעֹדֵף בִּירִיעֹת הָאֹהֶל חֲצִי הַיְרִיעָה הָעֹדֶפֶת תִּסְרַח עַל אֲחֹרֵי הַמִּשְׁכָּן:
And the overhanging excess in the curtains of the tent: over the curtains of the Mishkan. The curtains of the tent were the upper ones, [curtains] of goat hair. [They are] referred to as “tent,” as it is written about them, “for a tent over the Mishkan” (verse 7). Every expression of “tent” (אֹהֶל) stated in their context [i.e., referring to the upper curtains] is only an expression meaning a roof, for they form a tent and a roof over the lower [curtains]. They [the upper curtains] exceeded the lower ones by half a curtain on the west[ern side], since half of the extra eleventh curtain was folded opposite the front of the tent. [Hence,] there remained two cubits, [representing] the width of half of it [the upper curtains], exceeding the width of the lower [curtains]. וסרח העדף ביריעת האהל: על יריעות המשכן. יריעות האהל הן העליונות של עזים שקרויים אהל, כמו שכתוב בהן (פסוק ז) לאהל על המשכן, וכל אהל האמור בהן אינו אלא לשון גג, שמאהילות ומסככות על התחתונות, והן היו עודפות על התחתונות חצי היריעה למערב, שהחצי של יריעה אחת עשרה היתרה, היה נכפל אל מול פני האהל, נשארו שתי אמות רוחב חציה עודף על רוחב התחתונות:
shall hang over the rear of the Mishkan: to cover the two cubits of the planks that were exposed. תסרח על אחרי המשכן: לכסות שתי אמות שהיו מגולות בקרשים:
the rear of the Mishkan: This means the western side, since the entrance [to the Mishkan] was on the east[ern side], which is [referred to as] its front, and the north[ern] and south[ern sides] are referred to as sides to the right and to the left. :
13"And the cubit from here and the cubit from there of the excess in the length of the curtains of the tent shall hang over the sides of the Mishkan from here and from there to cover it. יגוְהָאַמָּה מִזֶּה וְהָאַמָּה מִזֶּה בָּעֹדֵף בְּאֹרֶךְ יְרִיעֹת הָאֹהֶל יִהְיֶה סָרוּחַ עַל צִדֵּי הַמִּשְׁכָּן מִזֶּה וּמִזֶּה לְכַסֹּתוֹ:
And the cubit from here and the cubit from there: on the north[ern] and on the south[ern] sides of the Mishkan]. והאמה מזה והאמה מזה: לצפון ולדרום:
of the excess in the length of the curtains of the tent: which exceed the length of the lower curtains of the Mishkan by two cubits. בעדף בארך יריעות האהל: שהן עודפות על אורך יריעות המשכן שתי אמות:
shall hang over the sides of the Mishkan: [I.e.,] on the northern and southern [sides], as I explained above [verse 12]. The Torah taught [us] manners, that one should spare the beautiful. — [from an unknown midrashic source, also quoted by Yalkut Shimoni 422] יהיה סרוח על צדי המשכן: לצפון ולדרום, כמו שפירשתי למעלה. למדה תורה דרך ארץ שיהא אדם חס על היפה:
14"And you shall make a covering for the tent of ram skins dyed red and a covering of tachash skins above. ידוְעָשִׂיתָ מִכְסֶה לָאֹהֶל עֹרֹת אֵילִם מְאָדָּמִים וּמִכְסֵה עֹרֹת תְּחָשִׁים מִלְמָעְלָה:
a covering for the tent: For the roof of goat hair curtains, make an additional covering of ram skins dyed red. Additionally, above it [place] a covering of tachash skins. These [two] coverings covered only the roof, their length being thirty [cubits] and their width ten. These are Rabbi Nehemiah’s words, but according to Rabbi Judah, there was [only] one cover, half of [it made from] ram skins dyed red and half of [it made from] tachash skins. -[from Shab. 28a] מכסה לאהל: לאותו גג של יריעות עזים עשה עוד מכסה אחד של עורות אילים מאדמים, ועוד למעלה ממנו מכסה עורות תחשים, ואותן מכסאות לא היו מכסין אלא את הגג, ארכן שלשים ורחבן עשר, אלו דברי רבי נחמיה, ולדברי רבי יהודה מכסה אחד היה, חציו של עורות אילים מאדמים, וחציו של עורות תחשים:Daily Tehillim: Psalms Chapters 135 - 139
• Chapter 135
1. Praise the Lord! Praise the Name of the Lord; offer praise, you servants of the Lord-
2. who stand in the House of the Lord, in the courtyards of the House of our God.
3. Praise the Lord, for the Lord is good; sing to His Name, for He is pleasant.
4. For God has chosen Jacob for Himself, Israel as His beloved treasure.
5. For I know that the Lord is great, our Master is greater than all supernal beings.
6. All that the Lord desired He has done, in the heavens and on earth, in the seas and the depths.
7. He causes mists to rise from the ends of the earth; He makes lightning for the rain; He brings forth the wind from His vaults.
8. It was He who struck down the firstborn of Egypt, of man and beast.
9. He sent signs and wonders into the midst of Egypt, on Pharaoh and on all his servants.
10. It was He who struck down many nations, and slew mighty kings:
11. Sichon, king of the Amorites; Og, king of Bashan; and all the kingdoms of Canaan.
12. And He gave their lands as a heritage, a heritage to His people Israel.
13. Lord, Your Name is forever; Lord, Your remembrance is throughout all generations.
14. Indeed, the Lord will judge on behalf of His people, and have compassion on His servants.
15. The idols of the nations are silver and gold, the product of human hands.
16. They have a mouth, but cannot speak; they have eyes, but cannot see;
17. they have ears, but cannot hear; nor is there breath in their mouth.
18. Like them will their makers become-all who trust in them.
19. House of Israel, bless the Lord; House of Aaron, bless the Lord;
20. House of Levi, bless the Lord; you who fear the Lord, bless the Lord.
21. Blessed is the Lord from Zion, who dwells in Jerusalem. Praise the Lord!
Chapter 136
This psalm contains twenty-six verses, corresponding to the twenty-six generations between the creation of the world and the giving of the Torah.
1. Praise the Lord for He is good, for His kindness is forever.
2. Praise the God of the supernal beings, for His kindness is forever.
3. Praise the Master of the heavenly hosts, for His kindness is forever.
4. Who alone performs great wonders, for His kindness is forever.
5. Who makes the heavens with understanding, for His kindness is forever.
6. Who spreads forth the earth above the waters, for His kindness is forever.
7. Who makes the great lights, for His kindness is forever.
8. The sun to rule by day, for His kindness is forever.
9. The moon and stars to rule by night, for His kindness is forever.
10. Who struck Egypt through its firstborn, for His kindness is forever.
11. And brought Israel out of their midst, for His kindness is forever.
12. With a strong hand and with an outstretched arm, for His kindness is forever.
13. Who split the Sea of Reeds into sections, for His kindness is forever.
14. And brought Israel across it, for His kindness is forever.
15. And cast Pharaoh and his army into the Sea of Reeds, for His kindness is forever.
16. Who led His people through the desert, for His kindness is forever;
17. Who struck down great kings, for His kindness is forever.
18. And slew mighty kings, for His kindness is forever.
19. Sichon, king of the Amorites, for His kindness is forever.
20. And Og, king of Bashan, for His kindness is forever.
21. And gave their land as a heritage, for His kindness is forever.
22. A heritage to Israel His servant, for His kindness is forever.
23. Who remembered us in our humiliation, for His kindness is forever.
24. And redeemed us from our oppressors, for His kindness is forever.
25. Who gives food to all flesh, for His kindness is forever.
26. Praise the God of heaven, for His kindness is forever.
Chapter 137
Referring to the time of the destruction of the Temple, this psalm tells of when Nebuchadnezzar would ask the Levites to sing in captivity as they had in the Temple, to which they would reply, "How can we sing the song of God upon alien soil?" They were then comforted by Divine inspiration.
1. By the rivers of Babylon, there we sat and wept as we remembered Zion.
2. There, upon the willows, we hung our harps.
3. For there our captors demanded of us songs, and those who scorned us-rejoicing, [saying,] "Sing to us of the songs of Zion.”
4. How can we sing the song of the Lord on alien soil?
5. If I forget you, Jerusalem, let my right hand forget [its dexterity].
6. Let my tongue cleave to my palate if I will not remember you, if I will not bring to mind Jerusalem during my greatest joy!
7. Remember, O Lord, against the Edomites the day of [the destruction of] Jerusalem, when they said, "Raze it, raze it to its very foundation!”
8. O Babylon, who is destined to be laid waste, happy is he who will repay you in retribution for what you have inflicted on us.
9. Happy is he who will seize and crush your infants against the rock!
Chapter 138
David offers awesome praises to God for His kindness to him, and for fulfilling His promise to grant him kingship.
1. By David. I will thank You with all my heart, in the presence of princes I shall praise You.
2. I will bow toward Your Holy Sanctuary, and praise Your Name for Your kindness and for Your truth; for You have exalted Your word above all Your Names.
3. On the day that I called out You answered me, You emboldened me, [You put] strength in my soul.
4. Lord, all the kings of the land will give thanks to You when they hear the words of Your mouth.
5. And they will sing of the Lord's ways, for the glory of the Lord is great.
6. For though the Lord is exalted, He sees the lowly; the High One castigates from afar.
7. If I walk in the midst of distress, keep me alive; against the wrath of my enemies stretch out Your hand, and let Your right hand deliver me.
8. Lord, complete [Your kindness] on my behalf. Lord, Your kindness is forever, do not forsake the work of Your hands.
Chapter 139
A most prominent psalm that guides man in the ways of God as no other in all of the five books of Tehillim. Fortunate is he who recites it daily.
1. For the Conductor, by David, a psalm. O Lord, You have probed me, and You know.
2. You know my sitting down and my standing up; You perceive my thought from afar.
3. You encircle my going about and my lying down; You are familiar with all my paths.
4. For there was not yet a word on my tongue-and behold, Lord, You knew it all.
5. You have besieged me front and back, You have laid Your hand upon me.
6. Knowledge [to escape You] is beyond me; it is exalted, I cannot know it.
7. Where can I go [to escape] Your spirit? And where can I flee from Your presence?
8. If I ascend to the heavens, You are there; if I make my bed in the grave, behold, You are there.
9. Were I to take up wings as the dawn and dwell in the furthest part of the sea,
10. there, too, Your hand would guide me; Your right hand would hold me.
11. Were I to say, "Surely the darkness will shadow me," then the night would be as light around me.
12. Even the darkness obscures nothing from You; and the night shines like the day-the darkness is as light.
13. For You created my mind; You covered me in my mother's womb.
14. I will thank You, for I was formed in an awesome and wondrous way; unfathomable are Your works, though my soul perceives much.
15. My essence was not hidden from You even while I was born in concealment, formed in the depths of the earth.
16. Your eyes beheld my raw form; all [happenings] are inscribed in Your book, even those to be formed in future days-to Him they are the same.
17. How precious are Your thoughts to me, O God! How overwhelming, [even] their beginnings!
18. Were I to count them, they would outnumber the sand, even if I were to remain awake and always with You.
19. O that You would slay the wicked, O God, and men of blood [to whom I say], "Depart from me!”
20. They exalt You for wicked schemes, Your enemies raise [You] for falsehood.
21. Indeed, I hate those who hate You, Lord; I contend with those who rise up against You.
22. I hate them with the utmost hatred; I regard them as my own enemies.
23. Search me, Lord, and know my heart; test me and know my thoughts.
24. See if there is a vexing way in me, then lead me in the way of the world.
Tanya: Likutei Amarim, beginning of Chapter 29• Lessons in Tanya
• Shevat 28, 5775 · February 17, 2015
Today's Tanya Lesson
Likutei Amarim, beginning of Chapter 29
In ch. 26 the Alter Rebbe stated that both depression and dullness of heart produce a state of sluggishness which prevents a person from overcoming the evil inclination of the animal soul. He therefore outlined in chs. 26-28 methods of overcoming depression arising from various causes. In this chapter the Alter Rebbe will discuss means of dealing with “dullness of heart” (timtum halev), after describing this state more clearly.
