הלכות קידוש החודש י״בSanctification of the New Month 12

Halacha 1א׳

מַהֲלַךְ הַשֶּׁמֶשׁ הָאֶמְצָעִי בְּיוֹם אֶחָד שֶׁהוּא כ"ד שָׁעוֹת נ"ט חֲלָקִים וּשְׁמוֹנֶה שְׁנִיּוֹת. סִימָנָם כ"ד נט"ח. נִמְצָא מַהֲלָכָהּ בַּעֲשָׂרָה יָמִים תֵּשַׁע מַעֲלוֹת וְנ"א חֲלָקִים וְכ"ג שְׁנִיּוֹת. סִימָנָם טנ"א כ"ג. וְנִמְצָא מַהֲלָכָהּ בְּמֵאָה יוֹם צ"ח מַעֲלוֹת וּשְׁלֹשָׁה וּשְׁלֹשִׁים חֲלָקִים וְנ"ג שְׁנִיּוֹת. סִימָנָם צ"ח ל"ג נ"ג. וְנִמְצָא שְׁאֵרִית מַהֲלָכָהּ בְּאֶלֶף יוֹם אַחַר שֶׁתַּשְׁלִיךְ כָּל ש"ס מַעֲלוֹת כְּמוֹ שֶׁבֵּאַרְנוּ. רס"ה מַעֲלוֹת וְל"ח חֲלָקִים וְנ' שְׁנִיּוֹת. סִימָנָם רס"ה לח"ן. וְנִמְצָא שְׁאֵרִית מַהֲלָכָהּ בַּעֲשֶׂרֶת אֲלָפִים יוֹם. קל"ו מַעֲלוֹת וְכ"ח חֲלָקִים וְכ' שְׁנִיּוֹת. סִימָנָם קל"ו כ"ח כ'. וְעַל הַדֶּרֶךְ הַזֶּה תִּכְפּל וְתוֹצִיא מַהֲלָכָהּ לְכָל מִנְיָן שֶׁתִּרְצֶה. וְכֵן אִם תִּרְצֶה לַעֲשׂוֹת סִימָנִין יְדוּעִים אֶצְלְךָ לְמַהֲלָכָהּ לִשְׁנֵי יָמִים וְלִשְׁלֹשָׁה וּלְאַרְבָּעָה עַד עֲשָׂרָה תַּעֲשֶׂה. וְכֵן אִם תִּרְצֶה לִהְיוֹת לְךָ סִימָנִין יְדוּעִים מוּכָנִין לְמַהֲלָכָהּ לְכ' יוֹם וּלְל' וּלְמ' עַד מֵאָה תַּעֲשֶׂה. וְדָבָר גָּלוּי הוּא וְיָדוּעַ מֵאַחַר שֶׁיָּדַעְתָּ מַהֲלַךְ יוֹם אֶחָד. וְרָאוּי הוּא לִהְיוֹת מוּכָן וְיָדוּעַ אֶצְלְךָ מַהֲלַךְ אֶמְצַע הַשֶּׁמֶשׁ לְכ"ט יוֹם וּלְשנ"ד יוֹם שֶׁהֵן יְמֵי שְׁנַת הַלְּבָנָה בִּזְמַן שֶׁחֳדָשֶׁיהָ כְּסִדְרָן. וְהִיא הַנִּקְרֵאת שָׁנָה סְדוּרָה. שֶׁבִּזְמַן שֶׁיִּהְיוּ לְךָ אֶמְצָעִיּוֹת אֵלּוּ מוּכָנִין יִהְיֶה הַחֶשְׁבּוֹן הַזֶּה קַל עָלֶיךָ לִרְאִיַּת הַחֹדֶשׁ. לְפִי שֶׁכ"ט יוֹם גְּמוּרִים מִלֵּיל הָרְאִיָּה עַד לֵיל הָרְאִיָּה שֶׁל חֹדֶשׁ הַבָּא וְכֵן בְּכָל חֹדֶשׁ וְחֹדֶשׁ אֵין פָּחוֹת מִכ"ט יוֹם וְלֹא יוֹתֵר. שֶׁאֵין חֶפְצֵנוּ בְּכָל אֵלּוּ הַחֶשְׁבּוֹנוֹת אֶלָּא לָדַעַת הָרְאִיָּה בִּלְבַד. וְכֵן מִלֵּיל הָרְאִיָּה שֶׁל חֹדֶשׁ זֶה עַד לֵיל הָרְאִיָּה לְאוֹתוֹ הַחֹדֶשׁ לַשָּׁנָה הַבָּאָה שָׁנָה סְדוּרָה אוֹ שָׁנָה וְיוֹם אֶחָד. וְכֵן בְּכָל שָׁנָה וְשָׁנָה. וּמַהֲלַךְ הַשֶּׁמֶשׁ הָאֶמְצָעִי לְכ"ט יוֹם כ"ח מַעֲלוֹת וְל"ה חֲלָקִים וּשְׁנִיָּה אַחַת. סִימָנָן כ"ח ל"ה א'. וּמַהֲלָכָהּ לְשָׁנָה סְדוּרָה שמ"ח מַעֲלוֹת וְנ"ה חֲלָקִים וְט"ו שְׁנִיּוֹת סִימָנָן שמ"ח נ"ה ט"ו:

