Halacha
הלכה א
לְפִי שֶׁאָמְרוּ חֲכָמִים שֶׁבּכְלַל דִּבָרִים 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 בִּרְאִיָּה כְּלָל. וּתְחִלַּת חֶשְׁבּוֹן זֶה לֵידַע נְטִיַּת הַמַּזָּלוֹת תְּחִלָּה:
כסף משנה
1.
Since our Sages1Rosh HaShanah 23b, cited in Chapter 2, Halachah 4. 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].
הלכה ב
הָעֲגֻלָּה שֶׁהִיא עוֹבֶרֶת בְּמַחֲצִית הַמַּזָּלוֹת שֶׁבָּהּ מַהֲלָךְ הַשֶּׁמֶשׁ. אֵינָהּ עוֹבֶרֶת בְּאֶמְצַע הָעוֹלָם מֵחֲצִי הַמִּזְרָח לַחֲצִי הַמַּעֲרָב. אֶלָּא נוֹטָה הִיא מֵעַל הַקַּו הַשָּׁוֶה הַמְסַבֵּב בְּאֶמְצַע הָעוֹלָם כְּנֶגֶד צָפוֹן וְדָרוֹם. חֶצְיָהּ נוֹטֶה לַצָּפוֹן וְחֶצְיָהּ נוֹטֶה לַדָּרוֹם:
כסף משנה
2.
The 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.הלכה ג
וּשְׁתֵּי נְקֻדּוֹת יֵשׁ בָּהּ שֶׁפּוֹגַעַת בָּהֶן בַּעֲגֻלַּת הַקַּו הַשָּׁוֶה הַמְסַבֵּב בְּאֶמְצַע הָעוֹלָם. הַנְּקֻדָּה הָאַחַת רֹאשׁ מַזַּל טָלֶה. הַנְּקֻדָּה 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:
כסף משנה
3.
There 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.2In 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.
הלכה ד
וּמֵרֹאשׁ מַזַּל טָלֶה יַתְחִילוּ הַמַּזָּלוֹת לִנְטוֹת מְעַט מְעַט וּלְהִתְרַחֵק מֵעַל הַקַּו הַשָּׁוֶה כְּנֶגֶד הַצָּפוֹן עַד רֹאשׁ סַרְטָן. וְיִהְיֶה רֹאשׁ סַרְטָן רָחוֹק מֵעַל הַקַּו הַשָּׁוֶה לְרוּחַ הַצָּפוֹן שָׁלֹשׁ וְעֶשְׂרִים מַעֲלוֹת וַחֲצִי מַעֲלָה בְּקֵרוּב. וְיַחְזְרוּ הַמַּזָּלוֹת לְהִתְקָרֵב לַקַּו 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 שָׁלֹשׁ וְעֶשְׂרִים מַעֲלוֹת וַחֲצִי מַעֲלָה. וְיַחְזְרוּ הַמַּזָּלוֹת לְהִתְקָרֵב מְעַט מְעַט כְּנֶגֶד הַקַּו הַשָּׁוֶה עַד רֹאשׁ טָלֶה:
כסף משנה
4.
From 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 Sagittarius 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.
הלכה ה
נִמְצָא רֹאשׁ טָלֶה וְרֹאשׁ מֹאזְנַיִם מְסַבֵּב עַל הַקַּו הַשָּׁוֶה. וּלְפִיכָךְ כְּשֶׁתִּהְיֶה הַשֶּׁמֶשׁ בִּשְׁנֵי רָאשִׁים אֵלּוּ לֹא תִּהְיֶה נוֹטָה לֹא לַצָּפוֹן וְלֹא לַדָּרוֹם. וְתִזְרַח בַּחֲצִי מִזְרָח וְתִשְׁקַע בַּחֲצִי מַעֲרָב. וְיִהְיֶה הַיּוֹם וְהַלַּיְלָה שָׁוִין בְּכָל הַיִּשּׁוּב:
כסף משנה
5.
