ב"ה
Rambam - 3 Chapters a Day
Kiddush HaChodesh - Chapter 6, Kiddush HaChodesh - Chapter 7, Kiddush HaChodesh - Chapter 8
Kiddush HaChodesh - Chapter 6
1When 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.אבִּזְמָן שֶׁעוֹשִׂין עַל הָרְאִיָּה, הָיוּ מְחַשְּׁבִין וְיוֹדְעִין שָׁעָה שֶׁיִּתְקַבַּץ בָּהּ הַיָּרֵחַ עִם הַחַמָּה בְּדִקְדּוּק הַרְבֵּה, כְּדֶרֶךְ שֶׁהָאִצְטַגְנִינִין עוֹשִׂין, כְּדֵי לֵידַע אִם יֵרָאֶה הַיָּרֵחַ אוֹ לֹא יֵרָאֶה.
The first level of these calculations represent approximations of the time of the conjunction, and their accuracy is not great.וּתְחִלַּת אוֹתוֹ הַחֶשְׁבּוֹן, הוּא הַחֶשְׁבּוֹן שֶׁמְּחַשְּׁבִין בְּקֵרוּב, וְיוֹדְעִין שְׁעַת קִבּוּצָם בְּלֹא דִּקְדּוּק.
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.וְשְׁעַת קִבּוּצָם בְּלֹא דִּקְדּוּק אֶלָא בְּמַהְלָכָם הָאֶמְצָעִי, הוּא הַנִּקְרָא 'מוֹלָד'.
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:וְעִיקְרֵי הַחֶשְׁבּוֹן שֶׁמְּחַשְּׁבִין בִּזְמָן שֶׁאֵין שָׁם בֵּית דִּין שֶׁיִּקְבְּעוּ עַל הָרְאִיָּה, וְהוּא חֶשְׁבּוֹן שֶׁאָנוּ מְחַשְּׁבִין הַיּוֹם - הוּא הַנִּקְרָא 'עִבּוּר'. וְאֵלּוּ הֵן:
2Day and night are constantly considered a twenty-four hour composite, on the average: twelve hours of daylight and twelve hours of night.בהַיּוֹם וְהַלַּיְלָה, אַרְבַּע וְעֶשְׂרִים שָׁעוֹת בְּכָל זְמָן, שְׁתֵּים עֶשְׂרֵה בַּיּוֹם, וּשְׁתֵּים עֶשְׂרֵה בַּלַּיְלָה.
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.וְהַשָּׁעָה, מְחֻלֶּקֶת לְאֶלֶף וּשְׁמוֹנִים חֲלָקִים. וְלָמָּה חָלְקוּ הַשָּׁעָה לְמִנְיָן זֶה - לְפִי שֶׁמִּנְיָן זֶה יֵשׁ לוֹ חֵצִי וּרְבִיעַ וּשְׁמִינִית וּשְׁלִישׁ וּשְׁתוּת וּתְשִׁיעַ וְחֹמֶשׁ וְעִשּׂוּר, וְהַרְבֵּה חֲלָקִים יֵשׁ לְכָל אֵלּוּ הַשֵּׁמוֹת.
3According 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.גמִשֶּׁיִּתְקַבֵּץ הַיָּרֵחַ וְהַחַמָּה לְפִי חֶשְׁבּוֹן זֶה, עַד שֶׁיִּתְקַבְּצוּ פַּעַם שְׁנִיָּה בְּמַהְלָכָם הָאֶמְצָעִי - תִּשְׁעָה וְעֶשְׂרִים יוֹם וּשְׁתֵּים עֶשְׂרֵה שָׁעוֹת מִיּוֹם שְׁלוֹשִׁים מִתְּחִלַּת לֵילוֹ, וּשְׁבַע מֵאוֹת שְׁלוֹשָׁה וְתִשְׁעִים חֲלָקִים מִשָּׁעַת שְׁלוֹשׁ עֶשְׂרֵה; וְזֶה הוּא הַזְּמָן שֶׁבֵּין כָּל מוֹלָד וּמוֹלָד, וְזֶה הוּא חָדְשָׁהּ שֶׁל לְּבָנָה.
4Accordingly, 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.4דשָׁנָה שֶׁל לְּבָנָה: אִם תִּהְיֶה שְׁנֵים עָשָׂר חֹדֶשׁ מֵחֳדָשִׁים אֵלּוּ - יִהְיֶה כְּלָלָהּ שְׁלוֹשׁ מֵאוֹת וְאַרְבָּעָה וַחֲמִשִּׁים יוֹם וּשְׁמוֹנֶה שָׁעוֹת וּשְׁמוֹנֶה מֵאוֹת וְשִׁשָּׁה וְשִׁבְעִים חֲלָקִים; וְאִם תִּהְיֶה מְעֻבֶּרֶת, וְתִהְיֶה הַשָּׁנָה שְׁלוֹשָׁה עָשָׂר חֹדֶשׁ - יִהְיֶה כְּלָלָהּ שְׁלוֹשׁ מֵאוֹת שְׁלוֹשָׁה וּשְׁמוֹנִים יוֹם וְאַחַת וְעֶשְׂרִים שָׁעוֹת וַחֲמֵשׁ מֵאוֹת תִּשְׁעָה וּשְׁמוֹנִים חֲלָקִים. וּשְׁנַת הַחַמָּה, הִיא שְׁלוֹשׁ מֵאוֹת חֲמִשָּׁה וְשִׁשִּׁים יוֹם וְשֵׁשׁ שָׁעוֹת.
Thus, a solar year exceeds an ordinary lunar year by ten days, twenty-one hours, and two hundred and four units.נִמְצָא תּוֹסֶפֶת שְׁנַת הַחַמָּה עַל שְׁנַת הַלְּבָנָה, עֲשָׂרָה יָמִים וְאַחַת וְעֶשְׂרִים שָׁעוֹת וּמָאתַיִם וְאַרְבָּעָה חֲלָקִים.
