Mishneh Torah, Sanctification of the New Month Chapter 16

Chapter 16

א הָעֲגֻלָה שֶׁסּוֹבֶבֶת בָּהּ הַיָּרֵחַ תָּמִיד הִיא נוֹטָה מֵעַל הָעֲגֵלָּה שֶׁסּוֹבֶבֶת בָּהּ הַשֶּׁמֶשׁ תָּמִיד. חֶצְיָהּ נוֹטֶה לְצָפוֹן וְחֶצְיָהּ נוֹטֶה לְדָרוֹם. וּשְׁתֵּי נְקֻדּוֹת יֵשׁ בָּהּ זוֹ כְּנֶגֶד זוֹ שֶׁבָּהֶן פּוֹגְעוֹת שְׁתֵּי הָעֲגֻלּוֹת זוֹ בָּזוֹ. לְפִיכָךְ כְּשֶׁיִּהְיֶה הַיָּרֵחַ בְּאַחַת מִשְּׁתֵּיהֶן נִמְצָא סוֹבֵב בְּעִגּוּלָהּ שֶׁל שֶׁמֶשׁ כְּנֶגֶד הַשֶּׁמֶשׁ בְּשָׁוֶה. וְאִם יֵצֵא הַיָּרֵחַ מֵאַחַת מִשְּׁתֵּי הַנְּקֻדּוֹת נִמְצָא מְהַלֵּךְ לִצְפוֹן הַשֶּׁמֶשׁ אוֹ לִדְרוֹמָהּ. הַנְּקֻדָּה שֶׁמִּמֶּנָּה יַתְחִיל הַיָּרֵחַ לִנְטוֹת לִצְפוֹן הַשֶּׁמֶשׁ הִיא הַנִּקְרֵאת רֹאשׁ. וְהַנְּקֻדָּה שֶׁמִּמֶּנָּה יַתְחִיל הַיָּרֵחַ לִנְטוֹת לִדְרוֹם הַשֶּׁמֶשׁ הִיא הַנִּקְרֵאת זָנָב. וּמַהֲלָךְ שָׁוֶה יֵשׁ לְזֶה הָרֹאשׁ שֶׁאֵין בּוֹ לֹא תּוֹסֶפֶת וְלֹא גֵּרָעוֹן. וְהוּא הוֹלֵךְ בַּמַּזָּלוֹת אֲחוֹרַנִּית מִטָּלֶה לְדָגִים וּמִדָּגִים לִדְלִי וְכֵן הוּא סוֹבֵב תָּמִיד:

1 The orbit in which the moon always veers from the orbit in which the sun always moves. Half of [the moon's] orbit veers to the north and half of it veers to the south. And there are two points in it – one across from the other – in which the two orbits intersect one another. Hence when the moon is in one of those two points, it comes out that it is moving [along] the orbit of the sun exactly opposite to the sun. But if the moon moves out of one of these two points, it comes out that it moves north of the sun or south of it. The point from which the moon starts to veer to the north of the sun is called the head. And the point from which the moon begins to veer to the south of the sun is called the tail. And there is an even movement to this head that has no addition or subtraction; and it moves backwards through the constellations, from Aries to Pisces, and Pisces to Aquarius. And likewise does it always move [regarding the other constellations].

ב מַהֲלַךְ הָרֹאשׁ הָאֶמְצָעִי בְּיוֹם אֶחָד ג' חֲלָקִים וְי"א שְׁנִיּוֹת. נִמְצָא מַהֲלָכוֹ בְּי' יָמִים ל"א חֲלָקִים וּמ"ז שְׁנִיּוֹת. וְנִמְצָא מַהֲלָכוֹ בְּק' יוֹם ה' מַעֲלוֹת וְי"ז חֲלָקִים וּמ"ג שְׁנִיּוֹת. סִימָנָם הי"ז מ"ג. וְנִמְצָא מַהֲלָכוֹ בְּאֶלֶף יוֹם נ"ב מַעֲלוֹת וְנ"ז חֲלָקִים וְי' שְׁנִיּוֹת. סִימָנָם נ"ב נז"י. וְנִמְצָא שְׁאֵרִית מַהֲלָכוֹ בַּעֲשֶׂרֶת אֲלָפִים יוֹם קס"ט מַעֲלוֹת וְל"א חֲלָקִים וּמ' שְׁנִיּוֹת. סִימָנָם קס"ט לא"מ. וְנִמְצָא מַהֲלָכוֹ לְכ"ט יוֹם מַעֲלָה אַחַת וְל"ב חֲלָקִים וְט' שְׁנִיּוֹת. סִימָנָם א' לב"ט. וְנִמְצָא מַהֲלָכוֹ לְשָׁנָה סְדוּרָה י"ח מַעֲלוֹת וּמ"ד חֲלָקִים וּמ"ב שְׁנִיּוֹת. סִימָנָם י"ח מ"ד מ"ב. וְאֶמְצַע הָרֹאשׁ בִּתְחִלַּת לֵיל ה' שֶׁהוּא הָעִקָּר הָיָה ק"פ מַעֲלוֹת וְנ"ז חֲלָקִים וְכ"ח שְׁנִיּוֹת. סִימָנָם ק"פ נ"ז כ"ח:

