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Rambam - 3 Chapters a Day

Kiddush HaChodesh - Chapter Six, Kiddush HaChodesh - Chapter Seven, Kiddush HaChodesh - Chapter Eight

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Kiddush HaChodesh - Chapter Six

1

When [the new moon] was sanctified [based on the testimony of witnesses regarding] the sighting of the moon, the court would calculate the time of the conjunction of the sun and the moon in an exact manner, as the astronomers do.1 [This enabled them] to know whether or not the moon would be sighted.

The first level of these calculations represent approximations of the time of the conjunction, and their accuracy is not great. This approximation of the time of the conjunction is calculated according to the mean rates of movements.2 The time of the conjunction as calculated in this manner is referred to as the molad.

The essentials of the calculations that are used when a court to sanctify [the new moon based on the testimony of witnesses of] the sighting [of the moon] does not exist - i.e., the calculations we use today - are referred to as ibbur. To explain:

א

בזמן שעושין על הראייה היו מחשבין ויודעין שעה שיתקבץ בו הירח עם החמה בדקדוק הרבה כדרך שהאיצטגנינין עושין. כדי לידע אם יראה הירח או לא יראה. ותחלת אותו החשבון הוא החשבון שמחשבין אותו בקירוב ויודעין שעת קיבוצן בלא דקדוק אלא במהלכם האמצעי הוא הנקרא מולד. ועיקרי החשבון שמחשבין בזמן שאין שם בית דין שיקבעו בו על הראייה והוא חשבון שאנו מחשבין היום הוא הנקרא עיבור:

2

Day and night are constantly considered a twenty-four hour composite, [on the average:] twelve [hours] of daylight and twelve [hours] of night. An hour can be divided into 1080 units. This number was chosen because it can be divided in half, into fourths, eighths, thirds, sixths, ninths, and tenths.3 Each of these fractions contains many of these units.

ב

היום והלילה ארבע ועשרים שעות בכל זמן. שתים עשרה ביום ושתים עשרה בלילה. והשעה מחולקת לאלף ושמנים חלקים. ולמה חלקו השעה למנין זה. לפי שמנין זה יש בו חצי ורביע ושמינית ושליש ושתות ותשע וחומש ועישור. והרבה חלקים יש לכל אלו השמות:

3

According to this calculation, [the interval] between one conjunction of the moon and the sun and the subsequent conjunction according to their mean movement is twenty-nine full days, twelve hours of the thirtieth day, and 793 units of the thirteenth hour. This is the interval between one conjunction and the next, [and thus,] the length of a lunar month.

ג

משיתקבץ הירח והחמה לפי חשבון זה עד שיתקבצו פעם שנייה במהלכם האמצעי. תשעה ועשרים יום ושתים עשרה שעות מיום שלשים מתחלת לילו. ושבע מאות ושלשה ותשעים חלקים משעת שלש עשרה. וזה הוא הזמן שבין כל מולד ומולד וזה הוא חדשה של לבנה:

4

[Accordingly,] an [ordinary] lunar year, which includes twelve of these months, would include three hundred fifty-four days, eight hours, and eight hundred seventy-six units.

A leap year, which would include thirteen of these months, would include three hundred eighty-three days, twenty-one hours, and five hundred eighty-nine units.

A solar year is three hundred sixty-five days and six hours.4 Thus, a solar year exceeds an [ordinary] lunar year by ten days, twenty-one hours, and two hundred and four units.

ד

שנה של לבנה אם תהיה שנים עשר חדש מחדשים אלו יהיה כללה שלש מאות יום וארבעה וחמשים יום ושמנה שעות ושמנה מאות וששה ושבעים חלקים. ואם תהיה מעוברת ותהיה השנה שלשה עשר חדש יהיה כללה שלש מאות ושמנים ושלשה יום ואחת ועשרים שעות וחמש מאות ותשעה ושמנים חלקים. ושנת החמה היא שלש מאות חמשה וששים יום ושש שעות. נמצא תוספת שנת החמה על שנת הלבנה עשרה ימים ואחת ועשרים שעות ומאתים וארבעה חלקים:

5

When the days of a lunar month are counted in groups of seven, according to the weekly cycle, there is a remainder of one day, twelve hours, and 793 units (in numerical terms, 1 - 12 - 793). This is the remainder for a lunar month.

Similarly, when the days of a lunar year are counted in groups of seven, according to the weekly cycle, there is a remainder of four days, eight hours, and 876 units (in numerical terms, 4 - 8 - 876). This is the remainder for an ordinary lunar year. The remainder for a leap year will be five days, twenty-one hours, and 589 units (in numerical terms, 5 - 21 - 589).

ה

כשתשליך ימי חדש הלבנה שבעה שבעה שהן ימי השבוע. ישאר יום אחד ושתים עשרה שעות ושבע מאות ושלשה ותשעים חלקים. סימן להם אי"ב תשצ"ג. וזו היא שארית חדש הלבנה. וכן כשתשליך ימי שנת הלבנה שבעה שבעה. אם שנה פשוטה היא ישאר ממנה ארבעה ימים ושמנה שעות ושמנה מאות וששה ושבעים חלקים. סימן לה ד"ח תתע"ו. וזו היא שארית שנה פשוטה. ואם שנה מעוברת היא תהיה שאריתה חמשה ימים ואחת ועשרים שעות וחמש מאות ותשעה ושמנים חלקים. סימן להם הכ"א תקפ"ט:

6

When you know the time of the conjunction [of the sun and the moon] for any particular month, and add 1 - 12 - 793, you will arrive at the time of the conjunction of the following month. Thus, you will be able to determine on which day of the week and at which hour it will take place, and how many units of that hour will have passed.5

ו

כשיהיה עמך ידוע מולד חדש מן החדשים ותוסיף עליו אי"ב תשצ"ג יצא מולד שאחריו. ותדע באי זה יום מימי השבוע ובאי זו שעה ובכמה חלקים יהיה:

7

What is implied? If the conjunction [of the moon and the sun] for the month of Nisan takes place on Sunday, five hours and 107 units after sunrise (in numerical terms 1 - 56 - 107), by adding the remainder for a lunar month, 1 - 12 - 793, you will be able to determine that the conjunction for the month of Iyar will take place on Tuesday night, five hours and 900 units after nightfall (in numerical terms, 3 - 5 - 900). One may follow this same method [of calculation] month after month for eternity.