The average movement of the sun in one day – which is twenty-four hours – is fifty-nine parts (minutes) and nine seconds. Its symbol is 24:59.9. It comes out that its movement in ten days is nine degrees, fifty-one parts and twenty-three seconds. Its symbol is 9.51.23. And it comes out that its movement in a hundred days is ninety-eight degrees, thirty-three parts and fifty-three seconds. Its symbol is 98.33.53. And it comes out that the remainder of its movement in a thousand days – after you remove each [set of] three hundred and sixty degrees, as we explained – is two hundred sixty-five degrees, thirty-eight parts and fifty seconds. Its symbol is 265.38.50. And it comes out that the remainder of its movement in ten thousand days is one hundred and thirty-six degrees, twenty-eight parts and twenty seconds. Its symbol is 136..28.20. And in this way you can multiply and come out with [the sun's] movement for any amount [of time] that you want. And so if you want to make familiar indicators for yourself for its movement in two days, three and four up until ten, you should do [so]. And likewise if you want to make familiar indicators ready for yourself for its movement in twenty days, thirty and forty up until a hundred, you should do [so]. And this is something revealed and known, once you have known the movement of one day. And it is fitting that the average movement of the sun in twenty-nine days and in three hundred and fifty-four days – which is a lunar year at the time when its months are in order, which is called an ordered year – be ready and familiar to you. For when these average movements will be known, this calculation for the sighting of the moon will be easy for you – since there are twenty-nine complete days from the night of one sighting to the night of the next new moon. And likewise for each and every month – there is no less than twenty-nine days and no more. For our desire in all of these calculations is only to know the sighting of the moon exclusively. And likewise from the night of the sighting of this month to the night of the sighting in the same month in the next year is an ordered year or a year and a day. And likewise for each and every year. And the average movement of the sun for twenty-nine days is twenty eight degrees, thirty-five parts and one second. Its symbol is 28.35.1. And its movement in an ordered year is two hundred and forty-eight degrees, fifty-five parts and fifteen seconds. Its symbol is 248.55.15.

Halacha 2ב׳

נְקֻדָּה אַחַת יֵשׁ בְּגַלְגַּל הַשֶּׁמֶשׁ וְכֵן בִּשְׁאָר גַּלְגַּלֵּי הַשִּׁבְעָה כּוֹכָבִים. בְּעֵת שֶׁיִּהְיֶה הַכּוֹכָב בָּהּ יִהְיֶה גָּבוֹהַּ מֵעַל הָאָרֶץ כָּל מְאוֹרוֹ. וְאוֹתָהּ הַנְּקֻדָּה שֶׁל גַּלְגַּל הַשֶּׁמֶשׁ וּשְׁאָר הַכּוֹכָבִים חוּץ מִן הַיָּרֵחַ סוֹבֶבֶת בְּשָׁוֶה. וּמַהֲלָכָהּ בְּכָל שִׁבְעִים שָׁנָה בְּקֵרוּב מַעֲלָה אַחַת. וּנְקֻדָּה זוֹ הִיא הַנִּקְרֵאת גֹּבַהּ הַשֶּׁמֶשׁ. מַהֲלָכוֹ בְּכָל עֲשָׂרָה יָמִים שְׁנִיָּה אַחַת וַחֲצִי שְׁנִיָּה שֶׁהִיא ל' שְׁלִישִׁיּוֹת. נִמְצָא מַהֲלָכוֹ בְּק' יוֹם ט"ו שְׁנִיּוֹת. וּמַהֲלָכוֹ בְּאֶלֶף יוֹם שְׁנֵי חֲלָקִים וּשְׁלֹשִׁים שְׁנִיּוֹת. וּמַהֲלָכוֹ בַּעֲשֶׂרֶת אֲלָפִים יוֹם כ"ה חֲלָקִים. וְנִמְצָא מַהֲלָכוֹ לְתִשְׁעָה וְעֶשְׂרִים יוֹם אַרְבַּע שְׁנִיּוֹת וְעוֹד. וּמַהֲלָכוֹ בְּשָׁנָה סְדוּרָה נ"ג שְׁנִיּוֹת. כְּבָר אָמַרְנוּ שֶׁהָעִקָּר שֶׁמִּמֶּנּוּ הַתְחָלַת חֶשְׁבּוֹן זֶה הוּא מִתְּחִלַּת לֵיל חֲמִישִׁי שֶׁיּוֹמוֹ שְׁלִישִׁי לְחֹדֶשׁ נִיסָן מִשְּׁנַת תתקל"ח וְאַרְבַּעַת אֲלָפִים לַיְצִירָה. וּמְקוֹם הַשֶּׁמֶשׁ בְּמַהֲלָכָהּ הָאֶמְצָעִי הָיָה בָּעִקָּר הַזֶּה בְּשֶׁבַע מַעֲלוֹת וּשְׁלֹשָׁה חֲלָקִים וְל"ב שְׁנִיּוֹת מִמַּזַּל טָלֶה. סִימָנָן ז"ג ל"ב. וּמְקוֹם גֹּבַהּ הַשֶּׁמֶשׁ הָיָה בְּעִקָּר זֶה בְּכ"ו מַעֲלוֹת מ"ה חֲלָקִים וּשְׁמוֹנֶה שְׁנִיּוֹת מִמַּזַּל תְּאוֹמִים. סִימָנָם כ"ו מ"ה ח'. כְּשֶׁתִּרְצֶה לֵידַע מְקוֹם הַשֶּׁמֶשׁ בְּמַהֲלָכָהּ הָאֶמְצָעִי בְּכָל זְמַן שֶׁתִּרְצֶה. תִּקַּח מִנְיַן הַיָּמִים שֶׁמִּתְּחִלַּת יוֹם הָעִקָּר עַד הַיּוֹם שֶׁתִּרְצֶה. וְתוֹצִיא מַהֲלָכָהּ הָאֶמְצָעִי בְּאוֹתָן הַיָּמִים מִן הַסִּימָנִין שֶׁהוֹדַעְנוּ. וְהוֹסֵיף הַכּל עַל הָעִקָּר וּתְקַבֵּץ כָּל מִין עִם מִינוֹ. וְהַיּוֹצֵא הוּא מְקוֹם הַשֶּׁמֶשׁ בְּמַהֲלָכָהּ הָאֶמְצָעִי לְאוֹתוֹ הַיּוֹם. כֵּיצַד. הֲרֵי שֶׁרָצִינוּ לֵידַע מְקוֹם הַשֶּׁמֶשׁ הָאֶמְצָעִי בִּתְחִלַּת לֵיל הַשַּׁבָּת שֶׁיּוֹמוֹ אַרְבָּעָה עָשָׂר לְחֹדֶשׁ תַּמּוּז מִשָּׁנָה זוֹ שֶׁהִיא שְׁנַת הָעִקָּר. מָצָאנוּ מִנְיַן הַיָּמִים מִיּוֹם הָעִקָּר עַד תְּחִלַּת הַיּוֹם זֶה שֶׁאָנוּ רוֹצִים לֵידַע מְקוֹם הַשֶּׁמֶשׁ בּוֹ מֵאָה יוֹם. לָקַחְנוּ אֶמְצַע מַהֲלָכָהּ לְק' יוֹם שֶׁהוּא צ"ח ל"ג נ"ג וְהוֹסַפְנוּ עַל הָעִקָּר שֶׁהוּא ז"ג ל"ב. יָצָא מִן הַחֶשְׁבּוֹן מֵאָה וְחָמֵשׁ מַעֲלוֹת וְל"ז חֲלָקִים וְכ"ה שְׁנִיּוֹת. סִימָנָן ק"ה ל"ז כ"ה. וְנִמְצָא מְקוֹמָהּ בְּמַהֲלַךְ אֶמְצָעִי בִּתְחִלַּת לַיִל זֶה בְּמַזַּל סַרְטָן בְּט"ו מַעֲלוֹת בּוֹ וְל"ז חֲלָקִים מִמַּעֲלַת ט"ז. וְהָאֶמְצָעִי שֶׁיָּצָא בְּחֶשְׁבּוֹן זֶה פְּעָמִים יִהְיֶה בִּתְחִלַּת הַלַּיְלָה בְּשָׁוֶה. אוֹ קֹדֶם שְׁקִיעַת הַחַמָּה בְּשָׁעָה. אוֹ אַחַר שְׁקִיעַת הַחַמָּה בְּשָׁעָה. וְדָבָר זֶה לֹא תָּחוּשׁ לוֹ בַּשֶּׁמֶשׁ בְּחֶשְׁבּוֹן הָרְאִיָּה. שֶׁהֲרֵי אָנוּ מַשְׁלִימִים קֵרוּב זֶה כְּשֶׁנַּחֲשֹׁב לְאֶמְצַע הַיָּרֵחַ. וְעַל הַדֶּרֶךְ הַזֹּאת תַּעֲשֶׂה תָּמִיד לְכָל עֵת שֶׁתִּרְצֶה וַאֲפִלּוּ אַחַר אֶלֶף שָׁנִים. שֶׁתְּקַבֵּץ כָּל הַשְּׁאֵרִית וְתוֹסִיף עַל הָעִקָּר יֵצֵא לְךָ הַמָּקוֹם הָאֶמְצָעִי. וְכֵן תַּעֲשֶׂה בְּאֶמְצַע הַיָּרֵחַ וּבְאֶמְצַע כָּל כּוֹכָב וְכוֹכָב. מֵאַחַר שֶׁתֵּדַע מַהֲלָכוֹ בְּיוֹם אֶחָד כַּמָּה הוּא וְתֵדַע הָעִקָּר שֶׁמִּמֶּנּוּ תַּתְחִיל. וּתְקַבֵּץ מַהֲלָכוֹ לְכָל הַשָּׁנִים וְהַיָּמִים שֶׁתִּרְצֶה וְתוֹסִיף עַל הָעִקָּר וְיֵצֵא לְךָ מְקוֹמוֹ בְּמַהֲלָךְ אֶמְצָעִי. וְכֵן תַּעֲשֶׂה בְּגֹבַהּ הַשֶּׁמֶשׁ תּוֹסִיף מַהֲלָכוֹ בְּאוֹתָם הַיָּמִים אוֹ הַשָּׁנִים עַל הָעִקָּר יֵצֵא לְךָ מְקוֹם גֹּבַהּ הַשֶּׁמֶשׁ לְאוֹתוֹ הַיּוֹם שֶׁתִּרְצֶה. וְכֵן אִם תִּרְצֶה לַעֲשׂוֹת עִקָּר אַחֵר שֶׁתַּתְחִיל מִמֶּנּוּ חוּץ מֵעִקָּר זֶה שֶׁהִתְחַלְנוּ מִמֶּנּוּ בְּשָׁנָה זוֹ. כְּדֵי שֶׁיִּהְיֶה אוֹתוֹ עִקָּר בִּתְחִלַּת שְׁנַת מַחֲזוֹר יָדוּעַ. אוֹ בִּתְחִלַּת מֵאָה מִן הַמֵּאוֹת. הָרְשׁוּת בְּיָדְךָ. וְאִם תִּרְצֶה לִהְיוֹת הָעִקָּר שֶׁתַּתְחִיל מִמֶּנּוּ מִשָּׁנִים שֶׁעָבְרוּ קֹדֶם עִקָּר זֶה אוֹ לְאַחַר כַּמָּה שָׁנִים מֵעִקָּר זֶה הַדֶּרֶךְ יְדוּעָה. כֵּיצַד הִיא הַדֶּרֶךְ. כְּבָר יָדַעְתָּ מַהֲלַךְ הַשֶּׁמֶשׁ לְשָׁנָה סְדוּרָה וּמַהֲלָכָהּ לְכ"ט יוֹם וּמַהֲלָכָהּ לְיוֹם אֶחָד. וְדָבָר יָדוּעַ שֶׁהַשָּׁנָה שֶׁחֳדָשֶׁיהָ שְׁלֵמִים הִיא יְתֵרָה עַל הַסְּדוּרָה יוֹם אֶחָד. וְהַשָּׁנָה שֶׁחֳדָשֶׁיהָ חֲסֵרִין הִיא חֲסֵרָה מִן הַסְּדוּרָה יוֹם אֶחָד. וְהַשָּׁנָה הַמְעֻבֶּרֶת אִם יִהְיוּ חֳדָשֶׁיהָ כְּסִדְרָן תִּהְיֶה יְתֵרָה עַל הַשָּׁנָה הַסְּדוּרָה שְׁלֹשִׁים יוֹם. וְאִם יִהְיוּ חֳדָשֶׁיהָ שְׁלֵמִים הִיא יְתֵרָה עַל הַסְּדוּרָה ל"א יוֹם. וְאִם יִהְיוּ חֳדָשֶׁיהָ חֲסֵרִין הִיא יְתֵרָה עַל הַסְּדוּרָה כ"ט יוֹם. וּמֵאַחַר שֶׁכָּל הַדְּבָרִים הָאֵלּוּ יְדוּעִים תּוֹצִיא מַהֲלַךְ אֶמְצַע הַשֶּׁמֶשׁ לְכָל הַשָּׁנִים וְהַיָּמִים שֶׁתִּרְצֶה וְתוֹסִיף עַל הָעִקָּר שֶׁעָשִׂינוּ. יֵצֵא לְךָ אֶמְצָעָהּ לַיּוֹם שֶׁתִּרְצֶה מִשָּׁנִים הַבָּאוֹת. וְתַעֲשֶׂה אוֹתוֹ הַיּוֹם עִקָּר. אוֹ תִּגְרַע הָאֶמְצַע שֶׁהוֹצֵאתָ מִן הָעִקָּר שֶׁעָשִׂינוּ וְיֵצֵא לְךָ הָעִקָּר לַיּוֹם שֶׁתִּרְצֶה מִשָּׁנִים שֶׁעָבְרוּ. וְתַעֲשֶׂה אוֹתוֹ אֶמְצַע הָעִקָּר. וְכָזֶה תַּעֲשֶׂה בְּאֶמְצַע הַיָּרֵחַ וּשְׁאָר הַכּוֹכָבִים אִם יִהְיוּ יְדוּעִים לְךָ. וּכְבָר נִתְבָּאֵר לְךָ מִכְּלַל דְּבָרֵינוּ שֶׁכְּשֵׁם שֶׁתֵּדַע אֶמְצַע הַשֶּׁמֶשׁ לְכָל יוֹם שֶׁתִּרְצֶה מִיָּמִים הַבָּאִים כָּךְ תֵּדַע אֶמְצָעָהּ לְכָל יוֹם שֶׁתִּרְצֶה מִיָּמִים שֶׁעָבְרוּ:

And there is one point in the orbit of the sun – and likewise in the orbits of the other seven stars – at which time the star is all of its light away from the Earth. And this point of the orbit of the sun and of the other seven stars rotates evenly. And its movement every seventy years is approximately one degree. And this point is called the apogee of the sun. Its movement every ten days is one and a half seconds – which is ninety thirds. It comes out that its movement in a hundred days is fifteen seconds, its movement in a thousand days is two parts and thirty seconds and its movement in ten thousand days is twenty-five parts. And it comes out that its movement in twenty-nine days is four seconds and a bit and its movement in an ordered year is fifty-three seconds. We have already said that the base time from which the calculation begins is from the beginning of the Fifth Night, the date of which is the Third of the month of Nissan of the year 4938 from the creation. And the place of the sun in its average movement [from] this base time was at seven degrees, three parts and thirty-two seconds from the [beginning of the] constellation of Aries. Its symbol is 7.3.32. And the place of the sun's apogee [from] this base time was at twenty-six degrees, forty-five parts and eight seconds from the constellation of Gemini. Its symbol is 26.45.8. When you want to know the place of the sun in its average movement at any time you want – take the amount of days from the beginning of the base time until the day you want. And you can arrive at its average movement for those days from the indicators that we have made known. [Then] add everything to the base time and take the sum of each type [of units] with its type. And what comes out is the place of the sun in its average movement for that day. How is this? See that [if] we wanted to know the place of the sun in its average movement from the beginning of Shabbat night, the date of which was the Fourteenth of the month of Tammuz from this year – which is the year of the base time: We found that the amount of days from the day of the base time until the beginning of this day for which we want to know the place of the sun is a hundred days. We took the average movement for one hundred days – which is 98.33.53 – and we added it to the base time – which is 7.3.32. From the calculation, it came out to one hundred and five degrees, thirty-seven parts and twenty-five seconds. Its symbol is 105.37.25. It comes out that its place according to its average movement at the beginning of this night is in the constellation of Cancer at fifteen degrees in it and thirty-seven parts of the sixteenth degree. The average movement that comes out from this calculation will sometimes be precisely at the beginning of the night [and sometimes] an hour before the sunset or an hour after the sunset. And you should not be concerned about this thing regarding the sun in the calculation of the sighting, as we will compensate for this approximation when we calculate the average [movement] of the moon. And you can do like this anytime you want, even after a thousand years: To take the sum of all of the remainders and add it to the base time – and it will come out for you [to] the place of the average [movement]. And likewise can you do this for the average [movement] of the moon and for the average [movement] of each and every star: Once you know how much its movement is for one day and know the base time from which you start – take the sum of its movement for all of the years and days that you want, and add it to base time. And what comes out is its place in its average movement. And likewise can you do this for the apogee of the sun: Add its movement for those days or years to the base time. What comes out is the place of the sun's apogee for that day that you want. And likewise if you want to make another base time from which to start, besides the base time from which we have started in this year – in order that [such a] base time be at the beginning of the [first] year of a specific cycle or at the beginning of one of the centuries – you have permission in your hand [to do so]. And if you want to make the base time from which you start to be in years that have passed before this base date or after several years from this base date, the procedure is known. How is the procedure? You already know the movement of the sun in an ordered year, its movement for twenty-nine days and its movement for one day. And it is well-known that a year the months of which are complete is one day more than an ordered year; and that a year the months of which are lacking is one day less than an ordered [one]. And [regarding] a leap year: If its months would be in their order, it will be thirty days more than a [simple] ordered year. And if its months would be complete, it will be thirty-one days more than an ordered [year]. And if its months would be lacking, it will be twenty-nine days more than an ordered [year]. And once all of these things are known, you may come out with the average movement of the sun for all of the years and days that you want. So you can add to the [original] base time that we made – and you will have the average [place of the movement] for the day that you want from the years to come. [Then] you can make that the base time. Or you can subtract the movement that you have come up with from the base time that we have made – and you will have the base time that you want from years that have passed. [Then] you can make that average [place of the movement] the base time. And you can do like this for the average [movement] of the moon and the other stars if they be known to you. And it has already been explained that in the same way that you can know the average [movement] of the sun from the days to come, so can you know its average [movement] for every day that you want from the days that have passed.