אך עוד זאת, צריך לשית עצות בנפשות הבינונים
Those whose souls are of the level of Beinonim must seek means of contending with yet another difficulty.
אשר לפעמים ועתים רבים יש להם טמטום הלב שנעשה כאבן, ולא יכול לפתוח לבו בשום אופן לעבודה שבלב, זו תפלה
Occasionally, and even frequently, they experience a dullness of the heart, as though it had turned to stone, and, try as they might, they cannot open their heart in prayer, which is by definition the1 “service of the heart.”
Chassidut explains that prayer is the “service of the heart” in a two-fold sense: (a) It takes place in the heart, for in prayer one strives to extend his intellectual apprehension of G‑dliness into the realm of emotions experienced in the heart — the love and fear of G‑d; (b) The object of prayer is the heart, for in prayer one tries to transform the nature of his heart — to steer it away from the mundane desires to which it naturally inclines, and to direct it instead towards a yearning for the spiritual and the G‑dly. To accomplish both these objectives of prayer, the heart must of course be open and receptive, and thus timtum halev is a major hindrance.
וגם לפעמים לא יוכל להלחם עם היצר לקדש עצמו במותר לו, מפני כבדות שבלבו
Also, the heaviness in his heart prevents him at times from waging war against the evil impulse, in sanctifying himself in permitted matters.
As the Alter Rebbe explained in ch. 27, it is the task of the Beinoni to suppress the desires of his heart, e.g., by not eating as soon as he has the urge to do so. This requires a battle with one’s evil impulse, which demands that he gratify all of his desires. When his heart is dull, heavy and insensitive he cannot fight the evil impulse.
וזאת היא עצה היעוצה בזהר הקדוש, דאמר רב מתיבתא בגן עדן: אעא דלא סליק ביה נהורא, מבטשין ליה כו׳, גופא דלא סליק ביה נהורא דנשמתא, מבטשין ליה כו׳
In this case, the advice given in the holy Zohar2 is, as the president of the academy of Gan Eden said: “A wooden beam which does not catch fire should be splintered, and similarly a body into which the light of the soul does not penetrate should be crushed,” and thereby the body becomes receptive to the soul’s light, as the Zohar concludes.
In the analogy quoted from the Zohar we see that the wood is made receptive to the flame, rather than the flame being increased or improved to the point where it overwhelms the wood. Similarly with the insensitive heart. Timtum halev must be eradicated (by removing its underlying cause, as the Alter Rebbe will soon conclude), rather than overwhelmed (by increasing the intellectual light of contemplation on the greatness of G‑d).
פירוש נהורא דנשמתא: שאור הנשמה והשכל אינו מאיר כל כך למשול על חומריות שבגוף
The reference to the “light of the soul” which, in this case, does not penetrate the bodymeans that the light of the soul and of the intellect does not illuminate to such an extent as to prevail over the coarseness of the body.
ואף שמבין ומתבונן בשכלו בגדולת ה׳, אינו נתפס ונדבק במוחו כל כך שיוכל למשול על חומריות הלב, מחמת חומריותן וגסותן
Thus, although he understands and meditates in his mind on the greatness of G‑d, yet that which he understands is not apprehended and implanted in his mind to the point where it enables him to prevail over the coarseness of the heart — because of the degree of their (the mind and heart’s) coarseness and crassness. 3
והסיבה היא גסות הקליפה, שמגביה עצמה על אור קדושת נפש האלקית, ומסתרת ומחשיכה אורה
The cause of this deficiency is the arrogance of the kelipah of the animal soul, which exalts itself above the holiness of the light of the divine soul, so that it obscures and darkens its light.
ולזאת צריך לבטשה ולהשפילה לעפר
Therefore, one must crush it and cast it down to the ground, just as in the previously quoted analogy the beam is splintered so that it will catch fire.
The Alter Rebbe now proceeds to explain how this is accomplished. He points out that the personality of the Beinoni is his animal soul. (When a Beinoni says “I,” he is referring to his animal soul.) Thus, by crushing his own spirit, he crushes the sitra achra, and thereby enables the light of the soul and intellect to penetrate himself.
דהיינו לקבוע עתים להשפיל עצמו, להיות נבזה בעיניו נמאס, ככתוב
This means that one must crush the sitra achra and cast it to the ground by setting aside appointed times for humbling oneself and considering himself4 “despicable and contemptible,” as it is written.
ולב נשבר רוח נשברה היא הסטרא אחרא, שהיא היא האדם עצמו בבינונים
Now5 “A broken heart [leads to] a broken spirit,” the “spirit” being the sitra achra which, in the case of Beinonim, is the very man himself.
שנפש החיונית המחיה הגוף היא בתקפה כתולדתה בלבו, נמצא היא היא האדם עצמו
For in his heart the vital soul which animates the body is in its full strength as it was at birth; hence it is indeed the very man himself.
ועל נפש האלקית שבו, נאמר: נשמה שנתת בי טהורה היא, שנתת בי דייקא, מכלל שהאדם עצמו איננו הנשמה הטהורה, כי אם בצדיקים
With regard to the divine soul within him it is said: 6 “The soul which You gave within me is pure.” The word “(within) me” cannot be understood as referring to the body alone: the body cannot speak for itself as a complete man. Thus, it must refer also to the (animating) soul. Therefore, the words “(which You gave) within me” imply that the man himself who is saying these words is not identified with the “pure soul”; i.e., the divine soul is a thing apart, which has been “placed within” this “me” — the body and animal soul — except in the case of tzaddikim.
שבהם הוא להפך: שנשמה הטהורה שהיא נפש האלקית הוא האדם, וגופם נקרא בשר אדם
With them the contrary is true: the man himself is the “pure soul,” i.e, the divine soul, while their body is called “the flesh of man” i.e., secondary to the man himself — the divine soul.
וכמאמר הלל הזקן לתלמידיו, כשהיה הולך לאכול היה אומר שהוא הולך לגמול חסד עם העלובה ועניה, הוא גופו, כי כמו זר נחשב אצלו, ולכן אמר שהוא גומל חסד עמו במה שמאכילו, כי הוא עצמו אינו רק נפש האלקית לבד, כי היא לבדה מחיה גופו ובשרו, שהרע שהיה בנפש החיונית המלובשת בדמו ובשרו נתהפך לטוב, ונכלל בקדושת נפש האלקית ממש בצדיקים
It was in this sense that Hillel the Elder would say to his disciples when he went to eat that he was going to do a favor to the7 “lowly and poor creature,” meaning his body. He regarded his body as a foreign thing, and therefore used this expression — that he was doing it a favor by giving it food. For he himself was nothing other than the divine soul. It alone animated his body and flesh, inasmuch as in tzaddikim the evil that was in the vital soul pervading their blood and flesh has been transformed into good and completely absorbed into the holiness of the divine soul, and thus, the divine soul is the man himself.
| FOOTNOTES | |
| 1. | Taanit 2a. |
| 2. | III, 168a. |
| 3. | Note the discrepancy: The Alter Rebbe began the chapter speaking of "dullness of heart"; here, the problem is identified as the crassness of mind and heart. It has accordingly been suggested - in light of the well-known doctrine that mind and heart have a cause-and-effect relationship, so that the emotions ought naturally to respond to any idea that the intellect apprehends - that any emotional insensitivity is indicative of a flaw in one's intellectual apprehension. The Rebbe rejects this suggestion, arguing that if this were the case, the Alter Rebbe would have mentioned the problem of this species of "mental block" at the beginning of the chapter. The Rebbe resolves the problem as follows: The Alter Rebbe, who addresses himself to the Beinoni, speaks of that type of insensitivity which can trouble the Beinoni. As explained earlier (in chapter 17), the Beinoni is always in control of his mind, and the Alter Rebbe therefore speaks only of "dullness of heart." When the Alter Rebbe mentions "the crassness of mind and heart" he is explaining the citation from the Zohar. The statement of the Zohar, while applicable to the Beinoni as well (which is why the Alter Rebbe cites it), does not address the Beinoni exclusively; it obviously deals with the rasha, too, who is not master over his mind; he indeed has a dual problem - the crassness of his mind as well as of his heart. |
| 4. | A play [on words] in Tehillim 15:4. |
| 5. | Cf. Tehillim 51:19. |
| 6. | Morning liturgy; Berachot 60b. |
| 7. | Vayikra Rabbah 34:3. |
• Sefer Hamitzvos:
Shevat 28, 5775 · February 17, 2015
Today's MitzvahA daily digest of Maimonides’ classic work "Sefer Hamitzvot"
Important Message Regarding This Lesson
The Daily Mitzvah schedule runs parallel to the daily study of 3 chapters of Maimonides' 14-volume code. There are instances when the Mitzvah is repeated a few days consecutively while the exploration of the same Mitzvah continues in the in-depth track.
Positive Commandment 153Calculating Months and Years
"This month shall be to you the beginning of months"—Exodus 12:2.
We are commanded to establish a calendar and calculate its months and years. The months are lunar months, with a new month established when the new moon appears; the years follow the solar seasonal cycle, necessitating the periodic addition of an extra (thirteenth) month to a year – which then becomes a "leap year" – because twelve lunar months are several days short of a solar year. This mitzvah is known as Sanctifying the New Moon.
This mitzvah is entrusted to the Jewish Supreme Court that presides in Israel. Unlike the counting of six days and then observing the Shabbat, a mitzvah that is incumbent upon every individual, no individual can unilaterally decide that a new month has arrived simply because he espied the new moon, and no individual can decide to add a month to the calendar based on his personal (even Torah-based) calculations.
Only the Supreme Court can make these calculations, and only in the Land of Israel. We follow the rulings issued by the Supreme Court in Israel even if they inadvertently established the "wrong" day as the New Moon, even if they did so under duress.
In the event that there are no qualified rabbis remaining in Israel, these calculations can be made, and months and leap years established, by a court that was ordained in Israel—even if it finds itself in the Diaspora.
Today we no longer sanctify the months based on the testimony of witnesses who saw the new moon, because there is no longer a sitting rabbinical Supreme Court in Israel—much as we no longer offer sacrifices, because we lack a Holy Temple.
But under no circumstances can an individual or court outside of Israel establish a new month or a leap year. Our calculations today in the Diaspora are only to determine which days the Court in Israel established as the New Moon, and which years they established as leap years.
[Editor's Note: Nachmanides asks, if so, how do we have holidays and a calendar today, when there is no rabbinical Supreme Court in Israel? He answers that there is a tradition that Hillel the Prince, who resided in Israel, established a calendar until the arrival of Moshiach, and sanctified all the new months and leap years until that time. Therefore, we can use our calculations to determine exactly what he previously established.]
Some laws associated with this mitzvah:
We are commanded to establish a calendar and calculate its months and years. The months are lunar months, with a new month established when the new moon appears; the years follow the solar seasonal cycle, necessitating the periodic addition of an extra (thirteenth) month to a year – which then becomes a "leap year" – because twelve lunar months are several days short of a solar year. This mitzvah is known as Sanctifying the New Moon.
This mitzvah is entrusted to the Jewish Supreme Court that presides in Israel. Unlike the counting of six days and then observing the Shabbat, a mitzvah that is incumbent upon every individual, no individual can unilaterally decide that a new month has arrived simply because he espied the new moon, and no individual can decide to add a month to the calendar based on his personal (even Torah-based) calculations.
Only the Supreme Court can make these calculations, and only in the Land of Israel. We follow the rulings issued by the Supreme Court in Israel even if they inadvertently established the "wrong" day as the New Moon, even if they did so under duress.
In the event that there are no qualified rabbis remaining in Israel, these calculations can be made, and months and leap years established, by a court that was ordained in Israel—even if it finds itself in the Diaspora.
Today we no longer sanctify the months based on the testimony of witnesses who saw the new moon, because there is no longer a sitting rabbinical Supreme Court in Israel—much as we no longer offer sacrifices, because we lack a Holy Temple.
But under no circumstances can an individual or court outside of Israel establish a new month or a leap year. Our calculations today in the Diaspora are only to determine which days the Court in Israel established as the New Moon, and which years they established as leap years.