ז

כיצד הרי שהיה מולד ניסן באחד בשבת בחמש שעות ביום ומאה ושבעה חלקים סימן להם אהק"ז. כשתוסיף עליו שארית חדש הלבנה והוא אי"ב תשצ"ג. יצא מולד אייר בליל שלישי חמש שעות בלילה ותשע מאות חלקים. סימן להם ג"ה תת"ק. ועל דרך זו עד סוף העולם חדש אחר חדש:

8

Similarly, if you know the time of the conjunction for a particular year and you add its remainder - either the remainder of an ordinary year or the remainder of a leap year - to the time of the conjunction, you will determine the time of the conjunction of the following year. This method [of calculation] may be followed year after year for eternity.

The first conjunction from which we begin, the conjunction of the first year of creation, was on Monday night, 5 hours and 204 units after nightfall7 (in numerical terms, 2 - 5 - 204). This is the starting point for these calculations.

ח

וכן כשיהיה עמך ידוע מולד שנה זו ותוסיף שאריתה על ימי המולד. אם פשוטה היא שארית הפשוטה ואם מעוברת היא שארית המעוברת. יצא לך מולד שנה שלאחריה. וכן שנה אחר שנה עד סוף העולם. והמולד הראשון שממנו תתחיל הוא מולד שהיה בשנה הראשונה של יצירה.והוא היה בליל שני חמש שעות בלילה ומאתים וארבעה חלקים. סימן להם בהר"ד וממנו הוא תחלת החשבון:

9

In all the calculations to determine the time of the conjunction, when the remainder [of one period] should be added to another remainder, [the following principles should be adhered to:] When a sum of 1080 units is reached, it should be counted as an hour, and added to the number of the hours. When a sum of twenty-four hours is reached, it should be counted as a day, and added to the number of days. When the number of days is greater than seven, [all multiples of] seven should be subtracted from the sum, and the remainder be focused on.

For the purpose of our calculations is not to know the number of days, but rather to know on which day of the week, and at what hour and after how many units will the conjunction take place.

ט

בכל החשבונות האלו שתדע מהן המולד. כשתוסיף שארית עם שארית כשיתקבץ מן החלקים אלף ושמנים תשליך שעה אחת ותוסיף אותו למנין השעות. וכשיתקבץ מן השעות ארבע ועשרים תשליך יום ותוסיף ממנו למנין הימים. וכשיתקבץ מן הימים יותר על שבעה תשליך שבעה מן המנין ותניח השאר. שאין אנו מחשבין לידע מניין הימים אלא לידע באי זה יום מימי השבוע ובאי זה שעה ואי זה חלק יהיה המולד:

10

[The fixed calendar is structured in] a nineteen-year cycle, including seven leap years and twelve ordinary years. This is called a machzor.

Why was this [structure] chosen? Because when you total the number of days in twelve ordinary years and seven leap years together with their hours and their units, counting all [sums of] 1080 units as an hour, [all sums of] twenty-four hours as a day, and adding them to the number of days, the total will equal nineteen solar years, each of these years being 365 days and six hours.

The difference between the days of the solar calendar [and the lunar calendar] will be only one hour and 485 units (in numerical terms, 1 - 485).8

י

כל תשע עשרה שנה שיהיו מהן שבע שנים מעוברות ושתים עשרה פשוטות נקרא מחזור. ולמה סמכנו על מנין זה. שבזמן שאתה מקבץ מנין ימי שתים עשרה שנה פשוטות ושבע מעוברות ושעותיהן וחלקיהן ותשליך כל אלף ושמנים חלקים שעה. וכל ארבע ועשרים שעות יום. ותוסיף למנין הימים תמצא הכל תשע עשרה שנה משני החמה שכל שנה מהן שלש מאות וחמשה וששים יום ושש שעות בשוה. ולא ישאר ממנין ימי החמה בכל תשע עשרה שנה חוץ משעה אחת וארבע מאות ושמנים וחמשה חלקים. סימן להם אתפ"ה:

11

Thus, in such a [nineteen-year] cycle, the months are lunar months, and the years are solar years. The seven leap years in each cycle should be the following: The third year of the cycle, the sixth year, the eighth year, the eleventh year, the fourteenth year, the seventeenth year, the nineteenth year9 (in numbers, 3, 6, 8, 11, 14, 17, 19).

יא

נמצא במחזור שהוא כזה החדשים כולם חדשי הלבנה והשנים שני החמה. והשבע שנים המעוברות שבכל מחזור ומחזור לפי חשבון זה. הם שנה שלישית מן המחזור וששית ושמינית ושנת אחת עשרה ושנת ארבע עשרה ושנת שבע עשרה ושנת י"ט. סימן להם גו"ח י"א י"ד י"ז י"ט:

12

When you add the remainders of each of the twelve ordinary years, [the remainder of each year] being 4 - 8 - 876, and the remainders of the seven leap years, [the remainder of each year] being 5 - 21 - 589, and then divide the entire sum in groups of seven, there is a remainder of two days, sixteen hours, and 595 units (in numerical terms, 2 - 16 - 595). This is the remainder of a [nineteen-year] cycle.