5When 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.הכְּשֶׁתַּשְׁלִיךְ יְמֵי חֹדֶשׁ הַלְּבָנָה שִׁבְעָה שִׁבְעָה, שֶׁהֵן יְמֵי הַשָּׁבוּעַ - יִשָּׁאֵר יוֹם אֶחָד וּשְׁתֵּים עֶשְׂרֵה שָׁעוֹת וּשְׁבַע מֵאוֹת וּשְׁלוֹשָׁה וְתִשְׁעִים חֲלָקִים, סִימָן לָהֶם א' י"ב תשצ"ג; וְזוֹ הִיא שְׁאֵרִית חֹדֶשׁ הַלְּבָנָה.
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).וְכֵן כְּשֶׁתַּשְׁלִיךְ יְמֵי שְׁנַת הַלְּבָנָה שִׁבְעָה שִׁבְעָה :אִם שָׁנָה פְּשׁוּטָה הִיא - יִשָּׁאֵר מִמֶּנָּה אַרְבָּעָה יָמִים וּשְׁמוֹנֶה שָׁעוֹת וּשְׁמוֹנֶה מֵאוֹת וְשִׁשָּׁה וְשִׁבְעִים חֲלָקִים, סִימָן לָהֶם ד' ח' תתע"ו; וְזוֹ הִיא שְׁאֵרִית שָׁנָה פְּשׁוּטָה. וְאִם שָׁנָה מְעֻבֶּרֶת הִיא - תִּהְיֶה שְׁאֵרִיתָהּ חֲמִשָּׁה יָמִים וְאַחַת וְעֶשְׂרִים שָׁעוֹת וַחֲמֵשׁ מֵאוֹת תִּשְׁעָה וּשְׁמוֹנִים חֲלָקִים, סִימָן לָהֶם ה' כ"א תקפ"ט.
6When 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.5וכְּשֶׁיִּהְיֶה עִמָּךְ יָדוּעַ מוֹלַד חֹדֶשׁ מִן הֶחֳדָשִׁים, וְתוֹסִיף עָלָיו א' י"ב תשצ"ג - יֵצֵא מוֹלַד חֹדֶשׁ שֶׁאַחֲרָיו, וְתֵדַע בְּאֵיזֶה יוֹם מִיְּמֵי הַשָּׁבוּעַ וּבְאֵי זוֹ שָׁעָה וּבְכַמָּה חֵלֶק יִהְיֶה.
7What 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 the night of the third day,7 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.זכֵּיצַד? הֲרֵי שֶׁהָיָה מוֹלַד נִיסָן בְּאֶחָד בַּשַּׁבָּת בַּחֲמֵשׁ שָׁעוֹת בַּיּוֹם וּמֵאָה וְשִׁבְעָה חֲלָקִים, סִימָן לָהֶם א' ה' ק"ז. כְּשֶׁתּוֹסִיף עָלָיו שְׁאֵרִית חֹדֶשׁ לְבָנָה, וְהוּא א' י"ב תשצ"ג - יֵצֵא מוֹלַד אִיָּר בְּלֵיל שְׁלִישִׁי חֲמֵשׁ שָׁעוֹת בַּלַּיְלָה וּתְשַׁע מֵאוֹת חֲלָקִים, סִימָן לָהֶם ג' ה' תת"ק. וְעַל דֶּרֶךְ זוֹ עַד סוֹף הָעוֹלָם, חֹדֶשׁ אַחַר חֹדֶשׁ.
8Similarly, 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.חוְכֵן כְּשֶׁיִּהְיֶה עִמָּךְ יָדוּעַ מוֹלַד שָׁנָה זוֹ, וְתוֹסִיף שְׁאֵרִיתָהּ עַל יְמֵי הַמּוֹלָד - אִם פְּשׁוּטָה הִיא, שְׁאֵרִית הַפְּשׁוּטָה, וְאִם מְעֻבֶּרֶת, שְׁאֵרִית הַמְּעֻבֶּרֶת - יֵצֵא לָךְ מוֹלַד שָׁנָה שֶׁל אַחֲרֶיהָ. וְכֵן שָׁנָה אַחַר שָׁנָה, עַד סוֹף הָעוֹלָם.
The first conjunction from which we begin, the conjunction of the first year of creation, was on the night of the second day,8 5 hours and 204 units after nightfall9 (in numerical terms, 2—5—204). This is the starting point for these calculations.וְהַמּוֹלָד הָרִאשׁוֹן שֶׁמִּמֶּנּוּ תַּתְחִיל, הוּא מוֹלָד שֶׁהָיָה בְּשָׁנָה רִאשׁוֹנָה שֶׁל יְּצִירָה, וְהוּא הָיָה בְּלֵיל שֵׁנִי חֲמֵשׁ שָׁעוֹת בַּלַּיְלָה וּמָאתַיִם וְאַרְבָּעָה חֲלָקִים, סִימָן לָהֶם ב' ה' ר"ד; וּמִמֶּנּוּ הִיא הַתְחָלַת הַחֶשְׁבּוֹן.
9In 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.טבְּכָל הַחֶשְׁבּוֹנוֹת הָאֵלּוּ שֶׁתֵּדַע מֵהֶן הַמּוֹלָד, כְּשֶׁתּוֹסִיף שְׁאֵרִית עִם שְׁאֵרִית, כְּשֶׁיִּתְקַבֵּץ מִן הַחֲלָקִים אֶלֶף וּשְׁמוֹנִים, תִּשְׁלֹם שָׁעָה אַחַת וְתוֹסִיף אוֹתָהּ לְמִנְיַן הַשָּׁעוֹת; וּכְשֶׁיִּתְקַבֵּץ מִן הַשָּׁעוֹת אַרְבַּע וְעֶשְׂרִים, תִּשְׁלֹם יוֹם וְתוֹסִיף לְמִנְיַן הַיָּמִים; וּכְשֶׁיִּתְקַבֵּץ מִן הַיָּמִים יוֹתֵר עַל שִׁבְעָה, תַּשְׁלִיךְ שִׁבְעָה מִן הַמִּנְיָן וְתַנִּיחַ הַשְּׁאָר, שֶׁאֵין אָנוּ מְחַשְּׁבִין לֵידַע מִנְיַן הַיָּמִים, אֶלָא לֵידַע בְּאֵיזֶה יוֹם מִיְּמֵי הַשָּׁבוּעַ וּבְאֵיזוֹ שָׁעָה וְאֵיזֶה חֵלֶק יִהְיֶה הַמּוֹלָד.
10The fixed calendar is structured in a nineteen-year cycle, including seven leap years and twelve ordinary years. This is called a machzor.יכָּל תְּשַׁע עֶשְׂרֵה שָׁנָה, שֶׁיִּהְיוּ מֵהֶן שֶׁבַע שָׁנִים מְעֻבָּרוֹת וּשְׁתֵּים עֶשְׂרֵה פְּשׁוּטוֹת - נִקְרָא 'מַחְזוֹר'.
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.וְלָמָּה סָמַכְנוּ עַל מִנְיָן זֶה, שֶׁבִּזְמָן שָׁאַתָּה מְקַבֵּץ מִנְיַן יְמֵי שְׁתֵּים עֶשְׂרֵה שָׁנָה פְּשׁוּטוֹת וְשֶׁבַע מְעֻבָּרוֹת וּשְׁעוֹתֵיהֶן וְחֶלְקֵיהֶן, וְתַשְׁלִים כָּל אֶלֶף וּשְׁמוֹנִים חֲלָקִים שָׁעָה, וְכָל אַרְבַּע וְעֶשְׂרִים שָׁעוֹת יוֹם, וְתוֹסִיף לְמִנְיַן הַיָּמִים - תִּמְצָא הַכֹּל תְּשַׁע עֶשְׂרֵה שָׁנָה מִשְּׁנֵי הַחַמָּה, שֶׁכָּל שָׁנָה מֵהֶן שְׁלוֹשׁ מֵאוֹת וַחֲמִשָּׁה וְשִׁשִּׁים יוֹם וְשֵׁשׁ שָׁעוֹת בְּשָׁוֶה.
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).10וְלֹא יִשָּׁאֵר מִמִּנְיַן יְמֵי הַחַמָּה בְּכָל תְּשַׁע עֶשְׂרֵה שָׁנָה זוֹ, חוּץ מִשָּׁעָה אַחַת וְאַרְבַּע מֵאוֹת וּשְׁמוֹנִים וַחֲמִשָּׁה חֲלָקִים, סִימָן לָהֶם א' תפ"ה.
11Thus, 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 year11 (in numbers, 3, 6, 8, 11, 14, 17, 19).יאנִמְצָא בְּמַחְזוֹר שֶׁהוּא כָּזֶה, הֶחֳדָשִׁים כֻּלָּם חָדְשֵׁי הַלְּבָנָה, וְהַשָּׁנִים שְׁנֵי הַחַמָּה; וְהַשֶּׁבַע הַשָּׁנִים הַמְּעֻבָּרוֹת שֶׁבְּכָל מַחְזוֹר וּמַחְזוֹר לְפִי חֶשְׁבּוֹן זֶה, הֵם שָׁנָה שְׁלִישִׁית מִן הַמַּחְזוֹר וְשִׁשִּׁית וּשְׁמִינִית וּשְׁנַת אַחַת עֶשְׂרֵה וּשְׁנַת אַרְבַּע עֶשְׂרֵה וּשְׁנַת שְׁבַע עֶשְׂרֵה וּשְׁנַת תְּשַׁע עֶשְׂרֵה.
12When 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.יבכְּשֶׁתְּקַבֵּץ שְׁאֵרִית כָּל שָׁנָה מִשְּׁתֵּים עֶשְׂרֵה שָׁנָה הַפְּשׁוּטוֹת, שֶׁהִיא ד' ח' תתע"ו, וּשְׁאֵרִית כָּל שָׁנָה מִשֶּׁבַע שָׁנִים הַמְּעֻבָּרוֹת, שֶׁהִיא ה' כ"א תקפ"ט, וְתַשְׁלִיךְ הַכֹּל שִׁבְעָה שִׁבְעָה - יִשָּׁאֵר שְׁנֵי יָמִים וְשֵׁשׁ עֶשְׂרֵה שָׁעוֹת וַחֲמֵשׁ מֵאוֹת וַחֲמִשָּׁה וְתִשְׁעִים חֲלָקִים, סִימָן לָהֶם ב' י"ו תקצ"ה. וְזֶה הוּא שְׁאֵרִית הַמַּחְזוֹר.
13When 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.יגכְּשֶׁיִּהְיֶה לָךְ יָדוּעַ מוֹלַד תְּחִלַּת מַחְזוֹר, וְתוֹסִיף עָלָיו ב' י"ו תקצ"ה, יֵצֵא לָךְ מוֹלַד תְּחִלַּת הַמַּחְזוֹר שֶׁאַחֲרָיו. וְכֵן מוֹלַד כָּל מַחְזוֹר וּמַחְזוֹר, עַד סוֹף הָעוֹלָם.
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.12וּכְבָר אָמַרְנוּ שֶׁמּוֹלַד תְּחִלַּת הַמַּחְזוֹר הָרִאשׁוֹן הָיָה ב' ה' ר"ד. וּמוֹלַד הַשָּׁנָה, הוּא מוֹלַד תִּשְׁרֵי שֶׁל אוֹתָהּ הַשָּׁנָה.