2 The average movement of the head in one day is three parts and eleven seconds. It comes out that its movement in ten days is thirty-one parts and forty-seven seconds. And it comes out that its movement in a hundred days is five degrees, seventeen parts and forty-three seconds. Its symbol is 5.17.43. And it comes out that its movement in a thousand days is fifty-two degrees, fifty-seven parts and ten seconds. Its symbol is 52.57.10. And it comes out that its movement in ten thousand days is one hundred and sixty-nine degrees, thirty-one parts and forty seconds. Its symbol is 169.31.40. And it comes out that its movement in twenty-nine days is one degree, thirty-two parts and nine seconds. Its symbol is 1.32.9. And it comes out that its movement in an ordered year is eighteen degrees, forty-four parts and forty-two seconds. And the average [place] of the head at the beginning of the Night of the Fifth (Wednesday night) which was the base time is one hundred and eighty degrees, fifty-seven parts and twenty-eight seconds. Its symbol is 180. 57. 28.

ג אִם תִּרְצֶה לֵידַע מְקוֹם הָרֹאשׁ בְּכָל עֵת שֶׁתִּרְצֶה. תּוֹצִיא אֶמְצָעָם לְאוֹתוֹ הָעֵת כְּדֶרֶךְ שֶׁתּוֹצִיא אֶמְצַע הַשֶּׁמֶשׁ וְאֶמְצַע הַיָּרֵחַ. וְתִגְרַע הָאֶמְצַע מִש"ס מַעֲלוֹת. וְהַנִּשְׁאָר הוּא מְקוֹם הָרֹאשׁ בְּאוֹתָהּ הָעֵת. וּכְנֶגְדּוֹ לְעוֹלָם יִהְיֶה מְקוֹם הַזָּנָב:

3 If you want to know the place of the head at any time that you want, produce their average [place] for that time in the way that you produce the average [place] of the sun and the average [place] of the moon. [Then] subtract the average from three hundred and sixty degrees; and the remainder is the place of the head at that time. And the place of the tail will always be across from it.

ד כֵּיצַד. הֲרֵי שֶׁרָצִינוּ לֵידַע מְקוֹם הָרֹאשׁ לִתְחִלַּת לֵיל עֶרֶב שַׁבָּת שֶׁיּוֹמוֹ שֵׁנִי לְחֹדֶשׁ אִיָּר מִשָּׁנָה זוֹ שֶׁהִיא שְׁנַת הָעִקָּר. וּמִנְיַן הַיָּמִים הַגְּמוּרִים מִתְּחִלַּת לֵיל הָעִקָּר עַד תְּחִלַּת לַיִל זוֹ שֶׁאָנוּ רוֹצִים לֵידַע מְקוֹם הָרֹאשׁ בּוֹ כ"ט יוֹם:

4 How is this? See that [if] we wanted to know the place of the head of the beginning of the night [following] the eve of Shabbat (Friday night), the day of which was the Second of Iyar from this year, which is the base year. And the completed days from the beginning of the night of the base time until the beginning of this night upon which we want to know the place of the head is twenty-nine days.