יב

כשתקבץ שארית כל שנה משתים עשרה שנה הפשוטות שהיא ד"ח תתע"ו. ושארית כל שנה משבע שנים המעוברות שהיא הכ"א תקפ"ט. ותשליך הכל שבעה שבעה ישאר שני ימים ושש עשרה שעות וחמש מאות וחמשה ותשעים חלקים. סימן להם בי"ו תקצ"ה. וזה הוא שארית המחזור:

13

When you know the time of the conjunction of the beginning of a [nineteen-year] cycle, by adding 2 - 16 - 595 to it you will be able to determine the beginning of the next [nineteen-year] cycle, and similarly all the [subsequent nineteen-year] cycles for eternity. As stated above, the conjunction [marking] the beginning of the first [nineteen-year] cycle took place on 2 - 5 - 204. [The expression,] the conjunction of a year refers to the conjunction of the month of Tishrei for that year.10

יג

כשיהיה לך ידוע מולד תחלת מחזור ותוסיף עליו בי"ו תקצ"ה. יצא לך תחלת המחזור שאחריו. וכן מולד כל מחזור ומחזור עד סוף העולם. וכבר אמרנו שמולד תחלת המחזור הראשון היה לבהר"ד. ומולד השנה הוא מולד תשרי של אותה השנה:

14

Using the above method, it is possible to know the conjunction [marking] the beginning of any particular year, or any particular month, whether for the years that have passed or for the years to come.

What is implied? One should take the number of years that have passed until Tishrei of the [desired] year and group them in nineteen- year cycles. Thus, one will be able to determine the number of nineteen-year cycles that have passed and the number of years that have passed within the [nineteen-year] cycle that has not been completed [until the desired year]. One should add 2 - 16 - 595 for each cycle, 4 - 8 - 876 for every ordinary year of the cycle that has not been completed, and 5 - 21 - 589 for every leap year [of the cycle that has not been completed].

One should then add together the entire sum, calculating [the groups of 1080] units as hours, the [groups of 24] hours as days, and the groups of seven days [as weeks]. [By adding] the remainder of the days, hours, and units [to 2 - 5 - 204], one can determine the time of the conjunction of the desired year.

יד

ובדרך הזאת תדע מולד כל שנה ושנה שתרצה ומולד כל חדש וחדש שתרצה. משנים שעברו או משנים שעתידים לבא. כיצד תקח שני יצירה שעברו וגמרו ותעשה אותם מחזורין של תשע עשרה תשע עשרה שנה עד תשרי של אותה השנה. ותדע מנין המחזורין שעברו ומנין השנים שעברו ממחזור שעדיין לא נשלם. ותקח לכל מחזור ומחזור בי"ו תקצ"ה. ולכל שנה ושנה פשוטה משני המחזור שלא נשלם ד"ח תתע"ו. ולכל שנה מעוברת הכ"א תקפ"ט. ותקבץ הכל ותשליך החלקים שעות. ותשליך השעות ימים. והימים תשליכם שבעה שבעה. והנשאר מן הימים ומן השעות והחלקים הוא מולד שנה הבאה שתרצה לידע מולדה:

15

The time of the conjunction of a year determined through the above method is the conjunction of Rosh Chodesh Tishrei. By adding 1 - 12 - 793 to this figure, one can determine the conjunction of Marcheshvan, and by adding 1 - 12 - 793 to [the conjunction of] Marcheshvan, one can determine the conjunction of Kislev. Similarly, one can determine the conjunction of all subsequent months for eternity.

טו

מולד השנה שיצא בחשבון זה הוא מולד ראש חדש תשרי. וכשתוסיף עליו אי"ב תשצ"ג יצא מולד מרחשון. וכשתוסיף על מרחשון אי"ב תשצ"ג יצא מולד כסליו. וכן לכל חדש וחדש זה אחר זה עד סוף העולם

Footnotes
1.

The term conjunction refers to the point when the sun, the moon and the earth are positioned in that order in a direct line. Therefore, as seen from the earth, the moon does not reflect the light of the sun. [When the sun and the moon have the same latitude (see Chapter 16) - i.e., when they are in the same plane - a conjunction is the cause of a solar eclipse. Ordinarily, however, there is a difference in latitude, and an alignment of this nature does not cause an eclipse.]

2.

Our translation differs from the standard published text of the Mishneh Torah, and is based on the version found in authoritative manuscripts and early printings.

The term mean rate of movement refers to the average movement of the sun or the moon in angular degrees over a particular period. To explain: It was easy to calculate the number of conjunctions between one solar eclipse and another. Afterwards, this number would be multiplied by 360 (the number of degrees in a circle) and then divided by the number of years, months, days, or hours (depending on the mean one wanted to reach) that had passed between the two eclipses.

In fact, however, the sun - and to a much greater extent, the moon - would deviate from this mean rate of movement - i.e., the position in which they are located in the heavens differs from the position that would be reached by calculating the mean rate of progress. As is explained in the succeeding chapters, there are various ways of correcting and adjusting these mean calculations so that the actual position of these celestial bodies can be determined.

3.

The only integer that cannot be divided into this sum is seven. The commentaries have noted that the number 360 also can be divided into all the fractions mentioned by the Rambam and question why he did not use this smaller figure.

4.

See Chapter 9, Halachah 1, which explains that there are two views concerning whether this is an approximation or an exact figure. See also Chapter 10, Halachah 6.

5.

As mentioned above, the Rambam is speaking about an average figure. Accordingly, this figure alone is not sufficient for the calculations of when the moon can be sighted. It is useful for structuring the fixed calendar, as explained in this and the following chapter.

6.

Kinat Eliyahu suggests that the Rambam should have stated 1 - 17, since five hours after sunrise is seventeen hours after the beginning of the day.

7.

Tosafot, Rosh HaShanah 8 a,b, explains that this follows the view of Rabbi Eliezer (Rosh HaShanah 10b), who states that the world was created in Tishrei. According to this conception, the conjunction for Rosh HaShanah, the day of Adam's creation, was the fourteenth hour of Friday (the second hour after sunrise). Since the first day of creation was the twenty-fifth of Elul, the year prior to that of Adam's creation is also significant. To calculate the conjunction of that year, we subtract the remainder of an ordinary year - 4 days, 8 hours, and 876 units - from six days and fourteen hours. This produces the figure cited by the Rambam.

8.

As mentioned in Halachah 4, each ordinary lunar year is 10 days, 21 hours, and 204 units shorter than a solar year. Thus, the difference between the 12 ordinary lunar years of a nineteen-year cycle and the corresponding solar years is 130 days, 14 hours, and 288 units.

A lunar leap year is 18 days, 15 hours, and 589 units longer than a solar year. Thus, the difference between the seven leap years of a nineteen-year cycle and the corresponding solar years is 130 days, 12 hours, and 883 units. When this sum is subtracted from the figure mentioned in the previous paragraph, the remainder mentioned by the Rambam is reached.

As explained in Chapter 10, Halachah 1, there is another reckoning, which maintains that the nineteen-year cycle produces a more exact interrelation between the two calendars.

9.

By structuring the pattern in this manner, an interrelation [albeit not a totally exact one] is established between the lunar and solar calendars in each of the years. After several years in which the number of days of the solar calendar exceeds those of the lunar calendar, a leap year reverses that pattern and establishes an approximate equivalence. In this way, we ensure that the Pesach is always celebrated after the vernal equinox.

10.

This point of clarification is necessary, because there are certain halachic matters regarding which Nisan is considered the beginning of the year.

Kiddush HaChodesh - Chapter Seven

1

[Rosh Chodesh is generally instituted on the day of the conjunction. Nevertheless,] Rosh Chodesh Tishrei1 should never be established on a Sunday, a Wednesday, or a Friday - in symbols, אד"ו - although, according to these calculations, [the conjunction for the month will occur on these days]. Instead, when the conjunction for the month of Tishrei occurs on any of these three days, Rosh Chodesh should be established on the following day.2

What is implied? When the conjunction occurs on Sunday, Rosh Chodesh Tishrei should be established on Monday. When the conjunction occurs on Wednesday, Rosh Chodesh Tishrei should be established on Thursday. When the conjunction occurs on Friday, Rosh Chodesh Tishrei should be established on the Sabbath.3

א

אין קובעין לעולם ראש חדש תשרי לפי חשבון זה לא באחד בשבת ולא ברביעי בשבת ולא בערב שבת. וסימן להם אד"ו. אלא כשיהיה מולד תשרי באחד משלשה ימים האלו קובעין ראש חדש ביום שלאחריו. כיצד הרי שהיה המולד באחד בשבת קובעין ראש חדש תשרי יום שני. ואם היה המולד ברביעי קובעין ראש חדש יום חמישי. ואם היה המולד בששי קובעין ראש חדש בשביעי:

2

Similarly, if the conjunction [for the month of Tishrei]4 takes place at noon or after noon, Rosh Chodesh should be established on the following day.5

What is implied? When the conjunction takes place on Monday, six hours after daybreak or later, Rosh Chodesh is established on Tuesday. If, however, the conjunction takes place before noon, even if only a single unit prior, Rosh Chodesh is established on the day of the conjunction, provided that day is neither Sunday, Wednesday, nor Friday.

ב

וכן אם יהיה המולד בחצי היום או למעלה מחצי היום קובעין ראש חדש ביום שלאחריו. כיצד הרי שהיה המולד ביום שני בשש שעות ביום או יתר על שש שעות קובעין ראש חדש בשלישי. ואם יהיה המולד קודם חצי היום אפילו בחלק אחד קובעין ראש החדש באותו יום המולד עצמו. והוא שלא יהיה אותו היום מימי אד"ו:

3

When the conjunction takes place at noon or after noon, and [Rosh Chodesh Tishrei would be] postponed to the following day - if that following day is either Sunday, Wednesday, or Friday, Rosh Chodesh is postponed again, and is established on the third day after the conjunction.

What is implied? If the conjunction takes place on the Sabbath after noon (in numbers, 7 - 186), in such a year Rosh Chodesh should be established on Monday.7 Similarly, if the conjunction takes place on Tuesday at noon or after noon, Rosh Chodesh should be established on Thursday.

ג

כשיהיה המולד בחצי היום או אחר חצות וידחה ליום שלאחריו. אם יהיה יום שלאחריו מימי אד"ו הרי זה נדחה שלאחריו ויהיה ראש החדש קבוע בשלישי מיום המולד. כיצד הרי שיהיה המולד בשבת בחצות סימן זי"ח קובעין ראש החדש בשנה שמולדה כזה בשני בשבת. וכן אם היה המולד בשלישי בחצות או אחר חצות קובעין ראש החדש בחמישי בשבת:

4

In an ordinary year, when the conjunction [of the month] of Tishrei falls on the night of the third day,8 nine hours and 204 units (in numbers, 3 - 9 - 204) or more after nightfall, Rosh Chodesh is postponed, and instead of being established on Tuesday, it is established on Thursday.9

ד

מולד תשרי שיצא בחשבון זה בליל שלישי בתשע שעות בלילה ומאתים וארבעה חלקים משעה עשירית סימנה ג"ט ר"ד. או יותר על זה. אם היתה שנה פשוטה דוחין את ראש החדש ואין קובעים אותו בשלישי בשנה זו אלא בחמישי בשבת:

5

A similar situation [may arise] in a year that follows a leap year: If the conjunction for Tishrei takes place on Monday, three hours and 589 units or more after daybreak (in numbers, 2 - 1510 - 589), Rosh Chodesh is not established on Monday, but on Tuesday.11

ה

וכן אם יצא מולד תשרי ביום שני בשלש שעות ביום ותקפ"ט חלקים משעה רביעית. סימנה בט"ו תקפ"ט. או יתר על כן. אם היתה אותה השנה מוצאי המעוברת שהיתה השנה הסמוכה לה שעברה מעוברת. אין קובעין ראש החדש בשני בשנה זו אלא בשלישי:

6

If, however, the conjunction of an ordinary year occurs [even] one unit earlier - i.e., were it to be 3 - 9 - 203 or earlier - [Rosh Chodesh] should be established on Tuesday, [rather than postponed until Thursday as mentioned above].

Similarly, if the conjunction of a year following a leap year occurs [even] one unit earlier - i.e., were it to be 2 - 15 - 588 or earlier - [Rosh Chodesh] should be established on Monday.

Thus, the way to determine [the day on which] Rosh Chodesh Tishrei will be established according to these calculations is as follows: One should first determine the day [of the week], the hour of the day - or night - and the number of units of the hour when the conjunction takes place. The day of the conjunction will be the day of Rosh Chodesh, except in the following instances:

a) [The conjunction] takes place on Sunday, Wednesday, or Friday;

b) The conjunction takes place at noon or after noon;

c) In an ordinary year, [the conjunction] takes place on the night of the third day, after 204 units of the tenth hour have passed, or later [that day];

d) In an ordinary year that follows a leap year, the conjunction takes place on Monday past 589 units of the fourth hour after daybreak has passed or later [that day].

If the conjunction occurs in one of these four instances, [Rosh Chodesh] is not established on the day of the conjunction, but rather on the day that follows, or on the day following that, as explained.

ו

היה מולד השנה הפשוטה שאמרנו שתדחה לחמישי פחות חלק אחד. כגון שיצא סימנה ג"ט ר"ג או פחות מזה. קובעין אותה בשלישי. וכן אם היה מולד מוצאי העיבור ביום שני פחות חלק. כגון שהיה סימנה בט"ו תקפ"ח או פחות מזה. קובעין אותה בשני. נמצא דרך קביעת ראש חדש תשרי לפי חשבון זה כך הוא. תחשוב ותדע המולד באי זה יום יהיה ובכמה שעות מן היום או מן הלילה ובכמה חלקים מן השעה. ויום המולד הוא יום הקביעה לעולם. אלא אם כן היה באחד בשבת או ברביעי או בערב שבת. או אם היה המולד בחצות היום או אחר חצות. או אם היה בר"ד חלקים משעה עשירית מליל שלישי או יותר על זה והיתה שנה פשוטה. או שהיה המולד בתקפ"ט חלקים משעה רביעית מיום שני והיתה השנה פשוטה שאחר המעוברת. שאם יארע באחד מארבעה דברים האלו אין קובעין ביום המולד אלא ביום שלאחריו או שלאחר אחריו כדרך שביארנו:

7

Why is [Rosh HaShanah] not established [on the day of the conjunction] when it falls on Sunday, Wednesday, or Friday? Because these calculations determine the conjunction of the sun and the moon only according to their mean [rate of] progress, and do not [necessarily] reflect the true position [of the sun and the moon in the celestial sphere], as explained. Therefore, they instituted that [on] one day [Rosh Chodesh] would be established and on the following day it would be postponed, so that they would ascertain the day when the true conjunction takes place.12

What is implied? [When according to our calculations, the conjunction occurs on] Tuesday, we establish [Rosh Chodesh]. [When it occurs] on Wednesday, we postpone it. [When it occurs] on Thursday, we establish [Rosh Chodesh]. [When it occurs] on Friday, we postpone it. [When it occurs] on the Sabbath, we establish [Rosh Chodesh]. [When it occurs] on Sunday, we postpone it. [When it occurs] on Monday, we establish [Rosh Chodesh].

ז

ומפני מה אין קובעין בחשבון זה בימי אד"ו. לפי שהחשבון הזה הוא לקיבוץ הירח והשמש בהלוכה האמצעי לא במקום האמיתי כמו שהודענו. לפיכך עשו יום קביעה ויום דחייה כדי לפגוע ביום קיבוץ האמיתי. כיצד בשלישי קובעין ברביעי דוחין. בחמישי קובעין בששי דוחין. בשבת קובעין אחד בשבת דוחין. בשני קובעין:

8

This same principle, that the calculations are based on the mean rate of progress, is also the motivating factor for the other four reasons for the postponement [of Rosh Chodesh]. As proof of this, there are times when [according to the calculations] the conjunction takes place on Tuesday, and [Rosh Chodesh] is postponed until Thursday,13 and yet the moon will not be seen Thursday night, nor even Friday night. This indicates that the true conjunction of the sun and the moon did not take place until Thursday.

ח

ועיקר שאר הארבע דחיות אלו הוא זה העיקר שאמרנו שהחשבון הזה במהלך אמצעי. וראיה לדבר שהמולד יהיה בליל שלישי וידחה לחמישי פעמים רבות לא יראה ירח בליל חמישי ולא בליל ששי מכלל שלא נתקבצו השמש והירח קבוץ אמיתי אלא בחמישי

Footnotes
1.

Which is also Rosh HaShanah.

2.

The Rambam mentions the reason for postponing Rosh Chodesh in Halachah 7.

3.

The first day of Rosh HaShanah is therefore celebrated frequently on Monday, Thursday, and the Sabbath, for the holiday is held on these days when the conjunction falls on the day itself or on the previous day. The first day of Rosh HaShanah is rarely celebrated on Tuesday, for the probability of the conjunction falling on that day is merely one out of seven, half that of the other days.

4.

The principle mentioned in this halachah - and indeed, in the entire chapter - applies to Rosh Chodesh Tishrei alone, and not to the other months.

5.

This condition is referred to as a molad zaken, literally, "an aged conjunction." The rationale for postponing Rosh HaShanah in such a situation can be explained as follows: In principle, Rosh Chodesh is dependent on the sighting of the moon, not on the conjunction. As is explained in the subsequent chapters of the text, the new moon does not become visible until several hours after the conjunction between the moon and the sun. Thus, if the conjunction takes place after noon, it is impossible for the moon to be sighted on that day. Therefore, Rosh HaShanah is celebrated on the following day. (See Rosh HaShanah 20b and commentaries.)

There is a slight difficulty in the Rambam's statements, for based on Chapter 15, Halachah 2, it would appear that at certain times it is possible to sight the moon only five hours after conjunction.

6.

I.e., after the eighteenth hour of the seventh day.

7.

It should not be established on the Sabbath, because of the principle of molad zaken. Nor should it be established on Sunday, as stated in Halachah 1.

8.

I.e., the night between Monday and Tuesday.

9.

The rationale for the postponement of Rosh HaShanah in such a situation can be explained as follows: As explained in the following chapter, the maximum length of a lunar year is 355 days. As mentioned previously, 4 days, 8 hours, and 876 units is the remainder of a normal year. To calculate the conjunction of Tishrei in the following year, this figure should be added to 3 - 9 - 204 (the day and the time mentioned by the Rambam above). The result is 12:00 noon on the Sabbath.

As explained above, when the conjunction takes place at 12:00 noon or later, the celebration of Rosh HaShanah is postponed to the following day. In this instance, however, the following day is Sunday, and Rosh HaShanah never begins on that day. Thus, the holiday would have to be celebrated on Monday. If Rosh HaShanah had been celebrated on Tuesday of the previous year, there would have been a six-day difference between the days on which the holiday was celebrated in these two successive years, producing a year of 356 days, one day longer than the maximum length of an ordinary year. To avoid this, Rosh HaShanah is not celebrated on Tuesday. Since it also is never celebrated on Wednesday, it is postponed until Thursday, producing a lunar year of 354 days (Tur, Orach Chayim 428).

10.

For three hours after daybreak is 15 hours after the beginning of the day.

11.

The rationale for the postponement of Rosh HaShanah in such a situation can be explained as follows: As explained in the following chapter, the minimum length of a lunar leap year is 383 days. As mentioned previously, the remainder of a leap year is five days, twenty-one hours, and 589 units. When, in an effort to calculate the time of the conjunction of the leap year, this figure is subtracted from 2 - 15 - 589 (the day and the time mentioned by the Rambam), the result is Tuesday at noon.

As mentioned, when the conjunction takes place at 12:00 noon or later, the celebration of Rosh HaShanah is postponed to the following day. In this instance, however, the following day is Wednesday, and Rosh HaShanah never begins on that day. Thus, in the leap year, Rosh HaShanah began on Thursday. If Rosh HaShanah were celebrated on Monday in the year after the leap year, this would produce only a four-day difference between the days on which the holiday was celebrated in these two successive years, causing the length of the year to be only 382 days. To avoid this, in the year following the leap year Rosh HaShanah is celebrated on Tuesday, rather than on Monday, causing the leap year to be 383 days long (Tur, Orach Chayim 428).

12.

The Rambam's statements have stirred the attention - and often the indignation - of the Ra'avad and other commentaries, because they appear to ignore the explanations given by Rosh HaShanah 20a why Rosh HaShanah never begins on these days. The Talmud states that if Rosh HaShanah falls on either Wednesday or Friday, Yom Kippur will fall on either Friday or Sunday, and thus there would be two consecutive days, Yom Kippur and the Sabbath, when it would be forbidden to bury the dead. In the Talmudic era, this could have caused a corpse to deteriorate, detracting from its honor and respect.

Alternatively, the Sages state that if Rosh HaShanah fell on any of these three days, there would be two successive days when it would be forbidden to pick fresh vegetables, and the people would be unable to celebrate the festivals or the Sabbath properly.

Sukkah 43a gives another reason why Rosh HaShanah is not held on Sunday: were this to be the case, Hoshana Rabbah, the seventh day of Sukkot, would fall on the Sabbath. In such an instance, restrictions were placed on the willow ritual in the Temple. (See Hilchot Shofar, Sukkah V'Lulav 7:21-22.) To avoid such an instance, the Sages structured the calendar so that Rosh HaShanah never falls on Sunday.

In defense of the Rambam's position, it must be noted that both earlier (Rabbenu Chanan'el) and subsequent (the P'nei Yehoshua) Talmudic commentaries understood the reasons given by the Talmud as being merely the external dimension of the rationale for the calendar's adjustment, while the inner meaning is associated with the actual position of the sun and the moon in the heavenly sphere.

Even according to this perspective, there is, however, a difficulty with the Rambam's statements. Although it is correct that the true positions of the sun and the moon often differ from the position determined by calculating their mean movement, the concept of postponing the celebration of Rosh HaShanah on these three days appears arbitrary and without any obvious connection to the movement of these bodies in the celestial sphere. The commentaries note that explanations why Rosh HaShanah is not celebrated on these days are found in the Kabbalah.

13.

The instance mentioned in Halachah 4.

Kiddush HaChodesh - Chapter Eight

1

A lunar month is twenty-nine and one half days, and 793 units, as we have explained.1 It is impossible for Rosh Chodesh to begin in the middle of the day - i.e., that a portion of the day would be part of the previous month and a portion of the day would be part of the following month - as [implied by Numbers 11:20]: "For a month of days...." According to the Oral Tradition,2 this was interpreted [to mean], "You count the days of a month; you do not count the hours [of a month]."

א

חדשה של לבנה תשעה ועשרים יום ומחצה ותשצ"ג חלקים כמו שביארנו. ואי אפשר לומר שראש החדש יהיה במקצת היום עד שיהיה מקצת היום מחדש שעבר ומקצתו מהבא. שנאמר עד חדש ימים מפי השמועה למדו שימים אתה מחשב לחדש ואי אתה מחשב שעות:

2

Therefore, some lunar months are established as lacking [a day], and others as full. A month that is lacking has only twenty- nine days, even though a lunar month is several hours longer. A full month is thirty days, even though a lunar month is several hours shorter. In this manner, the months will be calculated according to complete days, not according to hours.

ב

לפיכך עושין חדשי הלבנה מהן חדש חסר ומהם חדש מלא. חדש חסר תשעה ועשרים יום בלבד ואע"פ שחדשה של לבנה יתר על זה בשעות. וחדש מלא משלשים יום ואף על פי שחדשה של לבנה פחות מזה בשעות. כדי שלא לחשב שעות בחדש אלא ימים שלמים:

3

If a lunar month were exactly twenty-nine and a half days [long], the years [would be divided evenly] into full and lacking months, and there would be exactly 354 days to a lunar year. Thus, there would be six full months and six lacking months. It is the units that exist in every month that exceed the half day - which ultimately add up to hours and days - that cause certain years to have more lacking months than full months, and other years to have more full months than lacking months.