Thus, [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],3I.e., at the vernal [spring] and autumnal equinoxes. 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.הלכה ו
הֲרֵי נִתְבָּרֵר לְךָ שֶׁכָּל מַעֲלָה וּמַעֲלָה מִמַּעֲלוֹת הַמַּזָּלוֹת נוֹטָה לַצָּפוֹן אוֹ לַדָּרוֹם וְיֵשׁ לִנְטִיָּתָהּ שִׁעוּר. (וְרֹב) [וְרֹחַב] הַנְּטִיָּה לֹא תִּהְיֶה יוֹתֵר עַל שָׁלֹשׁ וְעֶשְׂרִים מַעֲלוֹת וַחֲצִי בְּקֵרוּב:
כסף משנה
6.
Thus, 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.הלכה ז
וְאֵלּוּ הֵם הַשִּׁעוּרִים שֶׁל נְטִיּוֹת לְפִי מִנְיַן הַמַּעֲלוֹת שֶׁל מַזָּלוֹת. וְהַתְחָלָה מַתְחֶלֶת מַזַּל טָלֶה. י' מַעֲלוֹת נְטִיָּתָם ד' מַעֲלוֹת. כ' מַעֲלוֹת נְטִיָּתָם ח' מַעֲלוֹת. ל' מַעֲלוֹת נְטִיָּתָם י''א מַעֲלוֹת וּמֶחֱצָה. וּמ' מַעֲלוֹת נְטִיָּתָם ט''ו מַעֲלוֹת. נ' מַעֲלוֹת נְטִיָּתָם י''ח מַעֲלוֹת. ס' מַעֲלוֹת נְטִיָּתָם כ' מַעֲלוֹת. ע' מַעֲלוֹת נְטִיָּתָם כ''ב מַעֲלוֹת. פ' מַעֲלוֹת נְטִיָּתָם כ''ג מַעֲלוֹת. צ' מַעֲלוֹת נְטִיָּתָם כ''ג מַעֲלוֹת וַחֲצִי מַעֲלָה:
כסף משנה
7.
The 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 degrees4I.e., the beginning of the constellation of Cancer. In these ninety degrees, we will have passed through three constellations, Aries, Taurus, and Gemini. will be inclined 23 1/2 degrees.
הלכה ח
וְאִם יִהְיוּ אֲחָדִים בְּמִנְיָן תִּקַּח לָהֶם מְנָתָם מִבֵּין שְׁתֵּי הַנְּטִיּוֹת כְּמוֹ שֶׁבֵּאַרְנוּ בַּשֶּׁמֶשׁ וּבַיָּרֵחַ. כֵּיצַד. חָמֵשׁ מַעֲלוֹת נְטִיָּתָם שְׁתֵּי מַעֲלוֹת. וְאִם הָיָה מִנְיַן הַמַּעֲלוֹת כ''ג נְטִיָּתָם ט' מַעֲלוֹת. וְעַל דֶּרֶךְ זוֹ בְּכָל הָאֲחָדִים שֶׁהֵן עִם הָעֲשָׂרוֹת:
כסף משנה
8.
If 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.5See Chapter 13, Halachah 7, and Chapter 15, Halachah 7.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. This same pattern should be followed whenever calculating a number that has both units and tens.
הלכה ט
וּמֵאַחַר שֶׁתֵּדַע הַנְּטִיָּה שֶׁל מַעֲלוֹת מֵאַחַת עַד צ'. תֵּדַע נְטִיָּתָם כֻּלָּן כְּדֶרֶךְ שֶׁהוֹדַעְנוּךָ בְּרֹחַב הַיָּרֵחַ. שֶׁאִם הָיָה הַמִּנְיָן יֶתֶר עַל צ' עַד ק''פ תִּגְרַע אוֹתוֹ מִק''פ. וְאִם הָיָה יוֹתֵר עַל ק''פ עַד ר''ע תִּגְרַע מִמֶּנּוּ ק''פ. וְאִם הָיָה יוֹתֵר עַל ר''ע עַד ש''ס תִּגְרַע אוֹתוֹ מִש''ס. וְהַנִּשְׁאָר תֵּדַע נְטִיָּתוֹ וְהוּא נְטִיַּת אוֹתוֹ הַמִּנְיָן שֶׁבְּיָדְךָ בְּלֹא גֵּרָעוֹן וְלֹא תּוֹסֶפֶת:
כסף משנה
9.