ה תּוֹצִיא אֶמְצַע הָרֹאשׁ לָעֵת הַזֹּאת עַל הַדֶּרֶךְ שֶׁיָּדַעְתָּ. וְהוּא שֶׁתּוֹסִיף מַהֲלָכוֹ לְכ"ט יוֹם עַל הָעִקָּר. יֵצֵא לְךָ אֶמְצַע הָרֹאשׁ קפ"ב מַעֲלוֹת וְכ"ט חֲלָקִים וְל"ז שְׁנִיּוֹת. סִימָנָם קפ"ב כ"ט ל"ז. תִּגְרַע אֶמְצַע זֶה מִש"ס יִשָּׁאֵר לְךָ קע"ז מַעֲלוֹת וְל' חֲלָקִים וְכ"ג שְׁנִיּוֹת. סִימָנָם קע"ז לִכְ"ג. וְזֶה הוּא מְקוֹם הָרֹאשׁ. וְאַל תִּפְנֶה אֶל הַשְּׁנִיּוֹת. נִמְצָא מְקוֹם הָרֹאשׁ בְּמַזַּל בְּתוּלָה בְּכ"ז מַעֲלוֹת וְל' חֲלָקִים. וּמְקוֹם הַזָּנָב כְּנֶגְדּוֹ בְּמַזַּל דָּגִים בְּכ"ז מַעֲלוֹת וּשְׁלֹשִׁים חֲלָקִים:

5 Produce the mean [place] of the moon at that time in the way that you know. And that is that you add its movement for twenty days upon [its place] at the base time. It comes out for you that the mean [place] of the head is one hundred and eighty-two degrees, twenty-nine parts and thirty-seven seconds. Its symbol is 182.29.37. Subtract this mean from three hundred and sixty. Your remainder is one hundred and seventy five degrees, thirty parts and twenty-three seconds. Its symbol is 177.30.23. And do not pay attention to the seconds. It comes out that the place of the head is twenty-seven degrees and thirty parts into the constellation of Virgo. And [so] the place of the tail is across from it at twenty-seven degrees and thirty parts into the constellation of Pisces.

ו לְעוֹלָם יִהְיֶה בֵּין הָרֹאשׁ וּבֵין הַזָּנָב חֲצִי הַגַּלְגַּל בְּשָׁוֶה. לְפִיכָךְ כָּל מַזָּל שֶׁתִּמְצָא בּוֹ מְקוֹם הָרֹאשׁ יִהְיֶה הַזָּנָב בְּמַזַּל ז' מִמֶּנּוּ בִּכְמוֹ מִנְיַן הַמַּעֲלוֹת וְהַחֲלָקִים בְּשָׁוֶה. אִם יִהְיֶה הָרֹאשׁ בְּי' מַעֲלוֹת בְּמַזַּל פְּלוֹנִי יִהְיֶה הַזָּנָב בְּי' מַעֲלוֹת מִמַּזַּל ז' מִמֶּנּוּ:

6 There will always be exactly half an orbit between the head and the tail. Hence [for] any constellation in which you find the place of the head, you will find the tail in the constellation that is seventh from it, exactly in the same amount of degrees and parts [as the head]. If the head would be at ten degrees in constellation x, the tail would be at ten degrees in the seventh constellation from it.

ז וּמֵאַחַר שֶׁתֵּדַע מְקוֹם הָרֹאשׁ וּמְקוֹם הַזָּנָב וּמְקוֹם הַיָּרֵחַ הָאֲמִתִּי. הִתְבּוֹנֵן בִּשְׁלָשְׁתָּן. אִם מָצָאתָ הַיָּרֵחַ עִם הָרֹאשׁ אוֹ עִם הַזָּנָב בְּמַעֲלָה אַחַת בְּחֵלֶק אֶחָד. תֵּדַע שֶׁאֵין הַיָּרֵחַ נוֹטֶה לֹא לִצְפוֹן הַשֶּׁמֶשׁ וְלֹא לִדְרוֹמָהּ. וְאִם רָאִיתָ מְקוֹם הַיָּרֵחַ לִפְנֵי מְקוֹם הָרֹאשׁ וְהוּא הוֹלֵךְ כְּנֶגֶד הַזָּנָב. תֵּדַע שֶׁהַיָּרֵחַ נוֹטֶה לִצְפוֹן הַשֶּׁמֶשׁ. וְאִם הָיָה הַיָּרֵחַ לִפְנֵי מְקוֹם הַזָּנָב וַהֲרֵי הוּא הוֹלֵךְ כְּנֶגֶד הָרֹאשׁ. תֵּדַע שֶׁהַיָּרֵחַ נוֹטֶה לִדְרוֹם הַשֶּׁמֶשׁ:

7 And once you know the place of the head, the place of the tail and the true place of the moon, consider the three of them: If you found that the moon is with the head or with the tail, on the same degree and the same part – know that the moon is not inclining to the north of the sun, nor to its south. But if you saw that the place of the moon is past the place of the head and it is moving towards the tail, know that the moon is inclining to the north of the sun. And if the moon is past the place of the tail and it is surely moving towards the head, know that the moon is inclining to the south of the sun.

