Rambam - 1 Chapter a Day - Daily Torah Study

1Since our Sages1 said that among the questions posed to the witnesses in order to verify their testimony was “In which direction was the crescent of the moon inclined,” I feel that it is appropriate to explain how this factor can be calculated. My statements will not be exact, because this knowledge is of no consequence regarding the actual sighting of the moon. The starting point of these calculations is to know the degree of inclination of the constellations’ position.אלְפִי שֶׁאָמְרוּ חֲכָמִים, שֶׁבִּכְלַל דְּבָרִים שֶׁהָיוּ בּוֹדְקִין בָּהֶן אֶת הָעֵדִים, אוֹמְרִין לָהֶן 'לְהֵיכָן הָיָה הַיָּרֵחַ נוֹטֶה?' - כָּשֵׁר בְּעֵינַי לְהוֹדִיעַ דֶּרֶךְ חֶשְׁבּוֹן דָּבָר זֶה. וְאֵין אֲנִי מְדַקְדֵּק בּוֹ, לְפִי שֶׁאֵינוֹ מוֹעִיל בָּרְאִיָּה כְּלָל. וּתְחִלַּת חֶשְׁבּוֹן זֶה, לֵידַע נְטִיַּת הַמַּזָּלוֹת תְּחִלָּה.

2The orbit of the sun that passes through the center of the sphere of the constellations does not pass directly through the center of the earth from east to west. Instead, it is inclined above the equator which passes through the center of the earth, slightly to the north and to the south. Half of it is northerly in inclination and half is southerly in inclination.בהָעֲגֻלָּה שֶׁהִיא עוֹבֶרֶת בְּמַחֲצִית הַמַּזָּלוֹת שֶׁבָּהּ מְהַלֵּךְ הַשֶּׁמֶשׁ, אֵינָהּ עוֹבֶרֶת בְּאֶמְצַע הָעוֹלָם מֵחֲצִי הַמִּזְרָח לַחֲצִי הַמַּעְרָב, אֶלָא נוֹטָה הִיא מֵעַל הַקַּו הַשָּׁוֶה הַמְּסַבֵּב בְּאֶמְצַע הָעוֹלָם, כְּנֶגֶד צָפוֹן וְדָרוֹם - חֶצְיָהּ נוֹטָה לַצָּפוֹן וְחֶצְיָהּ נוֹטָה לַדָּרוֹם.

3There are two points at which the orbit of the sun intersects the equator, which passes through the center of the earth: The first point is the beginning of the constellation of Aries, and the second point, opposite to the first, is the beginning of the constellation of Libra. Thus, there are six constellations whose positions are inclined to the north, those between the beginning of the constellation of Aries and the end of the constellation of Virgo. And there are six whose positions are inclined to the south, those between the beginning of the constellation of Libra and the end of the constellation of Pisces.2גוּשְׁתֵּי נְקֻדּוֹת יֵשׁ בָּהּ שֶׁפּוֹגַעַת בָּהֶן בַּעֲגֻלַּת הַקַּו הַשָּׁוֶה הַמְּסַבֵּב בְּאֶמְצַע הָעוֹלָם - הַנְּקֻדָּה הָאַחַת רֹאשׁ מַזַּל טָלֶה, וְהַנְּקֻדָּה הַשְּׁנִיָּה שֶׁכְּנֶגְדָּהּ רֹאשׁ מַזַּל מֹאזְנַיִם. וְנִמְצְאוּ שִׁשָּׁה מַזָּלוֹת נוֹטוֹת לַצָּפוֹן, מִתְּחִלַּת טָלֶה עַד סוֹף בְּתוּלָה; וְשִׁשָּׁה נוֹטוֹת לַדָּרוֹם, מִתְּחִלַּת מַזַּל מֹאזְנַיִם עַד סוֹף מַזַּל דָּגִים.