14Using 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.ידוּבַדֶּרֶךְ הַזֹּאת תֵּדַע מוֹלַד כָּל שָׁנָה שֶׁתִּרְצֶה, וּמוֹלַד כָּל חֹדֶשׁ שֶׁתִּרְצֶה, מִשָּׁנִים שֶׁעָבְרוּ, אוֹ מִשָּׁנִים שֶׁעֲתִידִים לָבוֹא.
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.כֵּיצַד? תִּקַּח שְׁנֵי יְצִירָה שֶׁעָבְרוּ וְגָמְרוּ, וְתַעֲשֶׂה אוֹתָם מַחְזוֹרִין שֶׁל תְּשַׁע עֶשְׂרֵה תְּשַׁע עֶשְׂרֵה, וְתֵדַע מִנְיַן הַמַּחְזוֹרִין שֶׁעָבְרוּ, וּמִנְיַן הַשָּׁנִים שֶׁעָבְרוּ מִמַּחְזוֹר שֶׁעֲדַיִן לֹא נִשְׁלַם; וְתִקַּח לְכָל מַחְזוֹר וּמַחְזוֹר ב' י"ו תקצ"ה, וּלְכָל שָׁנָה פְּשׁוּטָה מִשְּׁנֵי הַמַּחְזוֹר שֶׁלֹּא נִשְׁלַם ד' ח' תתע"ו, וּלְכָל שָׁנָה מְעֻבֶּרֶת ה' כ"א תקפ"ט; וּתְקַבֵּץ הַכֹּל, וְתַשְׁלִים הַחֲלָקִים שָׁעוֹת, וְתַשְׁלִים הַשָּׁעוֹת יָמִים, וְהַיָּמִים תַּשְׁלִיכֵם שִׁבְעָה שִׁבְעָה; וְהַנִּשְׁאָר מִן הַיָּמִים וּמִן הַשָּׁעוֹת וְהַחֲלָקִים, הוּא מוֹלַד שָׁנָה הַבָּאָה שֶׁתִּרְצֶה לֵידַע מוֹלָדָהּ.
15The 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.טומוֹלַד הַשָּׁנָה שֶׁיֵּצֵא בְּחֶשְׁבּוֹן זֶה, הוּא מוֹלַד רֹאשׁ חֹדֶשׁ תִּשְׁרֵי. וּכְשֶׁתּוֹסִיף עָלָיו א' י"ב תשצ"ג, יֵצֵא מוֹלַד מַר-חֶשְׁוָן ; וּכְשֶׁתּוֹסִיף עַל מוֹלַד מַר-חֶשְׁוָן א' י"ב תשצ"ג, יֵצֵא מוֹלַד כִּסְלֵו; וְכֵן לְכָל חֹדֶשׁ וְחֹדֶשׁ זֶה אַחַר זֶה, עַד סוֹף הָעוֹלָם.
Kiddush HaChodesh - Chapter 7
1Rosh 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.אאֵין קוֹבְעִין לְעוֹלָם רֹאשׁ חֹדֶשׁ תִּשְׁרֵי לְפִי חֶשְׁבּוֹן זֶה, לֹא בְּאֶחָד בַּשַּׁבָּת, וְלֹא בִּרְבִיעִי בַּשַּׁבָּת, וְלֹא בְּעֶרֶב שַׁבָּת - סִימָן לָהֶם אד"ו.
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.2אֶלָא כְּשֶׁיִּהְיֶה מוֹלַד תִּשְׁרֵי בְּאֶחָד מִשְּׁלוֹשָׁה יָמִים הָאֵלּוּ, קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בַּיּוֹם שֶׁלְּאַחֲרָיו.
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.3כֵּיצַד? הֲרֵי שֶׁהָיָה הַמּוֹלָד בְּאֶחָד בַּשַּׁבָּת, קוֹבְעִין רֹאשׁ חֹדֶשׁ תִּשְׁרֵי יוֹם שֵׁנִי; וְאִם יִהְיֶה הַמּוֹלָד בִּרְבִיעִי, קוֹבְעִין רֹאשׁ חֹדֶשׁ בַּחֲמִישִׁי; וְאִם יִהְיֶה הַמּוֹלָד בְּשִׁשִּׁי, קוֹבְעִין רֹאשׁ חֹדֶשׁ בִּשְׁבִיעִי.
2Similarly, if the conjunction for the month of Tishrei4 takes place at noon or after noon, Rosh Chodesh should be established on the following day.5בוְכֵן אִם יִהְיֶה הַמּוֹלָד בַּחֲצִי הַיּוֹם אוֹ לְמַעֲלָה מֵחֲצִי הַיּוֹם, קוֹבְעִין רֹאשׁ חֹדֶשׁ בַּיּוֹם שֶׁלְּאַחֲרָיו.
What is implied? When the conjunction takes place on Monday, six hours after daybreak or later, Rosh Chodesh is established on Tuesday.כֵּיצַד? הֲרֵי שֶׁהָיָה הַמּוֹלָד בַּיּוֹם הַשֵּׁנִי שֵׁשׁ שָׁעוֹת בַּיּוֹם אוֹ יָתֵר עַל שֵׁשׁ שָׁעוֹת, קוֹבְעִין רֹאשׁ חֹדֶשׁ בַּשְּׁלִישִׁי.
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.וְאִם יִהְיֶה הַמּוֹלָד קֹדֶם חֲצִי הַיּוֹם, אֲפִלּוּ בְּחֵלֶק אֶחָד - קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בְּאוֹתוֹ יוֹם הַמּוֹלָד עַצְמוֹ: וְהוּא, שֶׁלֹּא יִהְיֶה אוֹתוֹ הַיּוֹם מִיְּמֵי אד"ו.
3When 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.גכְּשֶׁיִּהְיֶה הַמּוֹלָד בַּחֲצוֹת הַיּוֹם אוֹ אַחַר חֲצוֹת, וְיִדָּחֶה לְיוֹם שֶׁלְּאַחֲרָיו - אִם יִהְיֶה הַיּוֹם שֶׁלְּאַחֲרָיו מִיְּמֵי אד"ו, הֲרֵי זֶה נִדְחֶה לְשֶׁלְּאַחַר אַחֲרָיו, וְיִהְיֶה רֹאשׁ הַחֹדֶשׁ קָבוּעַ בַּשְּׁלִישִׁי מִיּוֹם הַמּוֹלָד.
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.כֵּיצַד? הֲרֵי שֶׁהָיָה הַמּוֹלָד בַּשַּׁבָּת בַּחֲצוֹת הַיּוֹם, סִימָן ז' י"ח - קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בַּשָּׁנָה שֶׁמּוֹלָדָהּ כְּזֶה, בְּשֵׁנִי בַּשַּׁבָּת; וְכֵן אִם הָיָה הַמּוֹלָד בַּשְּׁלִישִׁי בַּחֲצוֹת אוֹ אַחַר חֲצוֹת, קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בַּחֲמִישִׁי בַּשַּׁבָּת.
4In 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.9דמוֹלַד תִּשְׁרֵי שֶׁיָּצָא בְּחֶשְׁבּוֹן זֶה בְּלֵיל שְׁלִישִׁי בְּתֵשַׁע שָׁעוֹת בַּלַּיְלָה וּמָאתַיִם וְאַרְבָּעָה חֲלָקִים מִשָּׁעָה עֲשִׂירִית, סִימְנָהּ ג' ט' ר"ד, אוֹ יוֹתֵר עַל זֶה - אִם הָיְתָה שָׁנָה פְּשׁוּטָה, דּוֹחִין אֶת רֹאשׁ הַחֹדֶשׁ, וְאֵין קוֹבְעִים אוֹתוֹ בַּשְּׁלִישִׁי בְּשָׁנָה זוֹ, אֶלָא בַּחֲמִישִׁי בַּשַּׁבָּת.
5A 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.11הוְכֵן אִם יָצָא מוֹלָד תִּשְׁרֵי בְּיוֹם שֵׁנִי בְּשָׁלוֹשׁ שָׁעוֹת בַּיּוֹם וַחֲמֵשׁ מֵאוֹת וּשְׁמוֹנִים וְתִשְׁעָה חֲלָקִים מִשָּׁעָה רְבִיעִית, סִימָנָהּ ב' ט"ו תקפ"ט, אוֹ יָתֵר עַל כֵּן - אִם הָיְתָה אוֹתָהּ הַשָּׁנָה מוֹצָאֵי הַמְּעֻבֶּרֶת, שֶׁתִּהְיֶה הַשָּׁנָה הַסְּמוּכָה לָהּ שֶׁעָבְרָה מְעֻבֶּרֶת, אֵין קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בַּשֵּׁנִי בְּשָׁנָה זוֹ, אֶלָא בַּשְּׁלִישִׁי.
6If, 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.והָיָה מוֹלַד הַשָּׁנָה הַפְּשׁוּטָה שֶׁאָמַרְנוּ שֶׁתִּדָּחֶה לַחֲמִישִׁי פָּחוֹת חֵלֶק אֶחָד, כְּגוֹן שֶׁיָּצָא סִימָנָהּ ג' ט' ר"ג אוֹ פָּחוֹת מִזֶּה - קוֹבְעִין אוֹתָהּ בַּשְּׁלִישִׁי.
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.וְכֵן אִם הָיָה מוֹלַד מוֹצָאֵי הָעִבּוּר פָּחוֹת חֵלֶק, כְּגוֹן שֶׁהָיָה סִימָנָהּ ב' ט"ו תקפ"ח אוֹ פָּחוֹת מִזֶּה - קוֹבְעִין אוֹתָהּ בַּשֵּׁנִי.
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.נִמְצָא דֶּרֶךְ קְבִיעַת רֹאשׁ חֹדֶשׁ תִּשְׁרֵי לְפִי חֶשְׁבּוֹן זֶה, כָּךְ הוּא: תְּחַשַּׁב וְתֵדַע הַמּוֹלָד בְּאֵיזֶה יוֹם יִהְיֶה, וּבְכַמָּה שָׁעוֹת מִן הַיּוֹם אוֹ מִן הַלַּיְלָה, וּבְכַמָּה חֲלָקִים מִן הַשָּׁעָה.
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.וְיוֹם הַמּוֹלָד הוּא יוֹם הַקְּבִיעָה לְעוֹלָם, אֶלָא אִם כֵּן הָיָה בְּאֶחָד בַּשַּׁבָּת אוֹ בִּרְבִיעִי אוֹ בְּעֶרֶב שַׁבָּת, אוֹ אִם הָיָה הַמּוֹלָד בַּחֲצוֹת הַיּוֹם אוֹ אַחַר חֲצוֹת, אוֹ אִם הָיָה בר"ד חֲלָקִים מִשָּׁעָה עֲשִׂירִית מִלֵּיל שְׁלִישִׁי אוֹ יוֹתֵר עַל זֶה וְהָיְתָה שָׁנָה פְּשׁוּטָה, אוֹ שֶׁהָיָה הַמּוֹלָד בתקפ"ט חֲלָקִים מִשָּׁעָה רְבִיעִית מִיּוֹם שֵׁנִי וְהָיְתָה הַשָּׁנָה פְּשׁוּטָה שֶׁאַחַר הַמְּעֻבֶּרֶת - שֶׁאִם יֵארַע אֶחָד מֵאַרְבָּעָה דְּבָרִים הָאֵלּוּ, אֵין קוֹבְעִין בְּיוֹם הַמּוֹלָד, אֶלָא בַּיּוֹם שֶׁלְּאַחֲרָיו אוֹ שֶׁלְּאַחַר אַחֲרָיו, כְּדֶרֶךְ שֶׁבֵּאַרְנוּ.