ח הַנְּטִיָּה שֶׁנּוֹטֶה הַיָּרֵחַ לִצְפוֹן הַשֶּׁמֶשׁ אוֹ לִדְרוֹמָהּ. הִיא הַנִּקְרֵאת רֹחַב הַיָּרֵחַ. וְאִם הָיָה נוֹטֶה לַצָּפוֹן נִקְרָא רֹחַב צְפוֹנִי. וְאִם הָיָה נוֹטֶה לַדָּרוֹם נִקְרָא רֹחַב דְּרוֹמִי. וְאִם הָיָה הַיָּרֵחַ בְּאַחַת מִשְּׁתֵּי הַנְּקֻדּוֹת לֹא יִהְיֶה לוֹ רֹחַב כְּמוֹ שֶׁבֵּאַרְנוּ:

8 The incline that the moon inclines to the north of the sun or to its south is that which is called the width of the moon. If it was inclining to the north, it is called a northern width; and if the moon was inclining to the south, it is called a southern width. But if the the moon was in one of the two points, it would not have a width, as we explained.

ט לְעוֹלָם לֹא יִהְיֶה רֹחַב הַיָּרֵחַ יֶתֶר עַל ה' מַעֲלוֹת בֵּין בַּצָּפוֹן בֵּין בַּדָּרוֹם. אֶלָּא כָּךְ הוּא דַּרְכּוֹ יַתְחִיל מִן הָרֹאשׁ וְיִתְרַחֵק מִמֶּנּוּ מְעַט מְעַט. וְהַמֶּרְחָק הוֹלֵךְ וְנוֹסָף עַד שֶׁיַּגִּיעַ לְחָמֵשׁ מַעֲלוֹת. וְיַחֲזֹר וְיִתְקָרֵב מְעַט מְעַט עַד שֶׁלֹּא יִהְיֶה לוֹ רֹחַב כְּשֶׁיַּגִּיעַ לַזָּנָב. וְיַחֲזֹר וְיִתְרַחֵק מְעַט מְעַט וְהַמֶּרְחָק נוֹסָף עַד שֶׁיַּגִּיעַ לְחָמֵשׁ מַעֲלוֹת. וְיַחֲזֹר וְיִתְקָרֵב עַד שֶׁלֹּא יִהְיֶה לוֹ רֹחַב:

9 The width of the moon will never be more than five degrees – whether to the north or to the south. Rather this is its way: It will begin at the head and diverge from it little by little. And the distance continues to grow until it gets to five degrees; and then it again approaches little by little until there be no width when it reaches the tail. And it again diverges little by little, and the divergence grows until it reaches five degrees. And it again approaches until it will not have a width.

י אִם תִּרְצֶה לֵידַע רֹחַב הַיָּרֵחַ כַּמָּה הוּא בְּכָל עֵת שֶׁתִּרְצֶה. וְאִם צְפוֹנִי הוּא אוֹ דְּרוֹמִי. תּוֹצִיא מְקוֹם הָרֹאשׁ וּמְקוֹם הַיָּרֵחַ הָאֲמִתִּי לְאוֹתָהּ הָעֵת. וְתִגְרַע מְקוֹם הָרֹאשׁ מִמְּקוֹם הַיָּרֵחַ הָאֲמִתִּי. וְהַנִּשְׁאָר הוּא הַנִּקְרָא מַסְלוּל הָרֹחַב. וְאִם יִהְיֶה מַסְלוּל הָרֹחַב מִמַּעֲלָה אַחַת עַד ק"פ. תֵּדַע שֶׁרֹחַב הַיָּרֵחַ צְפוֹנִי. וְאִם הָיָה הַמַּסְלוּל יֶתֶר עַל ק"פ תֵּדַע שֶׁרֹחַב הַיָּרֵחַ דְּרוֹמִי. וְאִם הָיָה ק"פ בְּשָׁוֶה אוֹ ש"ס בְּשָׁוֶה אֵין לַיָּרֵחַ רֹחַב כְּלָל. וְתַחֲזֹר וְתִרְאֶה מְנַת מַסְלוּל הָרֹחַב כַּמָּה הִיא. וְהוּא שִׁעוּר נְטִיָּתוֹ לַצָּפוֹן אוֹ לַדָּרוֹם. וְהוּא הַנִּקְרָא רֹחַב הַיָּרֵחַ הַדְּרוֹמִי אוֹ הַצְּפוֹנִי כְּמוֹ שֶׁבֵּאַרְנוּ:

10 If you want to know how much the width of the moon is at any time that you want, and whether it is northern or southern: Produce the place of the head and the true place of the moon for that time. Then subtract the place of the head from the true place of the moon. And the remainder is what is called the path of the width. And if the path of the width would be from one degree to one hundred and eighty, know that the width of the moon is northern. And if the path was more than one hundred and eighty, know that the width of the moon is southern. And if it was exactly one hundred and eighty or exactly three hundred and sixty, the moon has no width at all. Then go back and see how much is the divergence of the path of the width. And that is the amount of its incline to the north or to the south; and that is what is called the northern or southern width of the moon, as we explained.

יא וְכַמָּה הִיא מְנַת מַסְלוּל הָרֹחַב. אִם יִהְיֶה מַסְלוּל הָרֹחַב עֶשֶׂר מַעֲלוֹת תִּהְיֶה מְנָתוֹ נ"ב חֲלָקִים. וְאִם יִהְיֶה הַמַּסְלוּל הַזֶּה כ' מַעֲלוֹת תִּהְיֶה מְנָתוֹ מַעֲלָה אַחַת וּמ"ג חֲלָקִים. וְאִם יִהְיֶה הַמַּסְלוּל ל' תִּהְיֶה מְנָתוֹ שְׁתֵּי מַעֲלוֹת וְל' חֲלָקִים. וְאִם יִהְיֶה הַמַּסְלוּל מ' תִּהְיֶה מְנָתוֹ שָׁלֹשׁ מַעֲלוֹת וְי"ג חֲלָקִים. וְאִם יִהְיֶה הַמַּסְלוּל נ' מַעֲלוֹת תִּהְיֶה מְנָתוֹ שָׁלֹשׁ מַעֲלוֹת וְנ' חֲלָקִים. וְאִם יִהְיֶה הַמַּסְלוּל ס' תִּהְיֶה מְנָתוֹ אַרְבַּע מַעֲלוֹת וְכ' חֲלָקִים. וְאִם יִהְיֶה הַמַּסְלוּל ע' תִּהְיֶה מְנָתוֹ ד' מַעֲלוֹת וּמ"ב חֲלָקִים. וְאִם יִהְיֶה הַמַּסְלוּל פ' תִּהְיֶה מְנָתוֹ ד' מַעֲלוֹת וְנ"ה חֲלָקִים. וְאִם יִהְיֶה הַמַּסְלוּל צ' תִּהְיֶה מְנָתוֹ ה' מַעֲלוֹת:

11 And how much is the divergence of the path of the width? If the path of the width would be ten degrees, its divergence would be fifty-two parts (minutes). And if this path would be twenty degrees, its divergence would be one degree and forty-three parts. And if the path would be thirty, its divergence would be two degrees and thirty parts. And if the path would be forty, its divergence would be three degrees and thirteen parts. And if the path would be fifty, its divergence would be three degrees and fifty parts. And if the path would be sixty, its divergence would be four degrees and twenty parts. And if the path would be seventy, its divergence would be four degrees and forty-two parts. And if the path would be eighty, its divergence would be four degrees and fifty-five parts. And if the path would be ninety, its divergence would be five degrees.

יב וְאִם יִהְיוּ אֲחָדִים עִם הָעֲשָׂרוֹת תִּקַּח הָרָאוּי לָהֶם לְפִי הַיֶּתֶר שֶׁבֵּין שְׁתֵּי הַמָּנוֹת כְּמוֹ שֶׁעָשִׂיתָ בְּמַסְלוּל הַשֶּׁמֶשׁ וּבְמַסְלוּל הַיָּרֵחַ. כֵּיצַד. הֲרֵי שֶׁהָיָה מַסְלוּל הָרֹחַב נ"ג מַעֲלוֹת. וּכְבָר יָדַעְתָּ שֶׁאִלּוּ הָיָה הַמַּסְלוּל נ' הָיְתָה מְנָתוֹ שָׁלֹשׁ מַעֲלוֹת וְנ' חֲלָקִים. וְאִלּוּ הָיָה הַמַּסְלוּל ס' הָיְתָה מְנָתוֹ ד' מַעֲלוֹת וְכ' חֲלָקִים. נִמְצָא הַיֶּתֶר בֵּין שְׁתֵּי הַמָּנוֹת ל' חֲלָקִים ג' חֲלָקִים לְכָל מַעֲלָה. וְנִמְצָא לְפִי חֶשְׁבּוֹן מַסְלוּל זֶה שֶׁהוּא נ"ג שָׁלֹשׁ מַעֲלוֹת וְנ"ט חֲלָקִים. וְעַל דֶּרֶךְ זוֹ תַּעֲשֶׂה בְּכָל מִנְיָן וּמִנְיָן:

12 And if there would be single digits with the tens, take [the proportional amount] that is fit for them according to the remainder between the two tens, as you did with the path of the sun and the path of the moon. How is that? See that [if] the path of the width was fifty-three degrees; and you already know that if the path was fifty, its divergence would be three degrees and fifty parts, and if the path was sixty degrees, the divergence would be four degrees and twenty parts. It comes out that the remainder between the two tens (after subtracting one from the other) is thirty parts – three parts for every degree. And it comes out according to the calculation of this path which is fifty-three, [that] it is three degrees and fifty-nine parts. And in this way you [can calculate] each and every amount.

יג מֵאַחַר שֶׁתֵּדַע מְנָתוֹ שֶׁל מַסְלוּל הָרֹחַב עַד צ' כְּמוֹ שֶׁהוֹדַעְנוּךָ. תֵּדַע מָנוֹת שֶׁל כָּל מִנְיְנוֹת הַמַּסְלוּל. שֶׁאִם יִהְיֶה הַמַּסְלוּל יֶתֶר עַל צ' עַד ק"פ תִּגְרַע הַמַּסְלוּל מִק"פ וְהַנִּשְׁאָר תֵּדַע בּוֹ הַמָּנָה:

13 Once you know the divergence of the path of the width up to ninety – as we have informed you – you will know the divergence of all the amounts of the path. For if the path is more than ninety, up to one hundred and eighty; subtract the width from one hundred and eighty. And you will know that the remainder is the divergence.

יד וְזֶה הוּא רֹחַב הַיָּרֵחַ בִּתְחִלַּת לַיִל זֶה. וְהוּא דְּרוֹמִי שֶׁהֲרֵי הַמַּסְלוּל יֶתֶר עַל ק"פ. וְכֵן אִם הָיָה הַמַּסְלוּל יֶתֶר מִק"פ עַד ר"ע תִּגְרַע מִמֶּנּוּ ק"פ וְהַנִּשְׁאָר תֵּדַע בּוֹ הַמָּנָה:

14 (And that is the width of the moon on the beginning of that night; and it is southern. For the path is surely more than one hundred and eighty.) And likewise if the path was more than one hundred and eighty, up until two hundred and seventy; subtract one hundred and eighty from it. And you will know that the remainder is the divergence.

טו וְאִם הָיָה הַמַּסְלוּל יֶתֶר עַל ר"ע עַד ש"ס. תִּגְרַע אוֹתוֹ מִש"ס וְהַנִּשְׁאָר תֵּדַע בּוֹ הַמָּנָה:

15 And if the path was more than two hundred and seventy, up until three hundred and sixty; subtract it from two hundred and sixty. And you will know that the remainder is the divergence.

טז כֵּיצַד. הֲרֵי שֶׁהָיָה הַמַּסְלוּל ק"נ תִּגְרַע אוֹתוֹ מִק"פ נִשְׁאָר ל'. וּכְבָר יָדַעְתָּ שֶׁמְּנַת שְׁלֹשִׁים שְׁתֵּי מַעֲלוֹת וּשְׁלֹשִׁים חֲלָקִים וְכָךְ תִּהְיֶה מְנַת ק"נ שְׁתֵּי מַעֲלוֹת וּשְׁלֹשִׁים חֲלָקִים:

16 How is that? See that [if] the path was one hundred and fifty, subtract it from one hundred and eighty. The remainder is thirty. And you already know that the divergence of thirty is two degrees and thirty parts. Hence the divergence of one hundred and fifty is two degrees and thirty parts.

יז הֲרֵי שֶׁהָיָה הַמַּסְלוּל ר'. תִּגְרַע מִמֶּנּוּ ק"פ יִשָּׁאֵר כ'. וּכְבָר יָדַעְתָּ שֶׁמְּנַת כ' הִיא מַעֲלָה אַחַת וּמ"ג חֲלָקִים. וְכֵן אִם תִּהְיֶה מְנַת ר' תִּהְיֶה מַעֲלָה אַחַת וּמ"ג חֲלָקִים:

17 See that [if] the path was two hundred, subtract one hundred and sixty from it. The remainder is twenty. And you already know that the divergence of twenty is one degree and forty-three parts. Hence the divergence of one hundred and fifty is one degree and forty-three parts.

יח הֲרֵי שֶׁהָיָה הַמַּסְלוּל ש' תִּגְרַע אוֹתוֹ מִש"ס נִשְׁאַר ס'. וּכְבָר יָדַעְתָּ שֶׁמְּנַת שִׁשִּׁים אַרְבַּע מַעֲלוֹת וְכ' חֲלָקִים. וְכָךְ הִיא מְנַת ש' ד' מַעֲלוֹת וְכ' חֲלָקִים. וְעַל דֶּרֶךְ זוֹ בְּכָל הַמִּנְיָנוֹת:

18 See that [if] the path was three hundred, subtract it from three hundred and sixty. The remainder is sixty. And you already know that the divergence of sixty is four degrees and twenty parts. Hence the divergence of one hundred and fifty is four degrees and twenty parts. And in this way [is the calculation] for all the amounts.

יט הֲרֵי שֶׁרָצִינוּ לֵידַע רֹחַב הַיָּרֵחַ כַּמָּה הוּא וּבְאֵיזוֹ רוּחַ הוּא אִם צְפוֹנִי אוֹ דְּרוֹמִי בִּתְחִלַּת לֵיל עֶרֶב שַׁבָּת שֵׁנִי לְחֹדֶשׁ אִיָּר מִשָּׁנָה זוֹ. וּכְבָר יָדַעְתָּ שֶׁמְּקוֹם הַיָּרֵחַ הָאֲמִתִּי הָיָה בְּלַיִל זֶה בְּי"ח מַעֲלוֹת וְל"ו חֲלָקִים מִמַּזַּל שׁוֹר. סִימָנוֹ י"ח ל"ו. וּמְקוֹם הָרֹאשׁ הָיָה בְּאוֹתָהּ הָעֵת בְּכ"ז מַעֲלוֹת וְל' חֲלָקִים מִמַּזַּל בְּתוּלָה. סִימָנוֹ כז"ל. תִּגְרַע מְקוֹם הָרֹאשׁ מִמְּקוֹם הַיָּרֵחַ. יֵצֵא לְךָ מַסְלוּל הָרֹחַב רל"א מַעֲלוֹת ו' חֲלָקִים. סִימָנוֹ רל"א ו'. לְפִי שֶׁאֵין מַשְׁגִּיחִין עַל הַחֲלָקִים בְּכָל הַמַּסְלוּל. וְנִמְצֵאת הַמָּנָה שֶׁל מַסְלוּל זֶה בַּדְּרָכִים שֶׁבֵּאַרְנוּ בְּפֶרֶק זֶה שָׁלֹשׁ מַעֲלוֹת וְנ"ג חֲלָקִים. וְזֶהוּ רֹחַב הַיָּרֵחַ בִּתְחִלַּת לַיִל זֶה. וְהוּא דְּרוֹמִי שֶׁהֲרֵי הַמַּסְלוּל יֶתֶר עַל ק"פ:

19 See that [if] we wanted to know how much is the width of the moon and in which direction it is – whether north or south – at the beginning of the night of the eve of Shabbat on the Second of the month of Iyar from this year: And you already know that the true place of the moon on this night was eighteen degrees and thirty-six degrees into the Constellation of Taurus. Its symbol is 18.36. [Likewise you know that] the place of the head at that time was twenty-seven degrees and thirty parts into the Constellation of Virgo. Its symbol is 27.30. Subtract the place of the head from the place of the moon. Your result will be a path of the width of two hundred thirty-one degrees and six parts. Its symbol is 236.6. Since we do not concern ourselves with the parts in any of the paths, it comes out that the divergence of this path according to the procedures that we have explained in this chapter is three hundred degrees and fifty-three parts. And that is the width of the moon on the beginning of that night; and it is southern. For the path is surely more than one hundred and eighty.

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