4From the beginning of the constellation of Aries, the constellations’ positions begin to be inclined slightly and diverge from the equator in a northerly direction until the beginning of the constellation of Cancer. The beginning of the constellation of Cancer is approximately twenty-three and one half degrees north of the equator. Afterwards, the constellations begin to proceed toward the equator slowly until the beginning of the constellation of Libra, which is positioned on the equator. From the beginning of the constellation of Libra, the constellations’ positions begin to be inclined slightly and diverge from the equator in a southerly direction until the beginning of the constellation of Sagittarius. The beginning of the constellation of Capricorn is approximately twenty-three and one half degrees south of the equator. Afterwards, the constellations begin to proceed toward the equator slowly until the beginning of the constellation of Aries.דוּמֵרֹאשׁ מַזַּל טָלֶה יַתְחִילוּ הַמַּזָּלוֹת לִנְטוֹת מְעַט מְעַט, וּלְהִתְרַחֵק מֵעַל הַקַּו הַשָּׁוֶה כְּנֶגֶד הַצָּפוֹן עַד רֹאשׁ סַרְטָן, וְיִהְיֶה רֹאשׁ סַרְטָן רָחוֹק מֵעַל הַקַּו הַשָּׁוֶה לְרוּחַ צָפוֹן, שָׁלוֹשׁ וְעֶשְׂרִים מַעֲלוֹת וַחֲצִי מַעֲלָה בְּקֵרוּב. וְיַחְזְרוּ הַמַּזָּלוֹת לְהִתְקָרֵב לְקַּו הַשָּׁוֶה מְעַט מְעַט, עַד רֹאשׁ מֹאזְנַיִם שֶׁהוּא עַל הַקַּו הַשָּׁוֶה. וּמֵרֹאשׁ מֹאזְנַיִם יַתְחִילוּ לִנְטוֹת וּלְהִתְרַחֵק כְּנֶגֶד רוּחַ דָּרוֹם, עַד רֹאשׁ גְּדִי, וְיִהְיֶה רֹאשׁ גְּדִי רָחוֹק מֵעַל הַקַּו הַשָּׁוֶה לְרוּחַ דָּרוֹם, שָׁלוֹשׁ וְעֶשְׂרִים מַעֲלוֹת וַחֲצִי מַעֲלָה. וְיַחְזְרוּ הַמַּזָּלוֹת לְהִתְקָרֵב מְעַט מְעַט כְּנֶגֶד הַקַּו הַשָּׁוֶה, עַד רֹאשׁ טָלֶה.

5Thus, in their daily orbits, the beginning of the constellation of Aries and the beginning of the constellation of Libra revolve on the equator. Therefore, when the sun is positioned in the beginning of these constellations,3 it will not be inclined either to the north or to the south. It will rise due east and set due west, and the daytime and the nighttime hours will be equal throughout the world.הנִמְצָא רֹאשׁ טָלֶה וְרֹאשׁ מֹאזְנַיִם, מְסַבֵּב עַל הַקַּו הַשָּׁוֶה. וּלְפִיכָךְ כְּשֶׁתִּהְיֶה הַשֶּׁמֶשׁ בִּשְׁנֵי רָאשִׁים אֵלּוּ, לֹא תִהְיֶה נוֹטָה לֹא לַצָּפוֹן וְלֹא לַדָּרוֹם, וְתִזְרַח מֵחֲצִי מִזְרָח וְתִשְׁקַע בַּחֲצִי מַעֲרָב, וְיִהְיֶה הַיּוֹם וְהַלַּיְלָה שָׁוִין בְּכָל הַיִּשּׁוּב.

6Thus, it should be clear to you that each of the degrees in the sphere of the constellations is inclined to the north or to the south, and that there is a specific measure to their inclination. The greatest inclination will be no more than approximately twenty-three and half degrees.והֲרֵי נִתְבָּרֵר לְךָ שֶׁכָּל מַעֲלָה וּמַעֲלָה מִמַּעֲלוֹת הַמַּזָּלוֹת נוֹטָה לַצָּפוֹן אוֹ לַדָּרוֹם, וְיֵשׁ לִנְטִיָּתָהּ שִׁעוּר; וְרֹחַב הַנְּטִיָּה, לֹא תִהְיֶה יוֹתֵר עַל שָׁלוֹשׁ וְעֶשְׂרִים מַעֲלוֹת וְחֵצִי בְּקֵרוּב.