[Editor's Note: Nachmanides asks, if so, how do we have holidays and a calendar today, when there is no rabbinical Supreme Court in Israel? He answers that there is a tradition that Hillel the Prince, who resided in Israel, established a calendar until the arrival of Moshiach, and sanctified all the new months and leap years until that time. Therefore, we can use our calculations to determine exactly what he previously established.]
Some laws associated with this mitzvah:
- The extra month added to a leap year is the one contiguous to the month of Passover—i.e. Adar.
- The establishment of new months and leap years must be done during daylight hours.
- A year must be comprised of complete months; a month must be comprised of complete days.
Translated by Berel Bell
The 153rd mitzvah is that G‑d (exalted be He) commanded us to calculate the months and years.1 This is the mitzvah of Kiddush HaChodesh (Sanctifying the Moon).
The source of this commandment is G‑d's statement2 (exalted be He), "[And G‑d said to Moshe and Aharon in the land of Egypt,] 'this month [Nissan] shall be the head month to you.' "
In their explanation of this mitzvah, the Sages said,3 "This testimony is givenlochem ["you", plural]."4 The meaning of this statement: This mitzvah is not incumbent on every individual as is Shabbos, for example, where every single individual counts six days and rests on the seventh. In our case, it would mean that every individual who sees the appearance of the new moon would consider that day Rosh Chodesh [the first of the month]; Or that an individual could use the Torah-approved calculations to himself determine Rosh Chodesh; Or that he could himself estimate that the produce would not yet ripen [by Pesach]5, or consider any of the other factors6 which are used in determining [the calendar] — and then [himself declare a leap year and] add a month!
However, this mitzvah can only be performed by the Bais Din Hagadol, and only in Eretz Yisroel7. Therefore, since today there is no Bais Din HaGadol, we no longer determine the months on the basis of testimony, just as we no longer bring sacrifices because there is no Holy Temple.
The group of heretics known here in the East8 as Karaites have erred in this principle.9 Not even all of the Rabbis have grasped it, and as a result, grope around with them together in deep darkness.10
One must understand that the calculations which we use today to know11 whenRosh Chodesh and the holidays occur, may only be done in Eretz Yisroel. Only in cases of dire need, when there are no Sages in Eretz Yisroel, and when the Bais Din outside Eretz Yisroel was previously ordained in Eretz Yisroel, is it permissible to declare a leap year or determine Rosh Chodesh outside Eretz Yisroel — as Rabbi Akiva did, as explained in the Gemara.12 This is a very extreme measure, and it is well known that in the majority of cases, it was done only in Eretz Yisroel. They [i.e. the Sages in Eretz Yisroel] are the ones to establish the months and declare a leap year, when they gather together and use the accepted methods.
There is a very important principle upon which the Torah's perspective13 on this subject is based, which is only understood and fully realized by those who delve deeply into the Torah, as follows. This that we outside Eretz Yisroel use our system to make calculations and we declare that "this day is the first of the month," and "this day is a holiday," does not in any way mean that we are making this day based on our calculations. Rather, it is because the Bais Din inEretz Yisroel has already established that the day is a holiday or Rosh Chodesh. The day becomes a holiday or Rosh Chodesh upon their declaration, "Today is Rosh Chodesh, or "Today is a holiday"; regardless of whether they based their actions on calculations or testimony.14
This [that the Bais Din HaGadol in Eretz Yisroel has absolute authority] is known to us through the verse15, "[Speak to the Israelites and tell them, 'These are the holidays] that you shall designate.' " Our Sages explain16, "These are the only holidays." The meaning of this statement, as passed down in the Oral Tradition: whatever they [i.e. the Bais Din] designate as holidays are considered holidays, even if they made an error, were forced [into making a declaration], or misled.
The calculations which we make today are only to know which day they established in Eretz Yisroel, since they use the exact same system to make calculations and to determine the day – not testimony. Therefore, we are really basing ourselves on their determination, rather than our own calculations, which are only used to reveal [what they already determined previously]. One must clearly understand this.
I will give some additional explanation: let us assume, for example, that there would be no Jewish inhabitants in Eretz Yisroel (G‑d forbid such a thing, since He has already promised that he will never completely wipe out or uproot the Jewish nation17); that there would be no Bais Din there, nor a Bais Din outsideEretz Yisroel which had been ordained in Eretz Yisroel. In such a case, our calculations would be totally futile,18 since we, who dwell outside Eretz Yisroel, may not make the calculations, nor declare leap years nor establish the months without the conditions mentioned above,19 since, "For from Zion shall go forth the Torah, and the word of the L‑rd from Jerusalem."20 A person who fully understands the words of the Talmud in this subject will, upon meditation, undoubtedly agree with the abovementioned.
The Torah contains brief references to the basic principles which are relied upon to know when Rosh Chodesh and the leap years occur. Among them: "This law must therefore be kept at its designated time (l'moadah)."21 Our Sages said,22 "This teaches you that one may add on to the leap year only close to the holiday" [moed, i.e. Pesach23].
They also said,24 "From which verse do we derive that only during the daytime may we officially add on to the month or officially declare Rosh Chodesh? From the verse,25 'miyamim yamimah.' "26
[So too,] G‑d's statement27 (exalted be He), "[This month shall be the head month to you; the first month] of the months of the year." On this our Sages said,28 "The year must be composed of months, not of [odd] days", meaning that when adding on to the year, a complete month must be added.29
There is also a verse,30 "a month of days." Our Sages commented,31 "the month must be composed of days, not of [odd] hours". [So too] the verse,32"safeguard the month of Aviv,"33 which implies that in calculating the year we must take into account the seasons. Therefore, they shall be years [based not only on the moon but also] based on the sun.
All the details of this mitzvah have been completely explained in the first chapter of Sanhedrin,34 in tractate Rosh Hashanah,35 and in Berachos.
FOOTNOTES
1. The lunar month has approximately 29 1/2 days. Since, as mentioned later in this mitzvah, a month may only consist of complete days, one must determine whether a particular month has 29 or 30 days. This could be done either by witnesses, who testified that they saw the moon appear on the 30th day, or by making the astronomical calculations.
In addition, the holidays must fall out in the proper season: Pesach in the spring, etc. Since the lunar year is only 354 days and the solar year 365 days, each lunar year is 11 days short. Therefore, an additional lunar month must be periodically added in order to maintain the proper timing of the holidays.
2. Ex. 12:2.
3. Rosh Hashanah 22a.
4. I.e. to Moshe and Aharon. In later generations, it applies to the most important heads of the generation. See Rashi, ibid.
5. This would be a sign that Pesach is too early and therefore a month must be added.
6. Such as the spring solstice falling out later than the 16th of Nissan.
7. Unless there is no Sage in Eretz Yisroel of sufficient stature. See below.
8. I.e. Egypt. See Heller edition, note 10.
9. And therefore, even in the Rambam's times, they attempted to do this mitzvah by determining the calendar on the basis of testimony, each location individually. See Yad Halevi, note 8.
10. Trying to disprove the Karaites with faulty reasoning — saying, for example, that the primarymitzvah is to base everything on calculations, rather than testimony, even when the Bais Din HaGadol was in existence (unlike the Rambam's reasoning). See Kapach, 5731, note 40. TheRambam therefore proceeds to explain the function of the calculations.
11. See below for the preciseness of this wording — that today we use the calculations only to "know" what was previously established, not to ourselves establish Rosh Chodesh.
12. Berachos 63a.
13. This phrase can also be translated, "full understanding." See Kapach, 5731, note 44.
14. See note below regarding today's situation, where there is no Bais Din Hagadol in Eretz Yisroel.
15. Lev. 23:2.
16. Rosh Hashanah 25a.
17. For the source of this statement, see Tzafnas Paneach; Yermiyahu 31:35-36 and Guide to the Perplexed Part II, ch.28 (quoted in Kapach, 5731, note 51.)
18. The Ramban asks, if so, how can we have holidays and a calendar today?
However, there is a tradition (see Rashba, responsa, Vol.4, No.254) that Hillel HaNassi, in Eretz Yisroel, established a calendar until the arrival of Moshiach. Therefore, we can use our calculations to determine exactly what was previously established. According to many commentaries (see, for example, Megillas Esther; Chinuch) this is also the opinion of theRambam. However, see Avnei Nezer, Orach Chaim, 310, 311; Maharam Shick, Mitzvah 4;Chasam Sofer, Yoreh Deah, 234.
19. I.e. in cases of dire need, when there are no Sages in Eretz Yisroel, and when the Bais Din outside Eretz Yisroel was previously ordained in Eretz Yisroel.
20. Yeshayahu 2:3.
21. Ex. 13:10.
22. Mechilta D'Rashbi.
23. The extra month of the leap must be an additional Adar, right before Nissan, the month of Pesach.
24. Mechilta D'Rashbi.
25. Ex. 13:10.
26. Literally, "from day to day." The standard translation of this verse, however, is "from year to year," or "every year."
27. Ex. 12:2.
28. Megilah 5a.
29. Unlike the solar leap year, where one day is added.
30. Num. 11:21.
31. Megillah 5a.
32. Deut. 16:1.
33. I.e. the spring solstice.
34. 11a.
35. 20a.
Tefilah and Birkat Kohanim - Chapter Three
Halacha 1
The mitzvah of reciting the Morning Prayer entails that one begin praying at sunrise. The time [for prayer, however,] extends until the fourth hour, i.e., a third of the day.
If one transgresses or errs and prays after the fourth hour, he has fulfilled the obligation of prayer, but not the obligation of prayer in its time. Just as prayer is a positive Scriptural commandment, so too, its recitation at the proper time is a Rabbinic commandment, as established for us by Sages and Prophets.
Halacha 2
We have already stated that the time of the Minchah Prayer was established in correspondence to the daily afternoon sacrifice. Since the daily [afternoon] sacrifice was offered every day at nine and a half hours, [the Sages] established its time as nine and a half hours. This is referred to as "the lesserMinchah."
When the eve of Pesach fell on Friday, they would slaughter the daily [afternoon] sacrifice at six and a half hours. Accordingly, [the Sages] ordained that one who prays [Minchah] after six and a half hours has fulfilled his obligation. When this time arrives, the time of its obligation begins. This is referred to as "the greater Minchah."
Halacha 3
Many people are accustomed to recite [the afternoon service at both Minchah]Gedolah and K'tanah, and [to consider] one of them as an optional prayer.
Some of the Geonim taught that it is proper to recite the optional prayer only [at the time of Minchah] Gedolah. This is reasonable, since it corresponds to [the offering of a sacrifice] which was not frequent every day.
If one recites [the service] as an obligatory prayer [at the time of Minchah]Gedolah, he should recite it only as an optional prayer [at the time of Minchah]K'tanah.
Halacha 4
Behold, you have learned that the time of Minchah Gedolah is from six and a half hours until nine and a half hours, and the time of Minchah K'tanah is from nine and a half hours until there are one and a quarter hours left in the day. One may [however,] recite [the afternoon service] until sunset.
Halacha 5
The proper time of the Musaf Prayer is after the Morning Prayer, until seven hours of the day. One who recites it after seven hours, even though he has acted negligently, fulfills his obligation, since its time is the entire day.
Halacha 6
Regarding the Evening Prayer - even though it is not obligatory - a person who does recite it [must know that] its proper time is from the beginning of the night until dawn.
The proper time of the Ne'ilah prayer is such that one completes it close to sunset.
Halacha 7
One who recites a prayer before its proper time does not fulfill his obligation and must recite it again at its time. If, due to extenuating circumstances, one recites the Morning Prayer after dawn, [but before the proper time], he does fulfill his obligation.
One may recite the Evening Prayer of the Sabbath night on the eve of the Sabbath before sunset. Similarly, he may recite the Evening Prayer of Saturday night on the Sabbath. Since the Evening Prayer is not obligatory, we are not especially careful about its time. Nevertheless, one must recite the Shema at its proper time after the appearance of the stars.
Halacha 8
Anyone who intentionally allowed the proper time for prayer to pass without praying, cannot rectify the situation and cannot compensate [for his failure to pray].