ג

אילו היה חדשה של לבנה תשעה ועשרים יום ומחצה בלבד היו כל השנים חדש מלא וחדש חסר. ויהיו ימי שנת הלבנה שנ"ד, ששה חדשים חסרים וששה חדשים מלאים. אבל מפני החלקים שיש בכל חדש וחדש יותר על חצי היום יתקבץ מהן שעות וימים. עד שיהיו מקצת השנים חדשים חסרים יותר על המלאים ובמקצת השנים חדשים מלאים יותר על החסרים:

4

According to this reckoning, the thirtieth day of the month is always established as Rosh Chodesh. If the month is lacking, the thirtieth day will be Rosh Chodesh of the coming month.

If the month is full [the coming month will have two days that are Rosh Chodesh]. The thirtieth day will be Rosh Chodesh, since a portion of it is [fit to be] Rosh Chodesh. [Nevertheless,] it will be counted as the completion of the previous month, which was full. The thirty-first day also will be Rosh Chodesh, and the reckoning [of the days of the coming month] will start from it. It is the day established [as Rosh Chodesh].

Thus, according to this calculation, there are some months that have only one day Rosh Chodesh, and other months that have two days Rosh Chodesh.

ד

יום שלשים לעולם עושין אותו ראש חדש בחשבון זה. אם היה החדש שעבר חסר יהיה יום שלשים ראש חדש הבא. ואם יהיה החדש שעבר מלא יהיה יום שלשים ראש חדש הואיל ומקצתו ראש חדש. ויהיה תשלום החדש המלא שעבר. ויהיה יום אחד ושלשים ראש חדש הבא וממנו הוא המנין. והוא יום הקביעה. ולפיכך עושין ראשי חדשים בחשבון זה חדש אחד יום אחד בלבד וחדש אחד שני ימים:

5

The following is the order of the full and lacking months according to [our] fixed calendar: Tishrei is always full. Tevet is always lacking. From Tevet on, there is one full month and one lacking month in sequence.

What is implied? Tevet is lacking; Shevat is full; Adar is lacking; Nisan is full; Iyar, lacking; Sivan, full; Tammuz, lacking; Av, full; Elul, lacking. In a leap year, the first Adar is full,3 and the second Adar is lacking.

ה

סדר החדשים המלאים והחסרים לפי חשבון זה כך הוא. תשרי לעולם מלא. וטבת לעולם חסר. ומטבת ואילך אחד מלא ואחד חסר על הסדר. כיצד טבת חסר שבט מלא. אדר חסר ניסן מלא. אייר חסר סיון מלא. תמוז חסר אב מלא. אלול חסר. ובשנה המעוברת אדר ראשון מלא ואדר שני חסר:

6

Two months remain: Marcheshvan and Kislev. Sometimes they are [both] full; sometimes they are [both] lacking; and sometimes Marcheshvan is lacking and Kislev is full.

A year in which both of these months are full is called a year of complete months. A year in which both these months are lacking is called a year of lacking months. And a year in which Marcheshvan is lacking and Kislev is full is called a year whose months [proceed] in order.4

ו

נשארו שני החדשים שהן מרחשון וכסליו. פעמים יהיו שניהם מלאים ופעמים יהיו שניהם חסרים ופעמים יהיה מרחשון חסר וכסליו מלא. ושנה שיהיה בה שני חדשים אלו מלאים היא שנקראו חדשיה שלמים. ושנה שיהיו בה שני חדשים אלו חסרים נקראו חדשיה חסרין. ושנה שיהיה בה מרחשון חסר וכסליו מלא נקראו חדשיה כסדרן:

7

The way to know whether the months of a year will be lacking, will be complete, or will [proceed] in order [can be explained] as follows: First, determine the day on which Rosh HaShanah will fall in the year about whose months you desire to know, as explained in Chapter 7. Then determine the day on which Rosh HaShanah will fall in the year that follows.

Afterwards, count the number of days between them without including the day on which Rosh HaShanah falls in either of these years. If there are only two days between them,5 the months of the year will be lacking. If there are three days between them,6 the months of the year will proceed in order. And if there are four days between them,7 the months of the year will be complete.

ז

דרך ידיעת השנה אם חדשיה מלאים או חסרין או כסדרן לפי חשבון זה כך הוא. תדע תחלה יום שנקבע בו ראש השנה שתרצה לידע סדור חדשיה כמו שביארנו בפרק שביעי. ותדע יום שיקבע בו ראש השנה שלאחריה, ותחשב מנין הימים שביניהן חוץ מיום הקביעה של זו ושל זו. אם תמצא ביניהן שני ימים יהיו חדשי השנה חסרין. ואם תמצא ביניהם שלשה ימים יהיו כסדרן. ואם תמצא ביניהם ארבעה ימים יהיו חדשי השנה שלמים:

8

When does the above apply? When the year in question is an ordinary year. When, however, [the year in question] is a leap year [different rules apply]: If there are only four days between the day on which [Rosh HaShanah] is established [in the leap year] and the day on which it will be established in the following year, the months of the year will be lacking.8 If there are five days between these [two days], the months of the year will proceed in order. And if there are six days between them, the months of the year will be complete.

ח

במה דברים אמורים כשהיתה השנה שתרצה לידע סדור חדשיה פשוטה. אבל אם היתה מעוברת. אם תמצא בין יום קביעתה ובין יום קביעת שנה שלאחריה ארבעה ימים יהיו חדשי אותה שנה המעוברת חסרים. ואם תמצא ביניהם חמשה ימים יהיו כסדרן. ואם תמצא ביניהם ששה יהיו שלמים:

9

What is implied? If we desire to know the order of the months of the present year, and [we know the following]: Rosh HaShanah falls on Thursday; it is an ordinary year; and in the following year Rosh HaShanah falls on Monday, there are three days between them and the months of the year proceed in order.9

If Rosh HaShanah falls on Tuesday in the following year, the months of the year will be complete.10 If Rosh HaShanah falls on the Sabbath in the present year, and on Tuesday in the following year, the months of the year will be lacking.11 Similar concepts should be applied regarding the calculation [of the order of the months] of a leap year, as was explained.