7Why 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.12זוּמִפְּנֵי מַה אֵין קוֹבְעִין בְּחֶשְׁבּוֹן זֶה בִּימֵי אד"ו - לְפִי שֶׁהַחֶשְׁבּוֹן הַזֶּה הוּא לְקִבּוּץ הַיָּרֵחַ וְהַשֶּׁמֶשׁ בְּהִלּוּכָם הָאֶמְצָעִי, לֹא בִּמְקוֹמָם הָאֲמִתִּי, כְּמוֹ שֶׁהוֹדַעְנוּ; לְפִיכָךְ עָשׂוּ יוֹם קְבִיעָה וְיוֹם דְּחִיָּה, כְּדֵי לִפְגֹעַ בְּיוֹם הַקִּבּוּץ הָאֲמִתִּי.
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.כֵּיצַד? בַּשְּׁלִישִׁי קוֹבְעִין, בָּרְבִיעִי דּוֹחִין, בַּחֲמִישִׁי קוֹבְעִין, בַּשִּׁשִּׁי דּוֹחִין, בַּשַּׁבָּת קוֹבְעִין, בְּאֶחָד בַּשַּׁבָּת דּוֹחִין, בַּשֵּׁנִי קוֹבְעִין.
8This 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.חוְעִיקַר שְׁאָר הָאַרְבַּע דְּחִיּוֹת הָאֵלּוּ, הוּא זֶה הָעִיקָר שֶׁאָמַרְנוּ, שֶׁהַחֶשְׁבּוֹן הַזֶּה בְּמַהְלָךְ אֶמְצָעִי.
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.וּרְאָיָה לַדָּבָר, שֶׁהֲרֵי הַמּוֹלָד יִהְיֶה בְּלֵיל שְׁלִישִׁי וְיִדָּחֶה לַחֲמִישִׁי, וּפְעָמִים רַבּוֹת לֹא יֵרָאֶה יָרֵחַ בְּלֵיל חֲמִישִׁי. וְלֹא עוֹד, אֶלָא וְלֹא בְּלֵיל שִׁשִּׁי, מִכְּלָל שֶׁלֹּא נִתְקַבְּצוּ הַשֶּׁמֶשׁ וְהַיָּרֵחַ קִבּוּץ אֲמִתִּי אֶלָא בַּחֲמִישִׁי.
Kiddush HaChodesh - Chapter 8
1A lunar month is twenty-nine and one half days, and 793 units, as we have explained.1אחָדְשָׁהּ שֶׁל לְּבָנָה, תִּשְׁעָה וְעֶשְׂרִים יוֹם וּמֶחְצָה וַחֲלָקִים כְּמוֹ שֶׁבֵּאַרְנוּ.
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.”וְאִי אֶפְשָׁר לוֹמַר שֶׁרֹאשׁ הַחֹדֶשׁ יִהְיֶה בְּמִקְצַת הַיּוֹם, עַד שֶׁיִּהְיֶה מִקְצַת הַיּוֹם מֵחֹדֶשׁ שֶׁעָבַר וּמִקְצָתוֹ מֵהַבָּא, שֶׁנֶּאֱמַר "עַד חֹדֶשׁ יָמִים" (במדבר יא,כ) - מִפִּי הַשְּׁמוּעָה לָמְדוּ שֶׁיָּמִים אַתָּה מְחַשֵּׁב לְחֹדֶשׁ, וְאֵין אַתָּה מְחַשֵּׁב שָׁעוֹת.
2Therefore, 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.בלְפִיכָךְ עוֹשִׂין חָדְשֵׁי הַלְּבָנָה, מֵהֶם חֹדֶשׁ חָסֵר תִּשְׁעָה וְעֶשְׂרִים יוֹם בִּלְבָד, וְאַף עַל פִּי שֶׁחָדְשָׁהּ שֶׁל לְּבָנָה יָתֵר עַל זֶה בְּשָׁעוֹת, וְחֹדֶשׁ מָלֵא מִשְּׁלוֹשִׁים יוֹם, וְאַף עַל פִּי שֶׁחָדְשָׁהּ שֶׁל לְּבָנָה פָּחוֹת מִזֶּה בְּשָׁעוֹת - כְּדֵי שֶׁלֹּא לְחַשֵּׁב בְּחֹדֶשׁ שָׁעוֹת, אֶלָא יָמִים שְׁלֵמִים.
3If 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.גאִלּוּ הָיָה חָדְשָׁהּ שֶׁל לְּבָנָה תִּשְׁעָה וְעֶשְׂרִים וּמֶחְצָה בִּלְבָד, הָיוּ כָּל הַשָּׁנִים חֹדֶשׁ מָלֵא וְחֹדֶשׁ חָסֵר, וְהָיוּ יְמֵי שְׁנַת הַלְּבָנָה שְׁלוֹשׁ מֵאוֹת אַרְבָּעָה וַחֲמִשִּׁים יוֹם, שִׁשָּׁה חֳדָשִׁים חֲסֵרִים וְשִׁשָּׁה מְלֵאִים.
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.אֲבָל מִפְּנֵי הַחֲלָקִים שֶׁיֵּשׁ בְּכָל חֹדֶשׁ וְחֹדֶשׁ יוֹתֵר עַל חֲצִי הַיּוֹם, יִתְקַבֵּץ מֵהֶן שָׁעוֹת וְיָמִים, עַד שֶׁיִּהְיוּ מִקְצַת הַשָּׁנִים חֳדָשִׁים חֲסֵרִים יוֹתֵר עַל הַמְּלֵאִים, וּבְמִקְצַת הַשָּׁנִים חֳדָשִׁים מְלֵאִים יוֹתֵר עַל הַחֲסֵרִים.
4According 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.דיוֹם שְׁלוֹשִׁים, לְעוֹלָם עוֹשִׂין אוֹתוֹ רֹאשׁ חֹדֶשׁ בְּחֶשְׁבּוֹן זֶה: אִם הָיָה הַחֹדֶשׁ שֶׁעָבַר חָסֵר - יִהְיֶה יוֹם שְׁלוֹשִׁים רֹאשׁ הַחֹדֶשׁ הַבָּא; וְאִם הָיָה הַחֹדֶשׁ שֶׁעָבַר מָלֵא - יִהְיֶה יוֹם שְׁלוֹשִׁים רֹאשׁ חֹדֶשׁ, הוֹאִיל וּמִקְצָתוֹ רֹאשׁ חֹדֶשׁ, וְיִהְיֶה תַּשְׁלוּם הַחֹדֶשׁ הַמָּלֵא שֶׁעָבַר, וְיִהְיֶה יוֹם אֶחָד וּשְׁלוֹשִׁים רֹאשׁ הַחֹדֶשׁ הַבָּא, וּמִמֶּנּוּ הוּא הַמִּנְיָן, וְהוּא יוֹם הַקְּבִיעָה.
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.וּלְפִיכָךְ עוֹשִׂין רָאשֵׁי חֳדָשִׁים בְּחֶשְׁבּוֹן זֶה, חֹדֶשׁ אֶחָד יוֹם אֶחָד בִּלְבָד, וְחֹדֶשׁ אֶחָד שְׁנֵי יָמִים.
5The 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.הסֵדֶר הֶחֳדָשִׁים הַמְּלֵאִים וְהַחֲסֵרִים לְפִי חֶשְׁבּוֹן זֶה, כָּךְ הוּא: תִּשְׁרֵי, לְעוֹלָם מָלֵא; וְחֹדֶשׁ טֵבֵת, לְעוֹלָם חָסֵר; וּמִטֵּבֵת וְאִלַּךְ, אֶחָד מָלֵא וְאֶחָד חָסֵר עַל הַסֵּדֶר.
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.כֵּיצַד? טֵבֵת חָסֵר, שְׁבָט מָלֵא, אֲדָר חָסֵר, נִיסָן מָלֵא, אִיָּר חָסֵר, סִיוָן מָלֵא, תַּמּוּז חָסֵר, אָב מָלֵא, אֱלוּל חָסֵר. וּבַשָּׁנָה הַמְּעֻבֶּרֶת, אֲדָר רִאשׁוֹן מָלֵא, וַאֲדָר שֵׁנִי חָסֵר.
6Two months remain: Marcheshvan and Kislev. Sometimes they are both full; sometimes they are both lacking; and sometimes Marcheshvan is lacking and Kislev is full.ונִשְׁאֲרוּ שְׁנֵי הֶחֳדָשִׁים, שֶׁהֵן מַר-חֶשְׁוָן וְכִסְלֵו - פְּעָמִים יִהְיוּ שְׁנֵיהֶם מְלֵאִים, וּפְעָמִים יִהְיוּ שְׁנֵיהֶם חֲסֵרִים, וּפְעָמִים יִהְיֶה מַר-חֶשְׁוָן חָסֵר וְכִסְלֵו מָלֵא.
A year in which both of these months are full is called a year of complete months.וְשָׁנָה שֶׁיִּהְיוּ בָּהּ שְׁנֵי חֳדָשִׁים אֵלּוּ מְלֵאִים, הִיא שֶׁנִּקְרְאוּ חֳדָשֶׁיהָ שְׁלֵמִים.
A year in which both these months are lacking is called a year of lacking months.וְשָׁנָה שֶׁיִּהְיוּ בָּהּ שְׁנֵי חֳדָשִׁים אֵלּוּ חֲסֵרִים, נִקְרְאוּ חֳדָשֶׁיהָ חֲסֵרִין.
And a year in which Marcheshvan is lacking and Kislev is full is called a year whose months proceed in order.4וְשָׁנָה שֶׁיִּהְיֶה בָּהּ מַר-חֶשְׁוָן חָסֵר וְכִסְלֵו מָלֵא, נִקְרְאוּ חֳדָשֶׁיהָ כְּסִדְרָן.
7The 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.זדֶּרֶךְ יְדִיעַת הַשָּׁנָה אִם חֳדָשֶׁיהָ שְׁלֵמִים אוֹ חֲסֵרִין אוֹ כְּסִדְרָן, לְפִי חֶשְׁבּוֹן זֶה - כָּךְ הוּא: תֵּדַע תְּחִלָּה יוֹם שֶׁנִּקְבַּע בּוֹ רֹאשׁ הַשָּׁנָה שֶׁתִּרְצֶה לֵידַע סִדּוּר חֳדָשֶׁיהָ, כְּמוֹ שֶׁבֵּאַרְנוּ בְּפֵרֶק שְׁבִיעִי; וְתֵדַע יוֹם שֶׁיִּקָּבַע בּוֹ רֹאשׁ הַשָּׁנָה שֶׁלְּאַחֲרֶיהָ, וְתַחְשֹׁב מִנְיַן הַיָּמִים שֶׁבֵּינֵיהֶן חוּץ מִיּוֹם הַקְּבִיעָה שֶׁל זוֹ וְשֶׁל זוֹ.
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.אִם תִּמְצָא בֵּינֵיהֶן שְׁנֵי יָמִים, יִהְיוּ חָדְשֵׁי הַשָּׁנָה חֲסֵרִין; וְאִם תִּמְצָא בֵּינֵיהֶם שְׁלוֹשָׁה יָמִים, יִהְיוּ כְּסִדְרָן; וְאִם תִּמְצָא בֵּינֵיהֶם אַרְבָּעָה, יִהְיוּ שְׁלֵמִים.
8When does the above apply? When the year in question is an ordinary year.חבַּמֶּה דְּבָרִים אֲמוּרִים? בְּשֶׁהָיְתָה הַשָּׁנָה שֶׁתִּרְצֶה לֵידַע סִדּוּר חֳדָשֶׁיהָ פְּשׁוּטָה.
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.8אֲבָל אִם הָיְתָה מְעֻבֶּרֶת: אִם תִּמְצָא בֵּין יוֹם קְבִיעָתָהּ וּבֵין יוֹם קְבִיעַת שָׁנָה שֶׁלְּאַחֲרֶיהָ אַרְבָּעָה יָמִים, יִהְיוּ חָדְשֵׁי אוֹתָהּ הַשָּׁנָה הַמְּעֻבֶּרֶת חֲסֵרִים;
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.וְאִם תִּמְצָא בֵּינֵיהֶם חֲמִשָּׁה יָמִים, יִהְיוּ כְּסִדְרָן; וְאִם תִּמְצָא בֵּינֵיהֶם שִׁשָּׁה, יִהְיוּ שְׁלֵמִים.
9What 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.9טכֵּיצַד? הֲרֵי שֶׁרָצִינוּ לֵידַע סִדּוּר חָדְשֵׁי שָׁנָה זוֹ, וְהָיָה רֹאשׁ הַשָּׁנָה בַּחֲמִישִׁי וְהִיא פְּשׁוּטָה, וְרֹאשׁ הַשָּׁנָה שֶׁלְּאַחֲרֶיהָ בְּשֵׁנִי בַּשַּׁבָּת; נִמְצָא בֵּינֵיהֶן שְׁלוֹשָׁה יָמִים, יָדַעְנוּ שֶׁשָּׁנָה זוֹ חֳדָשֶׁיהָ כְּסִדְרָן.
If Rosh HaShanah falls on Tuesday in the following year, the months of the year will be complete.10וְאִלּוּ הָיָה רֹאשׁ הַשָּׁנָה שֶׁלְּאַחֲרֶיהָ בַּשְּׁלִישִׁי, הָיוּ חָדְשֵׁי שָׁנָה זוֹ שְׁלֵמִים.
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.11וְאִלּוּ הָיָה רֹאשׁ הַשָּׁנָה בְּשָׁנָה זוֹ בַּשַּׁבָּת, וּבַשָּׁנָה שֶׁלְּאַחֲרֶיהָ בַּשְּׁלִישִׁי בַּשַּׁבָּת, הָיוּ חָדְשֵׁי שָׁנָה זוֹ חֲסֵרִין.
Similar concepts should be applied regarding the calculation of the order of the months of a leap year, as was explained.וְעַל דֶּרֶךְ זוֹ תַּחְשֹׁב לַשָּׁנָה הַמְּעֻבֶּרֶת, כְּמוֹ שֶׁבֵּאַרְנוּ.
10There 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.ייֵשׁ שָׁם סִימָנִין שֶׁתִּסְמֹךְ עֲלֵיהֶם כְּדֵי שֶׁלֹּא תִטְעֶה בְּחֶשְׁבּוֹן סִדּוּר חָדְשֵׁי הַשָּׁנָה, וְהֵן בְּנוּיִין עַל עִיקְרֵי זֶה הַחֶשְׁבּוֹן וְהַקְּבִיעוֹת וְהַדְּחִיּוֹת שֶׁבֵּאַרְנוּ דַּרְכָּם, וְאֵלּוּ הֵן:
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.12כָּל שָׁנָה שֶׁיִּהְיֶה רֹאשׁ הַשָּׁנָה בָּהּ בַּשְּׁלִישִׁי, תִּהְיֶה לְעוֹלָם כְּסִדְרָן לְפִי חֶשְׁבּוֹן זֶה, בֵּין פְּשׁוּטָה, בֵּין מְעֻבֶּרֶת.
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.13וְאִם יִהְיֶה רֹאשׁ הַשָּׁנָה בַּשַּׁבָּת אוֹ בַּשְּׁנִי, לֹא תִהְיֶה כְּסִדְרָן לְעוֹלָם, בֵּין בִּפְשׁוּטָה, בֵּין בִּמְעֻבֶּרֶת.
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.15וְאִם יִהְיֶה רֹאשׁ הַשָּׁנָה בַּחֲמִישִׁי: אִם פְּשׁוּטָה הִיא, אִי אֶפְשָׁר שֶׁיִּהְיוּ חֳדָשֶׁיהָ חֲסֵרִים לְפִי חֶשְׁבּוֹן זֶה, וְאִם מְעֻבֶּרֶת הִיא, אִי אֶפְשָׁר שֶׁיִּהְיוּ חֳדָשֶׁיהָ כְּסִדְרָן לְפִי חֶשְׁבּוֹן זֶה.
Test Yourself on Kiddush HaChodesh Chapter 6
Test Yourself on Kiddush HaChodesh Chapter 7
Test Yourself on Kiddush HaChodesh Chapter 8
Footnotes for Kiddush HaChodesh - Chapter 6
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.
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.
I.e., the night between Monday and Tuesday.
8.
I.e., the night between Sunday and Monday.
9.
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.
10.
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.
11.
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.
12.
This point of clarification is necessary, because there are certain halachic matters regarding which Nisan is considered the beginning of the year.
Footnotes for Kiddush HaChodesh - Chapter 7
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.
Footnotes for Kiddush HaChodesh - Chapter 8
1.
Chapter 6, Halachah 3
3.
This supports the Rambam’s contention that it is the first Adar that is the extra month of the year.
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.
Rabbi Eliyahu Touger is a noted author and translator, widely published for his works on Chassidut and Maimonides.
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The text on this page contains sacred literature. Please do not deface or discard.
Vowelized Hebrew text courtesy Torat Emet under CC 2.5 license.
The text on this page contains sacred literature. Please do not deface or discard.