[If he unintentionally failed to pray or was unavoidably detained or distracted, he can compensate for the [missed] prayer during the time of the prayer closest to it. He should first recite the prayer of this time, and afterwards, the [prayer of] compensation.
Halacha 9
How is this [exemplified]?
One who errs and does not recite the Morning Prayer before half the day passes should recite the Minchah Prayer twice, the first as Minchah [itself] and the second as compensation for the Morning Prayer.
One who errs and does not recite the Minchah Prayer before sunset should recite the Evening Prayer twice, the first as the Evening Prayer [itself] and the second as compensation for the Minchah Prayer.
[Similarly,] one who errs and does not recite the Evening Prayer before dawn should recite the Morning Prayer twice, the first as the Morning Prayer [itself] and the second as compensation for the Evening Prayer.
Halacha 10
One who errs and does not recite two consecutive prayers can only compensate for the last of them. How is this [exemplified]?
One who errs and recites neither the Morning Prayer nor the Minchah Prayer should recite the Evening Prayer twice, the first as the Evening Prayer [itself] and the last as compensation for Minchah. The Morning Prayer, however, has no compensation, since its time has already passed. This is also the case for other prayers.
Halacha 11
If two prayers are before him, Minchah and Musaf, he should first reciteMinchah and afterwards Musaf. There are those who teach that one should not do this in a congregation, in order that people not err.
Kiddush HaChodesh - Chapter Fifteen
Halacha 1
If you desire to know the true position of the moon1 on any particular date, first calculate the mean of the moon at the time of the sighting for the desired date. Then calculate the mean of the [moon within its] path and the sun's mean [position] for that date. Subtract the sun's mean from the moon's mean and double the remainder.2 The resulting figure is referred to as the double elongation.
Halacha 2
As mentioned previously, the intent of all the calculations in these chapters is to know how to sight the moon. [In this context, the size of this double elongation is significant.]
Halacha 3
Accordingly, it is necessary to contemplate [the length of] this double elongation. If the double elongation is five degrees or near that measure, there is no need to be concerned with an increase, and its measure need not be increased. If [the length of] the double elongation is between six and eleven degrees, one should add one degree to the mean of the [the moon] within its path.5
If [the length of] the double elongation is between twelve and eighteen degrees, one should add two degrees to the mean of [the moon] within its path. If [the length of] the double elongation is between nineteen and 24 degrees, one should add three degrees to the mean of [the moon] within its path. If [the length of] the double elongation is between 25 and 31 degrees, one should add four degrees to the mean of [the moon] within its path. If [the length of] the double elongation is between 32 and 38 degrees, one should add five degrees to the mean of [the moon] within its path.
If [the length of] the double elongation is between 39 and 45 degrees, one should add six degrees to the mean of [the moon] within its path. If [the length of] the double elongation is between 46 and 51 degrees, one should add seven degrees to the mean of [the moon] within its path. If [the length of] the double elongation is between 52 and 59 degrees, one should add eight degrees to the mean of [the moon] within its path. If [the length of] the double elongation is between 60 and 63 degrees, one should add nine degrees to the mean of [the moon] within its path.
The mean of [the moon] within its path that results after these additions have been made is referred to as the correct course.
Halacha 4
After the angular distance of the correct course is calculated,6 [the following procedure should be carried out]: If [the result] is less than 180 degrees, the angle of the course7 should be subtracted8 from the mean of the moon at the time of the sighting. If [the result] is more than 180 degrees, the angle of the course should be added9 to the mean of the moon at the time of the sighting.
The figure that remains after this addition or subtraction is made is the true position of the moon at the time of sighting.
Halacha 5
Know that if the correct course is an even 180 degrees or 360 degrees, there is no angle of the course. Instead, the mean position of the moon at the time of sighting is the true position of the moon at that time.
Halacha 6
What is the angle of its course? If the correct course is ten degrees, its angle will be 50 minutes. If the correct course is twenty degrees, its angle will be 1 degree and 38 minutes. If it is 30, its angle will be 2 degrees and 24 minutes. If it is 40, its angle will be 3 degrees and 6 minutes.10 If it is 50, its angle will be 3 degrees and 44 minutes. If it is 60, its angle will be 4 degrees and 16 minutes.
If it is 70, its angle will be 4 degrees and 41 minutes. If it is 80, its angle will be 5 degrees. If it is 90, its angle will be 5 degrees and 5 minutes. If it is 100, its angle will be 5 degrees and 8 minutes.11 If it is 110, its angle will be 4 degrees and 59 minutes. If it is 120, its angle will be 4 degrees and 40 minutes.12
If it is 130, its angle will be 4 degrees and 11 minutes. If it is 140, its angle will be 3 degrees and 33 minutes. If it is 150, its angle will be 213 degrees and 48 minutes. If it is 160, its angle will be 1 degree and 56 minutes. If it is 170, its angle will be 59 minutes. If it is an even 180 degrees, [the course] will not have an angle. Instead, as stated above, the moon's mean position will be identical with its true position.
Halacha 7
If the correct course is more than 180 degrees, you should subtract it from 360 to obtain its angle14, as you did for the course of the sun.15
Similarly, if the correct course includes units as well as tens, you should [calculate the average increase per degree and add the proportionate amount to the lower figure]. The procedure used to calculate the angle of the course for the course of the sun should be used to calculate the angle of the correct course [of the moon].16
Halacha 8
What is implied? Should we desire to know the true position of the moon on Friday night, the second of Iyar in the present year - the starting point for these calculations - the number of complete days that have passed from the date that is the starting point until the date on which we desire to know the true position of the moon is 29. One should [first] calculate the mean position of the sun for that night; this is 35 degrees, 38 minutes and 33 seconds, in symbols 35° 38' 33".
You should then calculate the mean of the moon at the time of the sighting, which is 53 degrees, 36 minutes and 39 seconds, in symbols 53° 36' 39". Afterwards, calculate the mean of [the moon] within its path for this time, which is 103 degrees, 21 minutes and 46 seconds, in symbols, 103° 21' 46". Then subtract the mean position of the sun from the moon's mean, producing a remainder of 17 degrees, 58 minutes and six seconds. This is the elongation. Doubling this figure produces a double elongation of 35 degrees, 56 minutes and 12 seconds, in symbols 35° 56' 12". Therefore, five degrees should be added to the course, as mentioned. Thus, the correct course will be 10817degrees and 21 minutes. As mentioned above with regard to the sun,18 the minutes are of no consequence in the calculation of the course.
Halacha 9
When calculating the angle for a course of 108, the result is 5 degrees and one minute. Since the correct course is less than 180 degrees, this figure should be subtracted from the moon's mean, leaving a remainder of 48 degrees, 3519minutes and 39 seconds.
The seconds should be rounded off and considered to be a minute. Accordingly, the true position of the moon at this time will be 18 degrees and 36 minutes of the nineteenth degree in the constellation of Taurus, in symbols 18° 36'.
In a similar manner, it is possible for you to calculate the true position of the moon at the time of sighting for any date that you desire from the beginning of this year that was chosen as the starting point until the end of all time.
| FOOTNOTES | |
| 1. |
I.e., the location of the moon as it appears in the sky.
|
| 2. |
The Rambam is following the notion that the Earth does not lie at the center of the moon's orbit. Hence, like the sun, the moon has an apogee and a perigee.
Also of significance here is the fact that, as mentioned in the notes on the previous chapter, the orbit of the moon is moving from east to west at a relatively fast pace, 11 degrees, 12 minutes and 19 seconds per day.
A conjunction refers to the time the sun, the moon, and the Earth are aligned in a straight line. Accordingly, the sun's rays are reflected back without being observed from the Earth, and the moon is therefore not seen in the heavens. At the time of the conjunction, the moon is always at its apogee.
(This can be explained as follows: When the moon is aligned directly between the sun and the Earth, it is at the point in its orbit that is closest to the sun. Therefore, the gravitational pull of the sun draws the moon away from the Earth.)
As the moon continues in its orbit, after the conjunction, it and its apogee move away from the sun in opposite directions. Significantly, the angular distance traveled by the moon and its apogee from the sun is the same.
To explain: The moon's mean is moving at rate of 13 degrees, 10 minutes and 35 seconds per day from west to east. Since the sun is also moving from west to east at the rate of 59 minutes and eight seconds per day, every day the moon will have traveled 12 degrees, 11 minutes and 27 seconds from the sun. Its apogee is moving from east to west at a speed of 11 degrees, 12 minutes and 19 seconds per day. When the sun's mean motion is added to that figure, the same total, 12 degrees, 11 minutes and 27 seconds, is reached. Thus, the double elongation, which is calculated by doubling the angular distance between the moon's mean and the sun's mean, represents the angular distance between the moon's mean and the apogee of its orbit.
(The moon also reaches its apogee when it is full. At this point, the sun, the Earth, and the moon are aligned in a straight line, and the gravitational pull of the sun draws the Earth away from the moon. According to contemporary science, however, these two figures are not alike, and the apogee reached at conjunction is greater than the apogee reached at a full moon.)
|
| 3. |
At this time, the mean position of the moon will have moved 2 1/2 degrees from the mean position of the sun. Unless it moves that distance, its crescent will be too small to be noticed in the sky. This distance will be covered by the moon in slightly less than five hours. Thus, within five hours of the conjunction of the sun and the moon, it will be possible to sight the new moon.
The commentaries have noted a slight incongruity between the Rambam's statements here and his statements at the beginning of Chapter 17, where he states that the longitude at the night of the sighting of the moon will not be less than nine degrees nor more than twenty-four degrees. There is a difference of approximately seven degrees between these two figures. They attempt to resolve this discrepancy by stating that in this chapter the Rambam is speaking in terms of mean distance, while in Chapter 17 he is speaking in terms of true distance. At times, there can be as great as a seven-degree fluctuation between the two figures (Perush, Ralbach).
|
| 4. |
At this time, 61 hours will have passed since the time of the conjunction, and the moon will have moved 31 degrees from the sun. Under such circumstances, the crescent of the moon will be large enough to be openly visible to all, and no calculations will be necessary.
|
| 5. |
The difference between the true position of the moon and its mean position depends on the progress of the moon in its epicycle - i.e., the mean of [the moon] within its path, which is moving at approximately 13 degrees a day from east to west, as stated in the previous chapter. The Rambam is stating that a further adjustment is necessary, depending on the distance between the moon and the sun.
During the first days of the month, as the distance between the sun and the moon increases, the moon's progress in its epicycle will vary from its standard rate of progress. According to the medieval science, this variation depends on the movement of the nekudah hanochachit, the point opposite the center of the moon's orbit. According to modern science, this difference depends on the gravitational pull of the sun and other celestial bodies.
|
| 6. |
I.e., the progress of the moon in its epicycle.
|
| 7. |
This refers to the angle between the line extending from the mean position of the moon to the Earth and the line extending from the adjusted position of the moon in its epicycle to the Earth.
|
| 8. |
When the correct course is less than 180 degrees, the angular distance between the moon's actual position and its mean is less than the mean distance. Hence, a subtraction should be made.
|
| 9. |
When the correct course is more than 180 degrees, the angular distance between the moon's actual position and its mean is more than the mean distance. Hence, an addition should be made.
|
| 10. |
The angle of the course of the moon is far larger than the angle of the course of the sun. The rationale for this difference is easily explainable. The moon is far closer to the Earth than the sun. Therefore, the angle between the two lines extending from either end of the course to the Earth will be greater.
|
| 11. |
The line from the Earth to the moon's mean varies only slightly, while the line from the Earth to the true position of the moon changes to a far greater degree as the moon proceeds along its epicycle, changing the size of the angle of the course. The angle of the course will be largest when the angle between the line extending from the Earth to the true position of the moon and the line extending from the true position of the moon to its mean position is ninety-six degrees - i.e., when these two lines are almost directly perpendicular to each other.
(The reason the largest angle is not at a direct 90-degree angle is that the line to the moon's mean is drawn from the center of the Earth, and the true position takes into consideration the fact that we are looking at the moon from the surface of the Earth, which is removed from its center.)
|
| 12. |
Our translation is based on the authentic manuscripts and early printings of the Mishneh Torah. The standard printed text reads 4 degrees and 20 minutes.
|
| 13. |
Here, also, there is a printing error in the standard printed texts of the Mishneh Torah, and those texts read 3 degrees.
|
| 14. |
For the same angle is produced regardless of whether one makes an increase or a decrease from 180° or 360°.
|
| 15. |
See Chapter 13, Halachot 5-6.
|
| 16. |
See Chapter 13, Halachah 7.
|
| 17. |
In the standard printed texts of the Mishneh Torah, there is a printing error, and those texts read 180 degrees.
|
| 18. |
See Chapter 13, Halachah 9.
|
| 19. |
Here also there is a printing error in the standard published text, which reads 33 minutes.
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Kiddush HaChodesh - Chapter Sixteen
Halacha 1
The orbit in which the moon revolves [intersects] the orbit in which the sun revolves at an angle,1 [so that] a portion of [the moon's orbit] is inclined to the north of the sun's orbit and a portion is inclined south of the sun's orbit.2 There are two points, one opposite the other, at which these orbits intersect.3
When the moon is at one of these points, it is revolving in the same plane as the sun. As the moon departs from these points, it is proceeding either to the north or to the south of the sun.
The point in the moon's [orbit] at which it begins to be inclined to the north of [the plane of] the sun's [orbit] is referred to as the head, while the point [in its orbit] from which it begins to be inclined to the south of [the plane of] the sun's [orbit] is referred to as the tail.*
Halacha 2
The mean movement of the head in one day is 3 minutes and 11 seconds.6Thus, its movement in ten days is 31 minutes and 47 seconds; its movement in one hundred days is 5 degrees, 17 minutes, and 43 seconds, in symbols 5° 17' 43". In one thousand days, its movement is 52 degrees, 57 minutes and 10 seconds, in symbols 52° 57' 10". The remainder [of the sum] of its progress in ten thousand days is 169 degrees, 31 minutes and 40 seconds, in symbols 169° 31' 40".
Thus, the distance it travels in twenty-nine days is 1 degree, 32 minutes and 9 seconds, in symbols 1° 32' 9". Its progress in a regular year is 18 degrees, 44 minutes and 42 seconds, in symbols 18° 44' 42". The mean position of the head on Thursday night [of the present year,] the starting point for these calculations, is 180 degrees, 57 minutes, and 28 seconds, in symbols 180° 57' 28".7
Halacha 3
If you desire to calculate the position of the head at any given date, [you should follow this procedure:] First, calculate the mean progress of the head as you calculated the mean of the sun and the mean of the moon. [Afterwards,] subtract this mean from 360 degrees,8 and the remainder will be the location of the head at that time. The tail's position will always be the [place in the moon's orbit] directly opposite it.
Halacha 4
What is implied? Let us suppose that we desired to know the location of the head on Friday night, the second of Iyar of this year - the starting point for these calculations. There are 29 complete days between the night of the starting point and the date for which we desire to know the location of the head.
Halacha 5
We should then calculate the mean of the head according to the familiar manner, adding its distance traveled in 29 days to the starting point. Thus, the mean of the head is 182 degrees, 29 minutes and 37 seconds, in symbols 182° 29' 37". This mean should be subtracted from 360, leaving a remainder of 177 degrees, 30 minutes and 23 seconds, in symbols 177° 30' 23".
This is the location of the head. The seconds are of no consequence. Thus, the position of the head will be 27 degrees and 30 minutes within the constellation of Virgo. The position of the tail will be [directly] opposite it: 27 degrees and 30 minutes within the constellation of Pisces.
Halacha 6
There will always be an even half of the celestial sphere between the position of the head and the position of the tail. Therefore, whenever the head is in a particular constellation, the tail will be seven constellations further in the order of constellations, at the same position with regard to degrees and minutes. For example, if the head is ten degrees within a particular constellation, the tail will be ten degrees within the seventh constellation from it.
Halacha 7
After having established the position of the head, the position of the tail, and the true position of the moon, consider [these three figures]: If the position of the moon is the same, both in degrees and in minutes, as its head or tail, then the moon will not be inclined to the north or the south.9
If the position of the moon has passed10 the head11 and it is proceeding in the direction of the tail, know that the moon will be inclined to the north of the [plane] of the sun's [orbit]. If the position of the moon is before the tail12 and it is proceeding in the direction of the head, know that the moon will be inclined to the south of the [plane] of the sun's [orbit].
Halacha 8
The inclination of the moon to the north or to the south is referred to as the moon's latitude.13 If the moon's incline is northerly, it is referred to as a northerly latitude. If the moon's incline is southerly, it is referred to as a southerly latitude. If the moon is positioned at either [the head or the tail], it has no latitude, as explained above.
Halacha 9
The moon's latitude14 will never exceed five degrees, whether to the north or to the south. This is the pattern it follows. [The moon] begins at the head and diverges slightly [from the sun's orbit, as it proceeds on its own orbit]. [The size of] this divergence continues to increase until it reaches five degrees.15 At this point, [the moon] begins to come slightly closer [to the sun's orbit], until it has no latitude at all when it reaches its tail.
[After it reaches the tail, the moon] will again begin to diverge slightly [from the sun's orbit], until this divergence reaches five degrees. It will then begin to approach [the sun's orbit], until ultimately it has no latitude at all.
Halacha 10
[The following procedure should be applied] if you desire to determine the latitude of the moon, and to [know] whether it is northerly or southerly: First, calculate the position of the head and the true position of the moon at the desired date. Then subtract the position of the head from the true position of the moon. The remainder is referred to as "the course of the latitude."16
If the course of the latitude is between one degree and 180 degrees, the latitude of the moon is northerly. If course of the latitude is more than 180 degrees, the latitude of the moon is southerly. If [the course] is an even 180 degrees or an even 360 degrees, the moon does not have any latitude at all.
Afterwards, determine the size of the angle of the course of the latitude17 - i.e., the extent to which the moon is inclined to the north or to the south. This figure is referred to as the moon's southerly latitude or northerly [latitude], as we explained.
Halacha 11
How large is the angle of the course of the latitude? If the course of the latitude is ten degrees, its angle will be 52 minutes. If the course is twenty degrees, its angle will be one degree and 43 minutes. If the course is thirty degrees, its angle will be 2 degrees and 30 minutes.
If the course is forty degrees, its angle will be 3 degrees and 13 minutes. If the course is fifty degrees, its angle will be 3 degrees and 50 minutes. If the course is sixty degrees, its angle will be 4 degrees and 20 minutes. If the course is seventy degrees, its angle will be 4 degrees and 42 minutes. If the course is eighty degrees, its angle will be 4 degrees and 55 minutes. If the course is ninety degrees, its angle will be 5 degrees.18
Halacha 12
If [the course of the latitude] has both units and tens, you should [calculate the average increase per degree and add the proportionate amount to the lower figure], as was done with regard to the course of the sun and the course of the moon.19
What is implied? When the course of the latitude is 53 degrees, [the size of the angle should be determined as follows]. It has already been established that when the course is 50 degrees, its angle is 3 degrees and 50 minutes. When the course is 60 degrees, its angle is 4 degrees and 20 minutes. Therefore, there is a difference of 30 minutes between them, 3 minutes for each degree. Accordingly, [when] calculating the angle for a course of 53 degrees, [the result] will be 3 degrees and 59 minutes. A similar process should be followed with regard to all other figures.
Halacha 13
Since you know the angles for all the values of the course of the latitude until ninety degrees, as was mentioned, you will be able to know the angle for all possible values of the course. For if the course is between 90 and 180 degrees, subtract the course from 180 and find the angle for the remainder.20
Halacha 14
Halacha 15
Similarly, if the course is between 270 and 360 degrees, subtract [the course] from 360 and find the angle for the remainder.24
Halacha 16
What is implied? If the course is 150°, subtract 150 from 180, leaving 30. As mentioned previously, the angle [of a course] of 30 [degrees] will be 2 degrees and 30 minutes. Thus, the angle [of a course] of 150 [degrees] also will be 2 degrees and 30 minutes.
Halacha 17
If the course is 200°, subtract 180 from 200, leaving 20. As mentioned previously, the angle [of a course] of 20 [degrees] will be 1 degree and 43 minutes. Thus, the angle [of a course] of 200 [degrees] also will be 1 degree and 43 minutes.
Halacha 18
If the course is 300°, subtract 300 from 360, leaving 60. As mentioned previously, the angle [of a course] of 60 [degrees] will be 4 degrees and 20 minutes. Thus, the angle [of a course] of 300 [degrees] also will be 4 degrees and 20 minutes. A similar process should be followed with regard to all other values.
Halacha 19
[The following procedure should be applied] if one desires to know the latitude of the moon and whether it is either northerly or southerly at the beginning of Friday night, the second of Iyar of this year: It has already been established that the true position of the moon on this night is 18 degrees and 36 minutes within the constellation of Taurus, in symbols 18° 36". [Similarly, it has been established that] the position of the head at that time is 27 degrees and 30 minutes within the constellation of Virgo, in symbols 27° 30'.
[To arrive at the latitude,] you must subtract the position of the head from the position of the moon, leaving a course of the latitude of 231 degrees and 6 minutes, in symbols 231° 6'. [As mentioned,] the minutes are of no consequence with regard to the course. Therefore, according to the principles explained in this chapter, the angle of this course will be 3 degrees and 53 minutes. This is the latitude of the moon at the beginning of this night. It is southerly, for the course is larger than 180 degrees.
| FOOTNOTES | |
| 1. |
More specifically, as mentioned in Halachah 9, the maximum angular distance between the two orbits is 5 degrees.
|
| 2. |
The importance of the concept the Rambam introduces here, the difference in latitude between the planes of the orbits of the sun and the moon, becomes significant in the following chapter.
To explain briefly: In the previous chapters, it was explained that the visibility of the moon depends upon the distance in longitude between it and the sun. At the time of conjunction, the sun and the moon are at the same longitudinal point. Therefore, they set at the same time. As the difference in longitude between them increases, the crescent of the moon grows and the time of its setting becomes later, increasing the chances of its visibility.
Nevertheless, the moon's latitude also affects its visibility. The greater the latitude of the moon [i.e., its inclination from the orbit of the sun] the larger its crescent will appear. Also, a northerly latitude causes the moon to set later and thus makes it easier to be sighted. A southerly latitude, by contrast, causes the moon to set earlier and thus makes sighting it more difficult.
|
| 3. |
The difference in latitude between the orbits of the sun and the moon explains why there is not a lunar eclipse at every full moon, and why there is not a solar eclipse at every conjunction - although at the time of the full moon, the sun, the earth and the moon are aligned in a single line, and at the time of conjunction, the sun, the moon and the earth are aligned in a single line.
Although the longitude of the sun and the moon is the same at these times, since their latitudes are different, the moon's shadow does not interfere with the light of the sun at a conjunction, and the earth's shadow does not prevent the light of the sun from reaching the moon at a full moon. Only when a conjunction or a full moon takes place at (or near) the point where the orbits of the moon and the sun intersect does an eclipse take place.
|
| 4. |
Because of the revolution of the head, the determination of the moon's longitude will require several stages of computation.
|
| 5. |
I.e., the head revolves from east to west.
|
| 6. |
As evident from the later figures given by the Rambam, this number is an approximation, and the actual figure is several thirds less.
|
| 7. |
The Rambam is giving a negative figure here, his intent being 360° - 180° 57' 28. In positive terms, it would be a position of 179° 2' 32.
|
| 8. |
This subtraction is necessary, since, as mentioned above, the head revolves from east to west, opposite to the direction of the heavenly sphere as a whole.
Thus, we begin with a negative value as a starting point and add to it the distance traveled by the head. When that total is subtracted from 360, we have a positive figure that is the true position of the head. The reason the Rambam uses a negative figure for his starting point is that as the numbers increase, it is easier to add the mean distance traveled by the head to the starting point of 180° 57' 28 and subtract the total from 360, than to define the starting point in positive terms and subtract the mean progress from it.
|
| 9. |
As mentioned previously, the head and the tail are the positions where the moon's orbit intersects with that of the sun. Thus, if the moon is at the head or the tail, it is not at all inclined.
|
| 10. |
We have used a non-literal translation of the word ינפל in this and the following sentence based on the context in this halachah.
|
| 11. |
I.e., the difference between the position of the moon and the position of the head is less than 180 degrees, as stated in Halachah 10.
|
| 12. |
I.e., the difference between the position of the moon and the position of the head is more than 180 degrees, as stated in Halachah 10.
|
| 13. |
The Hebrew term רחב הירח literally means "the width of the moon." It was given this name because its range from 0° to 5° is far less than that of the longitude of the moon, ארך הירח, the angular distance between the moon and the sun, which ranges from 0° to 360°.
|
| 14. |
According to contemporary science, the Rambam is making an approximation, for the latitude of the moon can reach 5 degrees and 9 minutes.
|
| 15. |
As indicated from Halachah 11, this is the mid-point between the head and the tail, 90° and 270°.
|
| 16. |
I.e., the distance the moon has traveled in its orbit from the head to its present position.
|
| 17. |
This refers to the angle between the plane of the sun's orbit and the position of the moon in its orbit.
|
| 18. |
As stated above, this is the greatest latitude reached.
|
| 19. |
See Chapter 13, Halachah 7, and Chapter 15, Halachah 7.
|
| 20. |
For, as mentioned above, 90 degrees is the even mid-point of the course, and its angle increases and decreases in the same proportions as one approaches or leaves that point.
|
| 21. |
In the standard printed texts of the Mishneh Torah, there is a printing error, and the concluding phrase from the chapter was added here by mistake.
|
| 22. |
At 270°, as at 90°, the course reaches its maximum latitude, 5 degrees.
|
| 23. |
For, as mentioned above, the course begins to increase as it progresses after reaching its tail in the same proportions as it increases as it progresses from its head.
|
| 24. |
For the rate of the angular decrease from 270 to 180 is equivalent to the rate of decrease from 90 to 180.
|
Kiddush HaChodesh - Chapter Seventeen
Halacha 1
All the principles we have explained above were intended so that you will be ready and prepared to know [how] to sight [the moon]. When you desire to know [how to sight the moon on a particular night], calculate the true position of the sun, the true position of the moon, and the position of the head [of the moon's orbit] for the time of the sighting [of the moon].
Afterwards, subtract the position of the sun from the position of the moon. The remainder is referred to as the first longitude.
Halacha 2
After having determined the position of the head and the moon's position,1 you will be able to determine the moon's latitude and whether this latitude is northerly or southerly. This figure is referred to as the first latitude. Be careful with regard to [these two symbols,] the first longitude and the first latitude, and have them at hand [for later calculations].
Halacha 3
Consider the first longitude:2 If the figure you arrive at is equal to nine degrees or less, know that it will definitely be impossible for the moon to be sighted on that night throughout Eretz Yisrael; no other calculation is necessary.
If the first longitude is more than fifteen degrees, know that the moon will definitely be sighted throughout Eretz Yisrael; no other calculation is necessary.3
If the first longitude is between nine and fifteen degrees, it will be necessary for you to make further calculations to know whether the moon will be sighted or not.
Halacha 4
When does the above apply? When the true position of the moon is located [in the area] between the beginning of the constellation of Capricorn and the end of the constellation of Gemini.4 If, however, the position of the moon [is located in the range] between the beginning of the constellation of Cancer and the end of the constellation of Sagittarius, and the first longitude is ten degrees or less,5know that it will definitely be impossible for the moon to be sighted on that night throughout Eretz Yisrael; no other calculation is necessary.
If the first longitude6 is more than twenty-four degrees, know that the moon will definitely be sighted throughout Eretz Yisrael; no other calculation is necessary.
If the first longitude is between ten and twenty-four degrees, it will be necessary to make further calculations to know whether or not the moon will be sighted.7
Halacha 5
These are the [further] calculations [necessary to determine] the sighting of the moon: Consider the constellation in which the moon is located.8 If it is the constellation of Aries, subtract9 59 minutes from the first longitude. If it is the constellation of Taurus, subtract one degree from the longitude.10 If it is the constellation of Gemini, subtract 58 minutes from the longitude.11 If it is the constellation of Cancer, subtract 5212 minutes from the longitude.
If it is the constellation of Leo, subtract 43 minutes from the longitude.13 If it is the constellation of Virgo, subtract 37 minutes from the longitude. If it is the constellation of Libra, subtract 34 minutes from the longitude.
If it is the constellation of Scorpio, subtract 34 minutes from the longitude. If it is the constellation of Sagittarius, subtract 36 minutes from the longitude.14 If it is the constellation of Capricorn, subtract 44 minutes from the longitude.15 If it is the constellation of Aquarius, subtract 53 minutes from the longitude. If it is the constellation of Pisces, subtract 58 minutes from the longitude.16The remainder after these minutes have been subtracted from the longitude is referred to as the second longitude.
Halacha 6
Why are these minutes subtracted? Because the true position of the moon is not the place where the moon will actually be sighted [in the sky]. Instead, there is a [small] difference in both longitude and latitude.17 This [difference] is referred to as the sighting adjustment.
The sighting adjustment for the moon's longitude at the hour of the sighting of the moon18 should always be subtracted from the longitude, as we explained.
Halacha 7
[The latter point is not necessarily true,] by contrast, with regard to the sighting adjustment for the moon's latitude.19If the moon's latitude is northerly, we subtract the minutes of the sighting adjustment for the moon's latitude from the moon's first latitude.20 If, however, the moon's latitude is southerly, we add the minutes of the sighting adjustment for the moon's latitude to the moon's first latitude.21 The result after the addition or subtraction of these minutes to or from the [moon's] first latitude is referred to as the second latitude.
Halacha 8
How many minutes are added or subtracted? If the moon is in the constellation of Aries, 9 minutes.22 If it is in the constellation of Taurus, 10 minutes. If it is in the constellation of Gemini, 16 minutes. If it is in the constellation of Cancer, 27 minutes. If it is in the constellation of Leo, 38 minutes. If it is in the constellation of Virgo, 44 minutes.
If it is in the constellation of Libra, 46 minutes.23 If it is in the constellation of Scorpio, 45 minutes. If it is in the constellation of Sagittarius, 44 minutes. If it is in the constellation of Capricorn, 36 minutes. If it is in the constellation of Aquarius, 2724 minutes. If it is in the constellation of Pisces, 12 minutes.
Halacha 9
Since you know the [number of] minutes [for the adjustment] for each constellation, add or subtract them to or from the first latitude, as was explained, and arrive at the second latitude. You already know whether it will be northerly or southerly,25 and you will know the number of degrees and minutes of this second latitude. Prepare this figure and have it at hand.
Halacha 10
Afterwards,26 you must set aside [for later use in subtracting or adding] a portion of this second latitude, because the moon fluctuates slightly in its orbit.27What is the size of the portion you must separate? [This depends on the position of the moon in the celestial sphere.]28
If the moon is located between the beginning of the constellation of Aries and its twentieth degree - and similarly, [when the moon is located] between the beginning of the constellation of Libra and its twentieth degree - separate two fifths of the second latitude.29
If the moon is located between the twentieth degree of the constellation of Aries and the tenth degree of the constellation of Taurus - and similarly, [when the moon is located] between the twentieth degree of the constellation of Libra and the tenth degree of the constellation of Scorpio - separate one third from the second latitude.
If the moon is located between the tenth degree of the constellation of Taurus and its twentieth degree - and similarly, [when the moon is located] between the tenth degree of the constellation of Scorpio and its twentieth degree - separate one fourth from the second latitude.
If the moon is located between the twentieth degree of the constellation of Taurus and its end - and similarly, [if the moon is located] between the twentieth degree of the constellation of Scorpio and its end - separate one fifth from the second latitude.
If the moon is located between the beginning of the constellation of Gemini and its tenth degree - and similarly, [if the moon is located] between the beginning of the constellation of Sagittarius and its tenth degree - separate one sixth of the second latitude.
If the moon is located between the tenth degree of the constellation of Gemini and its twentieth degree - and similarly, [if the moon is located] between the tenth degree of the constellation of Sagittarius and its twentieth degree - separate one twelfth from the second latitude.
If the moon is located between the twentieth degree of the constellation of Gemini and its twenty-fifth degree - and similarly, [if the moon is located] between the twentieth degree of the constellation of Sagittarius and its twenty-fifth degree - separate one twenty-fourth from the second latitude.
If the moon is located between the twenty-fifth degree of the constellation of Gemini and the fifth degree of the constellation of Cancer - and similarly, [if the moon is located] between the twenty-fifth degree of the constellation of Sagittarius and the fifth degree of the constellation of Capricorn - do not make any separation, because at this point the moon does not fluctuate at all from its orbit.30
If the moon is located between the fifth degree of the constellation of Cancer and its tenth degree - and similarly, [if the moon is located] between the fifth degree of the constellation of Capricorn and its tenth degree - separate one twenty-fourth from the second latitude.
If the moon is located between the tenth degree of the constellation of Cancer and its twentieth degree - and similarly, [if the moon is located] between the tenth degree of the constellation of Capricorn and its twentieth degree - separate one twelfth from the second latitude.
If the moon is located between the twentieth degree of the constellation of Cancer and its end - and similarly, [if the moon is located] between the twentieth degree of the constellation of Capricorn and its end - separate one sixth from the second latitude.
If the moon is located between the beginning of the constellation of Leo and its tenth degree - and similarly, [if the moon is located] between the beginning of the constellation of the Aquarius and its tenth degree - separate one fifth of the second latitude.
If the moon is located between the tenth degree of the constellation of Leo and its twentieth degree - and similarly, [if the moon is located] between the tenth degree of the constellation of Aquarius and its twentieth degree - separate one fourth from the second latitude.
If the moon is located between the twentieth degree of the constellation of Leo and the tenth degree of the constellation of Virgo, and similarly, [if the moon is located] between the twentieth degree of the constellation of Aquarius and tenth degree of the constellation of Pisces - separate one third from the second latitude.
If the moon is located between the tenth degree of the constellation of Virgo and its end - and similarly, [if the moon is located] between the tenth degree of the constellation of Pisces and its end - separate two fifths from the second latitude.
This portion that is separated from the second latitude is referred to as the circuit of the moon.
Halacha 11
Afterwards, go back and consider whether the latitude of the moon is northerly or southerly. If it is northerly, subtract [the adjustment referred to as] the circuit of the moon from the second longitude.31 If the moon's longitude is southerly, add the circuit of the moon to the second longitude.32
When does the above apply? When the moon's position is located between the beginning of the constellation of Capricorn and the end of the constellation of Gemini.33 If, however, the moon's position is located between the beginning of the constellation of Cancer and the end of the constellation of Sagittarius,34 the opposite is true: If the moon's latitude is northerly, the circuit should be added to the second longitude,35 and if the moon's latitude is southerly, the circuit should be subtracted from the second longitude.36
The remainder after the additions or subtractions have been made to the second longitude is referred to as the third longitude. Know that if there is no fluctuation within the circuit, and there is no figure to be separated from the second latitude,37 the second longitude also will serve as the third longitude, without any decrease or increase.
Halacha 12
Afterwards, go back and see the constellation in which the third longitude - i.e., [the amended figure representing] the distance between the sun and the moon - is located:38 If it is located in the constellation of Pisces or Aries, add one sixth [of its length] to the third longitude.39 If the [third] longitude is located in the constellation of Aquarius or the constellation of Taurus, add one fifth [of its length] to the third longitude.40 If the [third] longitude is located in the constellation of Capricorn or the constellation of Gemini, add one sixth [of its length] to the third longitude.
If the [third] longitude is located in the constellation of Sagittarius or the constellation of Cancer, leave the third longitude as it is, without making any addition or subtraction.41 If the [third] longitude is located in the constellation of Scorpio or the constellation of Leo, subtract one fifth [of its length] from the third longitude. If the [third] longitude is located in the constellation of Libra or the constellation of Virgo, subtract one third [of its length] from the third longitude.42
The figure resulting from these subtractions or additions to the third longitude, or from leaving it without adjustment, is referred to as the fourth longitude.
[Afterwards, a further correction is necessary:] Return to the first latitude,43 and set aside two thirds [of its length]. This is called the correction [resulting from geographic] latitude.44
Consider whether the latitude of the moon is northerly. If so, add the correction [resulting from geographic] latitude to the fourth longitude.45 If the latitude of the moon is southerly, subtract the correction [resulting from geographic] latitude from the fourth longitude.46 The figure resulting from these subtractions or additions to the fourth longitude is referred to as the arc of sighting.
Halacha 13
What is implied? For example, let us attempt to determine whether or not it will be possible to sight the moon on Friday night, the second of Iyar of this year: First, it is necessary to determine the true position of the sun, the true position of the moon, and the moon's latitude for this time47 according to the methods that were disclosed [in the previous chapters].
The result is that the true position of the sun is seven degrees and nine minutes in the constellation of Taurus, in symbols 7° 9'. The true position of the moon is eighteen degrees and thirty-six minutes in the constellation of Taurus, in symbols 18° 36'. The moon's latitude is three degrees and fifty-three minutes, in symbols 3° 53', and it is southerly. This is the first latitude.
Afterwards, you should subtract the position of the sun from the position of the moon, arriving at a remainder of eleven degrees and twenty-seven minutes, in symbols 11° 27'. This is the first longitude.
Since the moon is located in the constellation of Taurus, the sighting adjustment for the longitude will be one degree. This should be subtracted from the first longitude, producing a second longitude of 10 degrees and twenty-seven minutes, in symbols 10° 27'. The sighting adjustment for the latitude is ten minutes. Since the moon's latitude is southerly, this sighting adjustment of ten minutes should be added to the moon's latitude, producing a second latitude of four degrees and three minutes, in symbols 4° 3'.
Since the moon is located in the eighteenth minute of the constellation of Taurus, it is proper to set aside one fourth of the second latitude as the circuit of the moon. Thus, at this time, the circuit of the moon will be one degree and one minute. We pay no attention to the seconds.
Halacha 14
Since the latitude of the moon is southerly and the true position of the moon is located between the beginning [of the constellation] of Capricorn and the beginning [of the constellation] of Cancer, it is correct to add the circuit of the moon to the second longitude. Thus, the third longitude will be eleven degrees and twenty-eight minutes, in symbols 11° 28'.
Since this longitude is located in the constellation of Taurus, it is fitting to add one fifth to the third longitude - i.e., two degrees and eighteen minutes. Thus, the fourth longitude will be thirteen degrees and forty-six minutes, in symbols 13° 46'.
We then go back to the first latitude and separate two thirds of it. Thus, the correction [resulting from geographic] latitude is two degrees and thirty-five minutes. Since the latitude is southerly, the correction [resulting from geographic] latitude should be subtracted from the fourth longitude, leaving a remainder of eleven degrees and eleven minutes, in symbols 11° 11'. This is the arc of sighting on this night.
Following this process, you can determine the number of degrees and the number of minutes every night for the moon's sighting48, which you desire for all time.
Halacha 15
After you have determined this arc [of sighting], consider it. Know [these rules]: If the arc of sighting is nine degrees or less, it is impossible for the moon to be sighted anywhere in Eretz Yisrael. If the arc of sighting is more than fourteen degrees, it is impossible49 for it not to be seen and openly revealed throughoutEretz Yisrael.
Halacha 16
If the arc of sighting is between the beginning of the tenth degree and the end of the fourteenth degree, [the following procedure should be followed:] One should consider the arc of sighting in relation to the first longitude50 and determine whether or not the moon will be seen from the limits prevalent [at that time]. They are referred to as the sighting limits.
Halacha 17
The following are the sighting limits: If the arc of sighting is between nine and ten degrees, or more than ten [degrees], and the first longitude is thirteen degrees or more, [the moon] will surely be sighted. If the arc is less than this, or if the first longitude is less than this, it will not be sighted.
Halacha 18
If the arc of sighting is between ten and eleven degrees, or more than eleven [degrees], and the first longitude is twelve degrees or more, [the moon] will surely be sighted. If the arc is less than this, or if the first longitude is less than this, it will not be sighted.
Halacha 19
If the arc of sighting is between eleven and twelve degrees, or more than twelve [degrees], and the first longitude is eleven degrees or more, [the moon] will surely be sighted. If the arc is less than this, or if the first longitude is less than this, it will not be sighted.
Halacha 20
If the arc of sighting is between twelve and thirteen degrees, or more than thirteen [degrees], and the first longitude is ten degrees or more, [the moon] will surely be sighted. If the arc is less than this, or if the first longitude is less than this, it will not be sighted.
Halacha 21
If the arc of sighting is between thirteen and fourteen degrees, or more than fourteen [degrees], and the first longitude is nine degrees or more, [the moon] will surely be sighted. If the arc is less than this, or if the first longitude is less than this, it will not be sighted. This concludes the sighting limits.
Halacha 22
What is implied? If we were to consider the arc of sighting for Friday night, the second of Iyar of this year, we would calculate the arc of sighting to be eleven degrees and eleven minutes, as you have already determined.51
Since the arc of sighting is between ten and fourteen degrees, it is necessary to consider it in relation to the first longitude. It has already been established that on this night, the [first] longitude is ten degrees and twenty seven minutes. Since the first longitude is greater than eleven [degrees], we can be assured that the moon will be sighted on that night according to the limits established. Similar procedures should be followed [on every occasion when it is necessary to consider] the arc of sighting in relation to its first longitude.
Halacha 23
From all the above, you have seen the extent of the calculations, and the additions and the subtractions that required much effort to present a method that comes close [to being exact]52 without necessitating extremely complicated calculations. [This process is necessary] because the moon has major incongruities in its orbit.
In this vein, our Sages said,53 "'The sun knows the time of its setting'; the moon does not know the time of its setting." Similarly, our Sages said,54 "At times, its setting is prolonged, and at times, it is hastened." This is reflected in these calculations, where at times it is necessary to add, and at times it is necessary to subtract until we arrive at the arc of sighting. And as explained, at times the arc of sighting is great, and at times it is small.
Halacha 24
The rationales for all these calculations, and the reasons why this number is added, and why that subtraction is made, and how all these concepts are known, and the proofs for each of these principles are [the subject] of the wisdom of astronomy and geometry, concerning which the Greeks wrote many books.
These texts are presently in the hands of the sages. The texts written by the Sages of Israel in the age of the prophets from the tribe of Yissachar55 have not been transmitted to us. Nevertheless, since these concepts can be proven in an unshakable manner, leaving no room for question, the identity of the author, be he a prophet or a gentile, is of no concern.56 For a matter whose rationale has been revealed and has proven truthful in an unshakable manner, we do not rely on [the personal authority of] the individual who made these statements or taught these concepts, but on the proofs he presented and the reasons he made known.57
| FOOTNOTES | |
| 1. |
Our translation is based on authentic manuscript editions of the Mishneh Torah and early printings. There is a printing error in the standard published text.
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| 2. |
In this instance as well, our translation is based on authentic manuscript editions of the Mishneh Torah and early printings. There is a printing error in the standard published text, where the words "and the first latitude" were added unnecessarily.
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| 3. |
Note the apparent contradiction to the figures the Rambam mentions in Chapter 15, Halachah 2, and the resolution suggested in Note 4 of that chapter.
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| 4. |
In these months, the ecliptic (the plane of the sun's orbit as extended to the celestial sphere) is inclined to the north. After the conjunction, the moon proceeds away from the position of the sun. When the inclination of the ecliptic is northward, this movement places it in a more northerly position. Therefore, the moon will set later than would be foreseen otherwise, resulting in a greater possibility of seeing the new moon.
As mentioned in the notes of Chapter 16, as the longitude of the moon increases, seeing the moon also becomes easier. In these months, however, a lesser longitude is required.
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| 5. |
In these months, the ecliptic is inclined to the south. As the moon proceeds away from the position of the sun after conjunction, it will be in a more southerly position in these months. Therefore,the moon will set earlier than would be foreseen otherwise, resulting in a lesser possibility of seeing the new moon. To compensate for this difference, a greater longitude is required.
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| 6. |
Our translation is based on authentic manuscript editions of the Mishneh Torah and early printings. There is a printing error in the standard published text, and the word "latitude" was added unnecessarily.
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| 7. |
To summarize the Rambam's statements to this point: When the longitude of the moon (the angular distance between the moon and the sun) is minimal, the moon's crescent will be small and the interval between the time of its setting and that of the sun will be small. Hence, it is unlikely that the moon will be sighted.
When the longitude of the moon is greater, the size of the moon's crescent will increase, as will the interval between the time of its setting and that of the sun. Accordingly, the possibility of sighting the moon will increase.
When the longitude is significantly large, it is obvious that the moon will be seen and no other calculations are necessary. When, however, the longitude is of intermediate size, there is a question whether the moon will be seen. The resolution of this question depends on the inclination of the ecliptic and the latitude of the moon - i.e., the angle - and the direction of that angle - to which the moon is inclined from the plane of the sun.
[In this context, it is worthy to mention a question raised by several contemporary commentaries on Hilchot Kiddush HaChodesh: Seemingly, there is a direct connection between the concepts mentioned at the conclusion of Chapter 15 and those mentioned at the beginning of this chapter. Why does the Rambam interpose the discussion of the moon's latitude (the subject matter of Chapter 16, which becomes relevant only in subsequent halachot) between them?]
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| 8. |
The sighting adjustment for longitude is based on two different factors: a) whether the constellation is inclined to the north or to the south as it intersects the horizon of Jerusalem, and b) the extent of the southerly position of that constellation.
To explain: The constellations intersect the horizon at different angles, reflecting the pattern of their inclination in the heavenly sphere. The constellations from Capricorn until Gemini intersect the horizon at a northerly angle, and the constellations from Cancer to Sagittarius intersect the horizon at a southerly angle.
With regard to the second factor, all the constellations are located to the south of Jerusalem. Jerusalem is located 32 degrees north, and the constellation of Cancer, the most northerly of the constellations, is located 23 1/2 degrees north. The more northerly a constellation is located, however, the greater the need for a subtraction from its longitude.
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| 9. |
This is the constellation that the moon enters at the vernal (spring) equinox. It is inclined to the north and is not located in an extremely southerly position. Hence, a large sighting adjustment is necessary.
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| 10. |
Since the constellation of Taurus intersects the horizon at a northerly inclination and it is located in a relatively northerly position, the largest adjustment is necessary.
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| 11. |
Although this constellation is located in a very northerly position, its northerly inclination is less. Hence, a smaller subtraction is made.
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| 12. |
Here, too, our translation is an emendation of the standard published text, based on authentic manuscript editions of the Mishneh Torah and early printings.
Although Cancer is located in the most northerly position of all the constellations, since it has a southerly inclination the sighting adjustment required is less.
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| 13. |
This and the four constellations that follow have southerly inclinations. Hence, the figure subtracted from their longitude is less.
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| 14. |
This is the smallest sighting adjustment, because this constellation is located in a more southerly position than the others with a southerly inclination.
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| 15. |
From this point on, the sighting adjustment increases, because these constellations have a northerly inclination.
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| 16. |
The commentaries have noted that although the general thrust of the adjustments suggested by the Rambam conform to the calculations of the astronomers, the exact figures he gives follow neither the classic Greek figures nor those of modern astronomy. It is possible to explain that the Rambam was speaking merely in approximations, giving us a figure useful enough to calculate the position where the moon would be sighted, but not an exact scientific measure. This theory is borne out by the fact that he does not provide different measures for northern and southern latitudes, although according to science these figures vary.
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| 17. |
To explain: The true position of the moon reflects the line extending from the center of the earth through the center of the moon, as it is projected against the heavenly sphere. Since Jerusalem (or for that matter, any other location on the earth's surface) is not located at the center of the earth, but rather 4000 miles away, there will be a slight difference between the line described previously and the line extending from a person standing in Jerusalem to the center of the moon, as it is projected against the heavenly sphere. The closer the moon is to the horizon, the larger the sighting adjustment that has to be made.