7The following represent the extent of inclination from the equator vis-a-vis the number of degrees in the sphere of the constellations. Beginning with the constellation of Aries: A point located at 10 degrees in the celestial sphere will be inclined 4 degrees from the equator. A point located at 20 degrees will be inclined 8 degrees. A point located at 30 degrees will be inclined 11 1/2 degrees. A point located at 40 degrees will be inclined 15 degrees. A point located at 50 degrees will be inclined 18 degrees. A point located at 60 degrees will be inclined 20 degrees. A point located at 70 degrees will be inclined 22 degrees. A point located at 80 degrees will be inclined 23 degrees. A point located at 90 degrees4 will be inclined 23 1/2 degrees.זוְאֵלּוּ הֵם הַשִׁעוּרים שֶׁל נְטִיּוֹת, לְפִי מִנְיַן הַמַּעֲלוֹת שֶׁל מַזָּלוֹת, וְהַהַתְחָלָה מִתְּחִלַּת מַזַּל טָלֶה: עֶשֶׂר מַעֲלוֹת, נְטִיָּתָם אַרְבַּע מַעֲלוֹת; עֶשְׂרִים מַעֲלוֹת, נְטִיָּתָם שְׁמוֹנֶה מַעֲלוֹת; שְׁלוֹשִׁים מַעֲלוֹת, נְטִיָּתָם אַחַת עֶשְׂרֵה מַעֲלוֹת וּמֶחְצָה; אַרְבָּעִים מַעֲלוֹת, נְטִיָּתָם חָמֵשׁ עֶשְׂרֵה מַעֲלוֹת; חֲמִשִּׁים מַעֲלוֹת, נְטִיָּתָם שְׁמוֹנֶה עֶשְׂרֵה מַעֲלוֹת; שִׁשִּׁים מַעֲלוֹת, נְטִיָּתָם עֶשְׂרִים מַעֲלוֹת; שִׁבְעִים מַעֲלוֹת, נְטִיָּתָם שְׁתַּיִם וְעֶשְׂרִים מַעֲלוֹת; שְׁמוֹנִים מַעֲלוֹת, נְטִיָּתָם שָׁלוֹשׁ וְעֶשְׂרִים מַעֲלוֹת; תִּשְׁעִים מַעֲלוֹת, נְטִיָּתָם שָׁלוֹשׁ וְעֶשְׂרִים מַעֲלוֹת וַחֲצִי מַעֲלָה.

8If the number of degrees also includes units, you should calculate their degree of inclination by taking an average between the two figures, as was explained with regard to the determination of the position of the sun and the moon.5חוְאִם יִהְיוּ אֲחָדִים בַּמִּנְיָן, תִּקַּח לָהֶם מְנָתָם מִבֵּין שְׁתֵּי הַנְּטִיּוֹת, כְּמוֹ שֶׁבֵּאַרְנוּ בַּשֶּׁמֶשׁ וּבַיָּרֵחַ.

What is implied? Five degrees will be inclined 2 degrees. If the number of degrees in the celestial sphere is twenty-three, the inclination from the equator will be nine degrees.כֵּיצַד? חָמֵשׁ מַעֲלוֹת, נְטִיָּתָם שְׁתֵּי מַעֲלוֹת; וְאִם הָיָה מִנְיַן הַמַּעֲלוֹת שָׁלוֹשׁ וְעֶשְׂרִים, נְטִיָּתָם תֵּשַׁע מַעֲלוֹת.

This same pattern should be followed whenever calculating a number that has both units and tens.וְעַל דֶּרֶךְ זוֹ, בְּכָל הָאֲחָדִים שֶׁעִם הָעֲשָׂרוֹת.

9Since you know the extent of the inclination of all the degrees from one until ninety, you will be able to calculate the degree of inclination of the entire celestial sphere according to the method of calculation explained with regard to the moon’s latitude.6טוּמֵאַחַר שֶׁתֵּדַע הַנְּטִיָּה שֶׁל מַעֲלוֹת מֵאַחַת עַד תִּשְׁעִים, תֵּדַע נְטִיַּת כֻּלָּן כְּדֶרֶךְ שֶׁהוֹדַעְנוּךָ בְּרֹחַב הַיָּרֵחַ.

For if the number is between 90 and 180, the number should be subtracted from 180.7 If the number is between 180 and 270, 180 should be subtracted from the number.8 If the number is between 270 and 360, the number should be subtracted from 360.9שֶׁאִם הָיָה הַמִּנְיָן יוֹתֵר עַל תִּשְׁעִים עַד מֵאָה וּשְׁמוֹנִים, תִּגְרַע אוֹתוֹ מִמֵּאָה וּשְׁמוֹנִים; וְאִם הָיָה יוֹתֵר עַל מֵאָה וּשְׁמוֹנִים עַד מָאתַיִם וְשִׁבְעִים, תִּגְרַע מִמֶּנּוּ מֵאָה וּשְׁמוֹנִים; וְאִם הָיָה יוֹתֵר עַל מָאתַיִם וְשִׁבְעִים עַד שְׁלוֹשׁ מֵאוֹת וְשִׁשִּׁים, תִּגְרַע אוֹתוֹ מִשְּׁלוֹשׁ מֵאוֹת וְשִׁשִּׁים.

After these subtractions have been made, you will know the degree of inclination of the remainder, for it is the degree of inclination of the numbers mentioned previously without any addition or subtraction.וְהַנִּשְׁאָר, תֵּדַע נְטִיָּתוֹ, וְהוּא נְטִיַּת אוֹתוֹ הַמִּנְיָן שֶׁבְּיָדְךָ, בְּלֹא גֵּרָעוֹן וְלֹא תוֹסֶפֶת.

10If you desire to know the number of degrees by which the moon’s position deviates from the equator to the north or to the south, you should follow this procedure: Calculate the inclination of the degree in the celestial sphere that will be the true position, and see if its inclination is northerly or southerly. Afterwards, calculate the moon’s first latitude and see whether it is northerly or southerly. If the moon’s latitude and the inclination of the degree in the celestial sphere where it is located have the same direction, then they should be added together.10 If they are in different directions—i.e., one is southerly and one is northerly—the smaller figure should be subtracted from the larger one.11 The remainder is the angular distance of the moon from the equator to the direction in which the larger figure was inclined.יאִם תִּרְצֶה לֵידַע כַּמָּה מַעֲלוֹת הוּא הַיָּרֵחַ נוֹטֶה מֵעַל הַקַּו הַשָּׁוֶה כְּנֶגֶד צְפוֹן הָעוֹלָם אוֹ כְּנֶגֶד דְּרוֹם הָעוֹלָם - תֵּדַע תְּחִלָּה כַּמָּה נְטִיַּת הַמַּעֲלָה שֶׁהִיא מָקוֹם הַיָּרֵחַ הָאֲמִתִּי, וּלְאֵיזוֹ רוּחַ הִיא נוֹטָה לַצָּפוֹן אוֹ לַדָּרוֹם; וְתַחְזֹר וּתְחַשֵּׁב וְתוֹצִיא רֹחַב הַיָּרֵחַ הָרִאשׁוֹן, וְתִרְאֶה אִם הוּא צְפוֹנִי אוֹ דְּרוֹמִי. אִם נִמְצְאוּ רֹחַב הַיָּרֵחַ וּנְטִיַּת מַעֲלָתוֹ בְּרוּחַ אַחַת, כְּגוֹן שֶׁהָיוּ שְׁנֵיהֶם צְפוֹנִיִּים אוֹ דְּרוֹמִיִּים - תְּקַבֵּץ שְׁנֵיהֶם; וְאִם נִמְצְאוּ בִּשְׁתֵּי רוּחוֹת, כְּגוֹן שֶׁהָיָה הָאֶחָד דְּרוֹמִי וְהָאֶחָד צְפוֹנִי - תִּגְרַע הַמְּעַט מִשְּׁנֵיהֶם מִן הָרַב, וְהַנִּשְׁאָר הוּא מֶרְחָק הַיָּרֵחַ מֵעַל הַקַּו הַשָּׁוֶה בְּאוֹתָהּ הָרוּחַ שֶׁהָיָה בָּהּ הָרַב מִשְּׁנֵיהֶם.

11What is implied? Let us say that we are trying to calculate the degree of inclination of the moon from the equator on the night of sighting, the second day of the month of Iyar of this year. You have already established that the angle in the celestial sphere at which the moon was located is the nineteenth degree of the constellation of Taurus. Thus, its inclination to the north will be approximately 18 degrees.12 The latitude of the moon is approximately four degrees to the south.13 After you subtract the lesser figure from the larger one, the position of the moon will be fourteen degrees to the north of the equator, for the largest figure is the eighteen degrees north at which the moon’s true position was located.יאכֵּיצַד? בָּאנוּ לֵידַע כַּמָּה הַיָּרֵחַ נוֹטֶה מֵעַל הַקַּו הַשָּׁוֶה בְּלֵיל הָרְאִיָּה שֶׁהוּא שֵׁנִי לְחֹדֶשׁ אִיָּר מִשָּׁנָה זוֹ - וּכְבָר יָדַעְתָּ שֶׁמַּעֲלַת הַיָּרֵחַ הָיְתָה תְּשַׁע עֶשְׂרֵה מִמַּזַּל שׁוֹר, נְטִיָּתָהּ בַּצָּפוֹן כְּמוֹ שְׁמוֹנֶה עֶשְׂרֵה מַעֲלוֹת, וְרֹחַב הַיָּרֵחַ הָיָה בַּדָּרוֹם כְּמוֹ אַרְבַּע מַעֲלוֹת, תִּגְרַע הַמְּעַט מִן הָרַב, יִשָּׁאֵר אַרְבַּע עֶשְׂרֵה מַעֲלוֹת. וְנִמְצָא הַיָּרֵחַ רָחוֹק מֵעַל הַקַּו הַשָּׁוֶה אַרְבַּע עֶשְׂרֵה מַעֲלוֹת לְרוּחַ צָפוֹן, שֶׁהֲרֵי הַמִּנְיָן הָרַב שֶׁהוּא שְׁמוֹנֶה עֶשְׂרֵה מַעֲלוֹת הָיָה צְפוֹנִי.