ט

כיצד הרי שרצינו לידע סידור חדשי שנה זו. והיה ראש השנה בחמישי והיא פשוטה וראש השנה שלאחריה בשני בשבת. נמצא ביניהן שלשה ימים. ידענו ששנה זו חדשיה כסדרן. ואילו היה ראש השנה שלאחריה בשלישי היו חדשי השנה זו שלמים. ואילו היה ראש השנה בשנה זו בשבת ובשנה שלאחריה בשלישי בשבת היו חדשי שנה זו חסרין. ועל דרך זו תחשב לשנה המעוברת כמו שביארנו:

10

There are certain indications upon which one can rely, so that one will not err regarding the calculation of the order of the months of a year. These principles are based on the fundamental principles of the fixed calendar and the determination of the days on which Rosh HaShanah will be established and those that will cause it to be postponed, as we explained previously.

Whenever Rosh HaShanah is celebrated on a Tuesday, [the months of] the year will [proceed] in order. [This applies regardless of whether the year] is an ordinary year or a leap year.12

Whenever Rosh HaShanah is celebrated on the Sabbath or on a Monday, [the months of] the year will never [proceed] in order. [This applies regardless of whether the year] is an ordinary year or a leap year.13

[The following rules apply when] Rosh HaShanah falls on a Thursday. If the year is an ordinary year, it is impossible for its months to be lacking.14 If it is a leap year, it is impossible for its months to proceed in order.15

י

יש שם סימנין שתסמוך עליהם כדי שלא תטעה בחשבון סידור חדשי השנה והן בנויין על עיקרי זה החשבון והקביעות והדחיות שביארנו דרכם. ואלו הן. כל שנה שיהיה ראש השנה בה בשלישי תהיה לעולם כסדרן לפי חשבון זה. בין פשוטה בין מעוברת. ואם יהיה ראש השנה בשבת או בשני לא תהיה כסדרן לעולם בין בפשוטה בין במעוברת. ואם יהיה ראש השנה בחמישי. אם פשוטה היא אי אפשר שיהיו חדשיה חסרים לפי חשבון זה. ואם מעוברת היא אי אפשר שיהיו חדשיה כסדרן לפי חשבון זה

Footnotes
1.

Chapter 6, Halachah 3.

2.

Megillah 5a.

3.

This supports the Rambam's contention that it is the first Adar that is the extra month of the year. (See the notes on Chapter 4, Halachah 1.)

4.

For all the months of the year from Marcheshvan onward proceed in sequence, one full and one lacking.

5.

The Rambam gives examples in Halachah 9 to illustrate this situation and those that follow. When there are two days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and three days - i.e., 353 days - long.

6.

When there are three days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and four days - i.e., 354 days - long.

7.

When there are four days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and five days - i.e., 355 days - long. The remainder of an ordinary lunar year is slightly more than four days, producing a year whose months proceed in order. Frequently, however, the year will contain an extra day, if, because of the reasons mentioned in the previous chapter, the celebration of Rosh HaShanah is postponed. Similarly, it may lack a day, because the celebration of Rosh HaShanah was postponed in the previous year.

8.

In such a situation, there will be 54 weeks and five days in the year, a total of 383 days.

9.

For there are three days - Friday, the Sabbath, and Sunday - between the days on which Rosh HaShanah is celebrated in the years in question.

10.

For there are four days - Friday, the Sabbath, Sunday, and Monday - between the days on which Rosh HaShanah is celebrated in these successive years.

11.

For there are only two days between them.

12.

As mentioned, Rosh HaShanah cannot fall on Sunday, Wednesday, or Friday. Therefore, in an ordinary year, if Rosh HaShanah falls on a Tuesday, the following year it cannot fall on a Thursday, for then there would be only one day between them, producing a year of only 352 days. Nor can it fall on a Monday, for then the year would be 356 days long. Thus, the only day on which it can fall is the Sabbath, producing a year of 354 days. In such a year, the months proceed in order.

When Rosh HaShanah falls on Tuesday in a leap year, it cannot fall on Thursday or the Sabbath in the following year, for that would produce a year that is too short (380 or 382) days. Nor can it fall on Tuesday itself, for Rosh HaShanah falls on Tuesday only when the conjunction takes place not later than Tuesday, before noon. When the remainder of a leap year - 5 days, 21 hours, and 589 units - is added to noon time on Tuesday, the result is that the conjunction of the following year will take place on Sunday. Since Rosh HaShanah is never celebrated on Sunday, the holiday will be postponed until Monday. Thus, the length of the leap year will be 384 days, the length of a year whose months proceed in order.

13.

For the months of an ordinary year to proceed in order, the year must be 354 days long. That means that if Rosh HaShanah fell on the Sabbath, it would have to fall on Wednesday in the following year, which is impossible. Similarly, if Rosh HaShanah fell on Monday, it would have to fall on Friday in the following year, which is also impossible.

For the months of a leap year to proceed in order, the year must be 384 days long. That means that if Rosh HaShanah had fallen on the Sabbath, in the following year it would have to fall on Friday, which is impossible. Similarly, if Rosh HaShanah had fallen on Monday, in the following year it would have to fall on Sunday, which is also impossible.

14.

When the months of an ordinary year are lacking, the year has only 353 days. Thus, if Rosh HaShanah fell on Thursday, it would have to fall on Sunday in the following year, which is impossible.

15.

When the months of a leap year are lacking, the year has 383 days. Thus, if Rosh HaShanah fell on Thursday, it would have to fall on Wednesday in the following year, which is impossible.

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The Mishneh Torah was the Rambam's (Rabbi Moses ben Maimon) magnum opus, a work spanning hundreds of chapters and describing all of the laws mentioned in the Torah. To this day it is the only work that details all of Jewish observance, including those laws which are only applicable when the Holy Temple is in place. Participating in the one of the annual study cycles of these laws (3 chapters/day, 1 chapter/day, or Sefer Hamitzvot) is a way we can play a small but essential part in rebuilding the final Temple.
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