[The same concept applies with regard to the sun. Nevertheless, since the distance between the earth and the sun is great, the angular difference between these two lines is not of consequence. The moon, by contrast, is located much closer to the earth and, at times, a difference of close to a degree can arise.]
In the evening, the moon will always appear slightly closer to the horizon than it actually is - i.e., it will appear closer to the position of the sun. Therefore, the angular difference between the two lines mentioned above should be subtracted from the moon's true position. As explained above, the extent of the adjustment to be made depends on the inclination at which constellation intersects the horizon and its latitude in the heavenly sphere.
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| 18. |
This principle applies during all the PM hours. During the AM hours, by contrast, the sighting adjustment should be added to the position of the moon (Ralbach).
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| 19. |
The sighting adjustment for the moon's latitude is derived by creating a parallax - i.e., a line directly parallel to the line running from the point of the moon's first longitude to its first latitude is drawn from the point of its second longitude. A second line is drawn from the position of an onlooker in Jerusalem through the point of the first latitude and intersecting the line of the moon's second latitude. The point where these two lines intersect is the moon's second longitude. The adjustment mentioned in the following halachah represents the angle between these two lines.
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| 20. |
Because Jerusalem is situated in a more northerly position than all the Zodiac constellations, the moon will always appear more southerly than it actually is. Therefore, if its latitude is northerly, a subtraction is necessary. To use geometric terms: When the moon's latitude is northerly, its second latitude will always be closer to the point of its longitude than to its first latitude.
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| 21. |
Since the moon will always appear more southerly, an addition is required when its original latitude is southerly. In geometric terms: When the moon's latitude is southerly, its second latitude will always be further removed from the point of its longitude than its first latitude.
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| 22. |
This is the point directly after the vernal (spring) equinox, when the sun is inclined northward and enters the northern part of its orbit.
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| 23. |
This is the point directly after the autumnal equinox, when the sun is inclined southward and enters the southern part of its orbit.
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| 24. |
Here, too, our translation is an emendation of the standard published text, based on authentic manuscript editions of the Mishneh Torah and early printings.
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| 25. |
The Rambam is speaking about the second latitude, since it is possible for the sighting adjustment to change a northerly latitude to a southerly one.
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| 26. |
The purpose of the calculations that follow (reaching a third longitude and a fourth longitude) is to calculate the time between the setting of the sun and the setting of the moon. The first longitude is sufficient to inform us whether or not the crescent of the moon will be large enough to be visible. The subsequent calculations are necessary to determine whether or not there will be sufficient time for actually sighting the moon. For when the crescent is small, it is difficult to detect unless there is ample time before it sets.
The third longitude reflects the point in the celestial sphere that will set at the same time as the moon does, as seen by a person standing on the equator. This is not the point in the celestial sphere where the moon appears to be located, but rather a point in the celestial sphere that is reached by drawing a line originating at the equator, running parallel to the horizon of the equator, and extending through the center of the moon. The point where this line intersects the celestial sphere is the third longitude.
The reason for associating the moon's position with the equator is to establish a connection with a standard measure of time. In Jerusalem (and for that matter, anywhere else in the northern or southern hemisphere), the apparent movement of the celestial sphere varies with the seasons. On the equator, by contrast, the movement of the celestial sphere is constant at all times, 15 minutes to the hour.
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| 27. |
Cf. Proverbs 2:15.
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| 28. |
The angle between each particular constellation in the celestial sphere and the equator varies. The size of the adjustment to be made for the third longitude depends on that angle.
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| 29. |
These are the points in the celestial sphere that intersect the horizon of the equator at the greatest angle. Therefore, the largest adjustment is necessary.
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| 30. |
These are the points within the celestial sphere that are more or less parallel to the equator.
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| 31. |
This means that when the moon's latitude is northerly, the third longitude will always be closer to the equator.
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| 32. |
This means that when the moon's latitude is southerly, the third longitude will always be further removed from the equator.
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| 33. |
These are the constellations that are inclined in a northerly direction.
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| 34. |
I.e., the constellations that are inclined in a southerly direction.
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| 35. |
This means that when the moon's latitude is northerly, the third longitude will always be further removed from the equator.
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| 36. |
This means that when the moon's latitude is southerly, the third longitude will always be closer to the equator.
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| 37. |
As happens when the moon is located in the beginning of the constellations of Cancer and Capricorn.
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| 38. |
The Rambam's intent in these sets of calculations is to reach a point on the equator that will set at the same time the third longitude sets in Jerusalem. For although the third longitude was able to relate the moon's position to the equator, it did not take into consideration the difference between the horizon of the equator and the horizon of Jerusalem. This is accomplished by drawing a line from the third longitude to the equator, which is parallel to the horizon of Jerusalem.
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| 39. |
Two factors are significant in determining the fourth longitude: a) The angle of the constellation's inclination to the horizon of the equator. The greater the inclination of the constellation, the closer the fourth longitude will be located to the equator.
b) whether the constellation is inclined to the north or to the south.
If the constellation is inclined to the north, the third longitude, and hence the place on the equator parallel to it, will be located further away from the horizon, resulting in a later setting and thus an extended fourth longitude. Conversely, if the inclination is southerly, the third longitude will be located closer to the horizon, resulting in a shortened fourth longitude.
Of these two factors, the latter is more significant, and causes a larger correction. To explain these factors with regard to the constellations of Pisces and Aries: These constellations are inclined to a great degree, a factor that would reduce the fourth longitude. Since, however, they are northerly inclined, and this is the stronger factor, a modest increase is required.
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| 40. |
These constellations are inclined to the north, and the degree of their inclination is less than that of Pisces and Aries. Hence, a greater increase is required.
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| 41. |
Here, the constellations begin a southerly inclination. Hence, although they are more parallel to the horizon of the equator, no addition is made.
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| 42. |
In this instance, the degree of inclination of these constellations is great and their inclination is southerly. Both of these factors lead to a reduction in the fourth longitude. Hence, the greatest subtraction is required.
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| 43. |
The Ralbach questions why the Rambam refers to the first latitude. Seemingly, it would be appropriate to make this correction based on the second latitude, for there is a significant difference between it and the first latitude. According to trigonometry, it also would appear that the calculations should be based on the second latitude.
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| 44. |
Although the fourth longitude established a relationship between the equator and Jerusalem, it is still dependent on the third longitude, which relates to the moon and the celestial sphere as they set on the horizon of the equator. Through the correction mentioned here, we find a place on the extension of the equator that will set at the same as the moon sets in Jerusalem. Having reached this point, we can calculate the difference in time (15 degrees to the hour) between the setting of the sun and this point (which will set at the same time as the setting of the moon). Accordingly, we will be able to determine whether or not this interval will allow for the sighting of the moon.
The correction for geographic longitude is reached by drawing a line from the position of the moon parallel to the horizon of Jerusalem. One might ask: If this was the Rambam's intent, why were so many intermediate steps - the definition of the second, third, and fourth latitudes - necessary? Why didn't he suggest drawing the above- mentioned line at the very beginning of his calculations?
The explanation is that the Rambam allowed an individual to follow his own steps in arriving at this final figure. I.e., these lines and distances are all artificial and can be determined only by calculations. Through trigonometry, if one knows the length of one side of a triangle and two angles, or the length of two sides and one angle, it is possible to calculate the size of all three angles and all three sides. To find the line extending from the moon to the equator parallel to the horizon of Jerusalem, the Rambam had to build sets of triangles, and calculate angles based on the relationship of one triangle to another. The process he followed is reflected in the series of corrections he offers.
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| 45. |
A northerly latitude means that the actual position of the moon is further removed from the horizon than the third longitude. This will result in a later setting of the moon. Accordingly, the correction based on geographic latitude will require addition to the fourth longitude. This applies regardless of whether the inclination of the constellation in which the moon is located is northerly or southerly.
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| 46. |
A southerly latitude means that the actual position of the moon is closer to the horizon than the third longitude. This will result in an earlier setting of the moon. Accordingly, the correction based on geographic latitude will require subtraction from the fourth longitude. This applies regardless of whether the inclination of the constellation in which the moon is located is northerly or southerly.
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| 47. |
Our translation represents a correction of the standard printed text of the Mishneh Torah.
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| 48. |
It is possible that the Rambam's wording alludes to a concept mentioned previously, that the calculations he suggests are applicable only at the beginning of the month, when the new moon might be sighted.
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| 49. |
I.e., barring clouds, as explained at the beginning of the following chapter.
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| 50. |
As mentioned at the beginning of this chapter, the first longitude gives us information regarding the size of the moon's crescent and the difference between the moon's setting and that of the sun. When the first longitude is sufficiently large or when it is sufficiently small, it is possible to determine whether or not the moon will be sighted without considering extenuating factors - e.g., its longitude, the inclination of the constellation in which it is located, and the extent of that inclination. When, however, the first longitude is of intermediate length, these extenuating factors must be considered. The establishment of a systematic method of considering these factors is the purpose of all the computations mentioned in this chapter.
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| 51. |
See Halachot 13 and 14.
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| 52. |
As the Rambam mentioned at the very beginning of this discussion (Chapter 11, Halachah 6), the figures that he gives are not exact. They do, however, give us sufficient information to determine when and where the moon will be sighted.
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| 53. |
Rosh HaShanah 25a, commenting on Psalms 104:19.
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| 54. |
Loc. cit.
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| 55. |
Commenting on I Chronicles 12:32, "From the descendants of Yissachar, men who had understanding of the times...," Bereshit Rabbah 72:5 explains that the sages of the tribe of Yissachar were those responsible for the determination of the calendar. (See also the commentary of the Radak on this verse.)
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| 56. |
The context of this commentary is not a proper place for a full discussion of the Rambam's perspective on the supposed conflicts between science and the Torah. It must be noted, however, that the statements made here, emphasizing the importance of the empirical evidence of science, should not be interpreted as indicating that the perspective science adopts at any given time should be accepted in place of the Torah's teachings. In this context, it is worthy to quote the Rambam's statements in Hilchot Shechitah 10:13:
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| 57. |
Our translation is based on authoritative manuscripts and early printings of the Mishneh Torah; it differs slightly from the standard printed text.
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• Shevat 28, 5775 · 02/17/2015
"Today's Day"
Torah lessons: Chumash: Mishpatim, Revi'i with Rashi.
Tehillim: 135-139.
Tanya: And the like (p. 107)...explained above. (p. 109).
One of the Baal Shem Tov's teachings:
"When you see chamor, a donkey"1 - when you carefully examine your chomer ("materiality"), your body, you will see...
..."your enemy" - meaning, that your chomer hates your Divine soul that longs for G-dliness and the spiritual, and furthermore, you will see that it is...
..."lying under its burden" placed upon it - (the body) by G-d, namely, that it should become refined through Torah and mitzvot; but the body is lazy to fulfill them. It may then occur to you that...
..."you will refrain from helping it" - to enable it to fulfill its mission, and instead you will follow the path of mortification2 of the flesh to break down the body's crass materiality. However, not in this approach will the light of Torah reside. Rather...
..."you must aid it" - purify the body, refine it, but do not break it by mortification.
FOOTNOTES
1. Sh'mot 23:5.
2. There was indeed a method of subordinating the body through afflicting it with ascetic practices, but the Baal Shem Tov rejected this path. He saw the body not as an obstacle to the spirit, something intrinsically evil and ungodly, but as a potential vehicle for the spiritual, a means for the soul to attain heights otherwise inaccessible. The "enemy" is to be transformed into an ally, an instrument. In great measure the Mitzvot employ gross physical matter to fulfill G-d's will, e.g. leather fortefillin thongs, wool for tzitzit, etc.
Daily Thought:
Teaching Despite Himself
He alone knows what he has done with life. In the privacy of his own home, he looks in the mirror and sees himself. And from head to toe, things are not good.
So he says, "I should teach others? I should provide guidance?!"
AAnd we tell him, “Yes. Because that is your place upon this planet: We live in a time when all those who know Alef must teach Alef and those who know what comes after Alef must teach that too.”
“And G‑d Above, who formed you and put you in the here and now, He knows who you are and how you are and what you are capable of accomplishing. If He believes in you, you must as well.”[13 Tamuz 5736:4.]
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