All of the phases of this calculation are approximations and are not exact, because they are of no consequence regarding the sighting.וְכָל חֶשְׁבּוֹן זֶה בְּקֵרוּב בְּלֹא דִּקְדּוּק, לְפִי שֶׁאֵינוֹ מוֹעִיל בָּרְאִיָּה.

12If you desire to know the direction to which the moon will appear to be inclined when sighted, it is governed by the following principles: Calculate the moon’s angular distance from the equator. If it is located on the equator or within two or three degrees to the north or to the south,14 it will appear due west and its crescent will appear to be pointed due east.יבאִם תִּרְצֶה לֵידַע לְאֵיזוֹ רוּחַ מֵרוּחוֹת הָעוֹלָם יֵרָאֶה הַיָּרֵחַ נוֹטֶה, תְּחַשֵּׁב וְתֵדַע מֶרְחָקוֹ מֵעַל הַקַּו הַשָּׁוֶה: אִם יִהְיֶה עַל הַקַּו הַשָּׁוֶה אוֹ קָרוֹב מִמֶּנּוּ בִּשְׁתַּיִם שָׁלוֹשׁ מַעֲלוֹת, בַּצָּפוֹן אוֹ בַּדָּרוֹם - יֵרָאֶה מְכֻוָּן כְּנֶגֶד אֶמְצַע מַעֲרָב, וְתֵרָאֶה פְּגִימָתוֹ מְכֻוֶּנֶת כְּנֶגֶד מִזְרַח הָעוֹלָם בְּשָׁוֶה.

13If the moon is inclined to the north of the equator, it will appear in the northwest, and its crescent will appear to be pointed southeast.יגוְאִם יִהְיֶה רָחוֹק מֵעַל הַקַּו הַשָּׁוֶה לִצְפוֹן הָעוֹלָם - יֵרָאֶה בֵּין מַעֲרַב הָעוֹלָם וּבֵין צְפוֹנוֹ, וְתֵרָאֶה פְּגִימָתוֹ נוֹטָה מִכְּנֶגֶד מִזְרַח הָעוֹלָם כְּנֶגֶד דְּרוֹם הָעוֹלָם.

14If the moon is inclined to the south of the equator, it will appear in the southwest, and its crescent will appear to be pointed northeast. To the extent of the moon’s distance from the equator, its inclination will increase.ידוְאִם הָיָה רָחוֹק מֵעַל הַקַּו הַשָּׁוֶה לִדְרוֹם הָעוֹלָם - יֵרָאֶה בֵּין מַעֲרַב הָעוֹלָם וּבֵין דְּרוֹמוֹ, וְתֵרָאֶה פְּגִימָתוֹ נוֹטָה מִכְּנֶגֶד מִזְרַח הָעוֹלָם כְּנֶגֶד צְפוֹן הָעוֹלָם. וּלְפִי רֹב הַמֶּרְחָק, וּלְפִי רֹב הַנְּטִיָּה.

15Among the other dimensions of the examination of the witnesses is the question: “How high in the sky did the moon appear?” This factor can be determined by the arc of sighting. If the arc is short, the moon will appear close to the earth, and when it is long, it will appear high above the earth. The length of the arc of sighting will determine the height at which the moon will appear above the earth to the witnesses.טווּמֵחֲקִירַת הָעֵדִים, שֶׁאוֹמְרִין לָהֶם 'כַּמָּה הָיָה גָּבוֹהַּ'? וְדָבָר זֶה יִוָּדַע מִקֶּשֶׁת הָרְאִיָּה - שֶׁבִּזְמַן שֶׁתִּהְיֶה קֶשֶׁת הָרְאִיָּה קְצָרָה, יֵרָאֶה הַיָּרֵחַ כְּאִלּוּ הוּא קָרוֹב מִן הָאָרֶץ, וּבִזְמָן שֶׁתִּהְיֶה אֲרוּכָה, יֵרָאֶה גָּבוֹהַּ מֵעַל הָאָרֶץ. וּלְפִי אֹרֶךְ קֶשֶׁת הָרְאִיָּה, לְפִי גָּבְהוֹ מֵעַל הָאָרֶץ בִּרְאִיַּת הָעֵינַיִם.

16Thus, we have explained all the calculations necessary for the sighting of the moon and the examination of the witnesses, so that everything will be comprehensible to men of understanding, and they will not lack awareness of any of the Torah’s paths. Therefore, they will not venture forth in search of it in other texts. “Seek out of the book of God, read it. None of these will be lacking” Isaiah 34:16.15טזהֲרֵי בֵּאַרְנוּ חֶשְׁבּוֹנוֹת כָּל הַדְּרָכִים שֶׁצְּרִיכִין לָהֶם בִּידִיעַת הָרְאִיָּה, וּבַחֲקִירַת הָעֵדִים, כְּדֵי שֶׁיִּהְיֶה הַכֹּל יָדוּעַ לַמְּבִינִים, וְלֹא יַחְסְרוּ דֶרֶךְ מִדַּרְכֵי הַתּוֹרָה וְלֹא יְשׁוֹטְטוּ לְבַקֵּשׁ אַחֲרֶיהָ בִּסְפָרִים אֲחֵרִים. "דִּרְשׁוּ מֵעַל סֵפֶר ה' וּקְרָאוּ אַחַת מֵהֵנָּה לֹא נֶעְדָּרָה" (ישעיהו לד, טז).

Footnotes

Rosh HaShanah 23b, cited in Chapter 2, Halachah 4.

In our previous notes, we explained that the constellations from Capricorn to Gemini were northerly inclined. There is no contradiction between those statements and the statements above; the difference is in the definition of the word “inclined.” In the present context, the Rambam is using the word “inclined” to refer to the position of the ecliptic as it passes through these constellations: Is it located above or below the equator, and what is the extent of its variance from the equator?
Previously, we had used the word “inclined” to refer to the direction of the path of movement of the stars in the sky. In the constellations from Capricorn to Gemini, as the constellations move in their orbit, they will be moving northward. Conversely, in the constellations from Cancer to Sagittarius, as the constellations move in their orbit, they will be moving southward.
The inclination of the constellations can be observed by a careful observer with a field compass. In the spring and in the fall, the sun rises due east and sets due west. In the summer (i.e., when the sun is located in the constellations from Taurus to Virgo), it rises in the northeast and sets in the northwest. In the winter (i.e., when the sun is located in the constellations from Scorpio to Pisces), it rises in the southeast and sets in the southwest. Throughout the year, these constellations rise and set in the place where the sun rises and sets when it is in these constellations.

I.e., at the vernal [spring] and autumnal equinoxes.

I.e., the beginning of the constellation of Cancer. In these ninety degrees, we will have passed through three constellations, Aries, Taurus, and Gemini.

See Chapter 13, Halachah 7, and Chapter 15, Halachah 7.

See Chapter 16, Halachah 13.

I.e., 110° has the same degree of inclination as 70°. For the angle of inclination proceeds in an even-balanced arc with 90 degrees as its center.

I.e., the southerly inclination beginning from the constellation of Libra parallels exactly the northerly inclination beginning from Aries.

Producing the inverse of the figures mentioned in the previous quadrant.

10.

E. g., if they are both northerly, the moon’s latitude will cause it to appear further north than the constellation in which its true position is located.

11.

I.e., if the moon’s true position is located in a northerly position and its latitude is southerly, the latitude should be subtracted from the angular distance of its true position.

12.

Actually, the true figure is a few minutes larger.

13.

Actually, the true figure is a few minutes less.

14.

The variance of two or three degrees will not produce a difference that is of consequence.

15.

With this halachah, the Rambam explains one of his motives for the inclusion of this section in the Mishneh Torah: so that a serious student would not have to resort to other texts, particularly those of the gentile scientific community, to obtain this knowledge. In this manner, he affirms one of the purposes for the Mishneh Torah stated in its introduction, to provide a text that includes every dimension of Jewish law.

Rambam - 1 Chapter a Day

Kiddush HaChodesh - Chapter 19

Kiddush HaChodesh - Chapter 19