Since 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.6See Chapter 16, Halachah 13. For if the number is between 90 and 180, the number should be subtracted from 180.7I.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.If the number is between 180 and 270, 180 should be subtracted from the number.8I.e., the southerly inclination beginning from the constellation of Libra parallels exactly the northerly inclination beginning from Aries. If the number is between 270 and 360, the number should be subtracted from 360.9Producing the inverse of the figures mentioned in the previous quadrant. [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.
הלכה י
אִם תִּרְצֶה לֵידַע כַּמָּה מַעֲלוֹת הוּא הַיָּרֵחַ נוֹטֶה מֵעַל הַקַּו הַשָּׁוֶה כְּנֶגֶד צְפוֹן הָעוֹלָם אוֹ כְּנֶגֶד דְּרוֹם הָעוֹלָם. תֵּדַע תְּחִלָּה כַּמָּה נְטִיַּת הַמַּעֲלָה שֶׁהִיא מְקוֹם הַיָּרֵחַ הָאֲמִתִּי וּלְאֵי זֶה רוּחַ הִיא נוֹטָה לַצָּפוֹן אוֹ לַדָּרוֹם. וְתַחֲזֹר וְתַחְשֹׁב וְתוֹצִיא רֹחַב הַיָּרֵחַ הָרִאשׁוֹן וְתִרְאֶה אִם הוּא צְפוֹנִי אוֹ דְּרוֹמִי. אִם נִמְצְאוּ רֹחַב הַיָּרֵחַ וּנְטִיַּת מַעֲלָתוֹ בְּרוּחַ אַחַת כְּגוֹן שֶׁהָיוּ שְׁנֵיהֶם צְפוֹנִים אוֹ דְּרוֹמִיִּים תְּקַבֵּץ שְׁנֵיהֶם. וְאִם נִמְצְאוּ בִּשְׁתֵּי רוּחוֹת כְּגוֹן שֶׁהָיָה הָאֶחָד דְּרוֹמִי וְהָאֶחָד צְפוֹנִי. תִּגְרַע הַמְּעַט מִשְּׁנֵיהֶם מִן הָרַב וְהַנִּשְׁאָר הוּא מֶרְחַק הַיָּרֵחַ מֵעַל הַקַּו הַשָּׁוֶה בְּאוֹתָהּ הָרוּחַ שֶׁהָיָה בָּהּ הָרַב בִּשְׁנֵיהֶם:
כסף משנה
10.
If 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.10E.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. 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.11I.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. The remainder is the [angular] distance of the moon from the equator to the direction in which the larger figure was inclined.
הלכה יא
כֵּיצַד בָּאנוּ לֵידַע כַּמָּה הַיָּרֵחַ נוֹטֶה מֵעַל הַקַּו הַשָּׁוֶה בְּלֵיל הָרְאִיָּה שֶׁהוּא שֵׁנִי לְחֹדֶשׁ אִיָּר מִשָּׁנָה זוֹ. וּכְבָר יָדַעְתָּ שֶׁמַּעֲלַת הַיָּרֵחַ הָיְתָה י''ט מִמַּזַּל שׁוֹר. נְטִיָּתָהּ בַּצָּפוֹן כְּמוֹ י''ח מַעֲלוֹת. וְרֹחַב הַיָּרֵחַ הָיָה בַּדָּרוֹם כְּמוֹ ד' מַעֲלוֹת. תִּגְרַע הַמְּעַט מִן הָרַב יִשָּׁאֵר י''ד מַעֲלוֹת. וְנִמְצָא הַיָּרֵחַ רָחוֹק מֵעַל הַקַּו הַשָּׁוֶה י''ד מַעֲלוֹת לְרוּחַ צָפוֹן. שֶׁהֲרֵי הַמִּנְיָן הָרַב שֶׁהוּא שְׁמוֹנֶה עֶשְׂרֵה מַעֲלוֹת הָיָה צְפוֹנִי. וְכָל חֶשְׁבּוֹן זֶה בְּקֵרוּב בְּלֹא דִּקְדּוּק לְפִי שֶׁאֵינוֹ מוֹעִיל בִּרְאִיָּה:
כסף משנה
11.
What 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.12Actually, the true figure is a few minutes larger.The latitude of the moon is approximately four degrees to the south.13Actually, the true figure is a few minutes less. 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]. All [of the phases] of this calculation are approximations and are not exact, because they are of no consequence regarding the sighting.
הלכה יב
אִם תִּרְצֶה לֵידַע לְאֵי זוֹ רוּחַ מֵרוּחוֹת הָעוֹלָם יֵרָאֶה הַיָּרֵחַ נוֹטֶה. תַּחְשֹׁב וְתֵדַע מֶרְחַקּוֹ מֵעַל הַקַּו הַשָּׁוֶה. אִם יִהְיֶה עַל הַקַּו הַשָּׁוֶה אוֹ קָרוֹב מִמֶּנּוּ בִּשְׁתַּיִם אוֹ שָׁלֹשׁ מַעֲלוֹת בַּצָּפוֹן אוֹ בַּדָּרוֹם. יֵרָאֶה מְכֻוָּן כְּנֶגֶד אֶמְצַע מַעֲרָב וְתֵרָאֶה פְּגִימָתוֹ מְכֻוֶּנֶת כְּנֶגֶד מִזְרַח הָעוֹלָם בְּשָׁוֶה:
כסף משנה
12.
If 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,14The variance of two or three degrees will not produce a difference that is of consequence. it will appear due west and its crescent will appear to be pointed due east.הלכה יג
וְאִם יִהְיֶה רָחוֹק מֵעַל הַקַּו הַשָּׁוֶה לִצְפוֹן הָעוֹלָם. יֵרָאֶה בֵּין מַעֲרַב הָעוֹלָם וּבֵין צְפוֹנוֹ. וְתֵרָאֶה פְּגִימָתוֹ נוֹטָה מִכְּנֶגֶד מִזְרַח הָעוֹלָם כְּנֶגֶד דְּרוֹם הָעוֹלָם:
כסף משנה
13.
If [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.הלכה יד
וְאִם 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:
כסף משנה
14.
If [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.הלכה טו
וּמֵחֲקִירַת הָעֵדִים שֶׁאוֹמְרִין לָהֶם כַּמָּה הָיָה גָּבוֹהַּ. וְדָבָר זֶה יִוָּדַע מִקֶּשֶׁת הָרְאִיָּה. שֶׁבִּזְמַן שֶׁתִּהְיֶה קֶשֶׁת הָרְאִיָּה קְצָרָה יֵרָאֶה הַיָּרֵחַ כְּאִלּוּ הוּא קָרוֹב מִן הָאָרֶץ. וּבִזְמַן שֶׁתִּהְיֶה אֲרֻכָּה יֵרָאֶה גָּבוֹהַּ מֵעַל הָאָרֶץ. וּלְפִי אֹרֶךְ קֶשֶׁת הָרְאִיָּה לְפִי גָּבְהוֹ מֵעַל הָאָרֶץ בִּרְאִיַּת הָעֵינַיִם:
כסף משנה
15.
Among 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.הלכה טז
הֲרֵי בֵּאַרְנוּ חֶשְׁבּוֹנוֹת כָּל הַדְּרָכִים שֶׁצְּרִיכִין לָהֶם בִּידִיעַת הָרְאִיָּה וּבַחֲקִירַת הָעֵדִים. כְּדֵי שֶׁיִּהְיֶה הַכּל יָדוּעַ לַמְּבִינִים וְלֹא יