Mishneh Torah, Sanctification of the New Month Chapter 14

Chapter 14

א הַיָּרֵחַ שְׁנֵי מַהֲלָכִים אְמְצָעיּים יֵשׁ לוֹ. הַיָּרֵחַ עַצְמוֹ מְסַבֵּב בְּגַלְגַּל קָטָן שֶׁאֵינוֹ מַקִּיף אֶת הָעוֹלָם כֻּלּוֹ. וּמַהֲלָכוֹ הָאֶמְצָעִי בְּאוֹתוֹ הַגַּלְגַּל הַקָּטָן נִקְרָא אֶמְצָעִי הַמַּסְלוּל. וְהַגַּלְגַּל הַקָּטָן עַצְמוֹ מְסַבֵּב בְּגַלְגַּל גָּדוֹל הַמַּקִּיף אֶת הָעוֹלָם. וּבְמַהֲלַךְ אֶמְצָעִי זֶה שֶׁל גַּלְגַּל הַקָּטָן בְּאוֹתוֹ הַגַּלְגַּל הַגָּדוֹל הַמַּקִּיף אֶת הָעוֹלָם הוּא הַנִּקְרָא אֶמְצַע הַיָּרֵחַ. מַהֲלַךְ אֶמְצַע הַיָּרֵחַ בְּיוֹם אֶחָד י"ג מַעֲלוֹת וְי' חֲלָקִים וְל"ה שְׁנִיּוֹת. סִימָנָם י"ג יל"ה:

1 The moon has two average movements: The moon itself revolves in a small orbit that does not encircle the [Earth] at all – and its average movement in that small orbit is called the average of the path. And the small orbit itself revolves in another large orbit that does encircle the world. And regarding this average movement of the small orbit in the large orbit that encircles the world – it is called the average movement of the moon. And the average movement of the moon in one day is thirteen degrees, ten parts (minutes) and thirty-eight seconds. Its symbol is 13.10.38.

ב נִמְצָא מַהֲלָכוֹ בַּעֲשָׂרָה יָמִים קל"א מַעֲלוֹת וּמ"ה חֲלָקִים וַחֲמִשִּׁים שְׁנִיּוֹת. סִימָנָם קל"א מה"נ. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּק' יוֹם רל"ז מַעֲלוֹת וְל"ח חֲלָקִים וְכ"ג שְׁנִיּוֹת. סִימָנָם רל"ז ל"ח כ"ג. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּאֶלֶף יוֹם רי"ו מַעֲלוֹת וְכ"ג חֲלָקִים וְנ' שְׁנִיּוֹת. סִימָנָם רי"ו כג"ן. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּי' אֲלָפִים יוֹם ג' מַעֲלוֹת וְנ"ח חֲלָקִים וְכ' שְׁנִיּוֹת. סִימָנָם ג' נ"ח כ'. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּכ"ט יוֹם כ"ב מַעֲלוֹת וְשִׁשָּׁה חֲלָקִים וְנ"ו שְׁנִיּוֹת. סִימָנָם כב"ו ונ"ו. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּשָׁנָה סְדוּרָה שמ"ד מַעֲלוֹת וְכ"ו חֲלָקִים וּמ"ג שְׁנִיּוֹת. סִימָן לָהֶם שד"ם כ"ו מ"ג. וְעַל דֶּרֶךְ זוֹ תִּכְפּל לְכָל מִנְיַן יָמִים אוֹ שָׁנִים שֶׁתִּרְצֶה:

2 It comes out that its movement in ten days is one hundred thirty-one degrees, forty-five parts and fifty seconds. Its symbol is 131.45.50. And it comes out that the remainder (according to the earlier equation) of its movement in one hundred days is two hundred and thirty-seven degrees, thirty-eight parts and twenty-three seconds. Its symbol is 237.38.23. And it comes out that the remainder of its movement in a thousand days is two hundred and sixteen degrees, twenty-three parts and fifty seconds. Its symbol is 216.23.50. And it comes out that the remainder of its movement in ten thousand days is three degrees, fifty-eight parts and twenty seconds. Its symbol is 3.58.20. And it comes out that the remainder of its movement in in twenty-nine days is twenty-two degrees, six parts and fifty-six seconds. Its symbol is 22.6.56. And it comes out that the remainder of its movement in an ordered year is three hundred forty-four degrees, twenty-six parts and forty-three seconds. Its symbol is 344. 26.43. And in this way, you can multiply [it] for any amount of days or years that you want.

ג וּמַהֲלַךְ אֶמְצַע הַמַּסְלוּל בְּיוֹם אֶחָד י"ג מַעֲלוֹת וּשְׁלֹשָׁה חֲלָקִים וְנ"ד שְׁנִיּוֹת. סִימָנָם י"ג גנ"ד. נִמְצָא מַהֲלָכוֹ בַּעֲשָׂרָה יָמִים ק"ל מַעֲלוֹת ל"ט חֲלָקִים בְּלֹא שְׁנִיּוֹת. סִימָנָם ק"ל ל"ט. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּמֵאָה יוֹם רכ"ו מַעֲלוֹת וְכ"ט חֲלָקִים וְנ"ג שְׁנִיּוֹת. סִימָנָם רכ"ו כ"ט נ"ג. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּאֶלֶף יוֹם ק"ד מַעֲלוֹת וְנ"ח חֲלָקִים וַחֲמִשִּׁים שְׁנִיּוֹת. סִימָנָם ק"ד נח"ן. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בַּעֲשֶׂרֶת אֲלָפִים יוֹם שכ"ט וּמ"ח חֲלָקִים וְעֶשְׂרִים שְׁנִיּוֹת. סִימָנָם שכ"ט מח"כ. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּכ"ט יוֹם י"ח מַעֲלוֹת וְנ"ג חֲלָקִים וְד' שְׁנִיּוֹת. סִימָנָם י"ח נג"ד:

3 And the average movement of the path in one day is thirteen degrees, three parts and fifty-four seconds. Its symbol is 13.3.54. It comes out that its movement in ten days is one hundred thirty degrees, thirty-nine parts and no seconds. Its symbol is 130.39. And it comes out that the remainder of its movement in one hundred days is two hundred and thirty-six degrees, twenty-nine parts and fifty-three seconds. Its symbol is 236.29.53. And it comes out that the remainder of its movement in a thousand days is one hundred and four degrees, fifty-eight parts and fifty seconds. Its symbol is 104.58.50. And it comes out that the remainder of its movement in ten thousand days is three hundred and twenty-nine degrees, forty-eight parts and twenty seconds. Its symbol is 329.48.20. And it comes out that the remainder of its movement in twenty-nine days is eighteen degrees, fifty-three parts and four seconds. Its symbol is 18.53.4.

ד וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בְּשָׁנָה סְדוּרָה ש"ה מַעֲלוֹת וְי"ג שְׁנִיּוֹת בְּלֹא חֲלָקִים. סִימָנָם ש"ה י"ג. מְקוֹם אֶמְצַע הַיָּרֵחַ הָיָה בִּתְחִלַּת לֵיל חֲמִישִׁי שֶׁהוּא הָעִקָּר לְחֶשְׁבּוֹנוֹת אֵלּוּ בְּמַזַּל שׁוֹר מַעֲלָה אַחַת וְי"ד חֲלָקִים וּמ"ג שְׁנִיּוֹת. סִימָנָם (א') [ל"א] י"ד מ"ג. וְאֶמְצַע הַמַּסְלוּל הָיָה בְּעִקָּר זֶה פ"ד מַעֲלוֹת וְכ"ח חֲלָקִים וּמ"ב שְׁנִיּוֹת. סִימָנָם פ"ד כ"ח מ"ב. מֵאַחֵר שֶׁתֵּדַע מַהֲלַךְ אֶמְצַע הַיָּרֵחַ וְהָאֶמְצַע שֶׁהוּא הָעִקָּר שֶׁעָלָיו תּוֹסִיף. תֵּדַע מְקוֹם אֶמְצַע הַיָּרֵחַ בְּכָל יוֹם שֶׁתִּרְצֶה עַל דֶּרֶךְ שֶׁעָשִׂיתָ בְּאֶמְצַע הַשֶּׁמֶשׁ. וְאַחַר שֶׁתּוֹצִיא אֶמְצַע הַיָּרֵחַ לִתְחִלַּת הַלַּיְלָה שֶׁתִּרְצֶה הִתְבּוֹנֵן בַּשֶּׁמֶשׁ וְדַע בְּאֵי זֶה מַזָּל הוּא:

4 And it comes out that the remainder of its movement in an ordered year is three hundred five degrees, thirteen parts and no seconds. Its symbol is 305.13. The place of the average [movement] of the moon at the beginning of the Fifth Night – which is the base of these calculations – was one degree, fourteen parts and forty-three seconds in the constellation of Taurus. Its symbol is [1.]14.43. And the [place of the] average movement of the path at this base time was eighty-four degrees, twenty-eight parts and forty-two seconds. Its symbol is 84.28.42. Once you know the average movement of the moon and the center, which is the base time upon which you add – you can know the place of the average movement of the moon at any time you want, according to the way that you used for the average movement of the sun. And once you have produced the [place of the] average movement of the moon for the beginning of the night that you want – [then] examine the sun and ascertain which constellation it is in:

ה אִם הָיְתָה הַשֶּׁמֶשׁ מֵחֲצִי מַזַּל דָּגִים עַד חֲצִי מַזַּל טָלֶה. תָּנִיחַ אֶמְצַע הַיָּרֵחַ כְּמוֹת שֶׁהוּא. וְאִם תִּהְיֶה הַשֶּׁמֶשׁ מֵחֲצִי מַזַּל טָלֶה עַד תְּחִלַּת מַזַּל תְּאוֹמִים. תּוֹסִיף עַל אֶמְצַע הַיָּרֵחַ ט"ו חֲלָקִים. וְאִם תִּהְיֶה הַשֶּׁמֶשׁ מִתְּחִלַּת מַזַּל תְּאוֹמִים עַד תְּחִלַּת מַזַּל אַרְיֵה. תּוֹסִיף עַל אֶמְצַע הַיָּרֵחַ ל' חֲלָקִים. וְאִם תִּהְיֶה הַשֶּׁמֶשׁ מִתְּחִלַּת מַזַּל אַרְיֵה עַד חֲצִי מַזַּל בְּתוּלָה תּוֹסִיף עַל אֶמְצַע הַיָּרֵחַ ט"ו חֲלָקִים. וְאִם תִּהְיֶה הַשֶּׁמֶשׁ מֵחֲצִי מַזַּל בְּתוּלָה עַד חֲצִי מֹאזְנַיִם. הָנַח אֶמְצַע הַיָּרֵחַ כְּמוֹת שֶׁהוּא. וְאִם תִּהְיֶה הַשֶּׁמֶשׁ מֵחֲצִי מֹאזְנַיִם עַד תְּחִלַּת מַזַּל קֶשֶׁת. תִּגְרַע מֵאֶמְצַע הַיָּרֵחַ ט"ו חֲלָקִים. וְאִם תִּהְיֶה הַשֶּׁמֶשׁ מִתְּחִלַּת מַזַּל קֶשֶׁת עַד תְּחִלַּת מַזַּל דְּלִי. תִּגְרַע מֵאֶמְצַע הַיָּרֵחַ ל' חֲלָקִים. וְאִם תִּהְיֶה הַשֶּׁמֶשׁ מִתְּחִלַּת מַזַּל דְּלִי עַד חֲצִי מַזַּל דָּגִים. תִּגְרַע מֵאֶמְצַע הַיָּרֵחַ ט"ו חֲלָקִים:

5 If the sun was from half the constellation of Pisces to half of the constellation of Aries, leave the [place] of the average [movement] of the moon as it is. And if the sun would be from half the constellation of Aries until the beginning of the constellation of Gemini, add fifteen parts to the [place of the] average [movement] of the moon. And if the sun would be from the beginning of the constellation of Gemini until the beginning of the constellation of Leo, add (fifteen) [thirty] parts to the [place of the] average [movement] of the moon. And if the sun would be from the beginning of the constellation of Leo until half the constellation of Virgo, add fifteen parts to the [place of the] average [movement] of the moon. And if the sun would be from half of the constellation of Virgo until half of Libra, leave the [place of the] average [movement] of the moon as it is. And if the sun would be from half of Libra to the beginning of the constellation of Sagittarius, subtract fifteen parts from the [place of the] average [movement] of the moon. And if the sun would be from the beginning of the constellation of Sagittarius until the beginning of the constellation of Aquarius, subtract thirty parts from the [place of the] average [movement] of the moon. And if the sun would be from the beginning of the constellation of Aquarius until the middle of the constellation of Pisces, subtract fifteen parts from the [place of the] average [movement] of the moon.

ו וּמַה שֶּׁיִּהְיֶה הָאֶמְצַע אַחַר שֶׁתּוֹסִיף עָלָיו אוֹ תִּגְרַע מִמֶּנּוּ אוֹ תָּנִיחַ אוֹתוֹ כְּמוֹת שֶׁהוּא. הוּא אֶמְצַע הַיָּרֵחַ לְאַחַר שְׁקִיעַת הַחַמָּה בִּכְמוֹ שְׁלִישׁ שָׁעָה בְּאוֹתוֹ הַזְּמַן שֶׁתּוֹצִיא הָאֶמְצַע לוֹ. וְזֶה הוּא הַנִּקְרָא אֶמְצַע הַיָּרֵחַ לִשְׁעַת הָרְאִיָּה:

6 And that which will be the average after you add or remove or leave alone (as above) is the [place of the] average position of the moon after the setting of the sun – within about a third of an hour – for that time for which you produce the average. This is what is called the average moon for the time of the sighting.

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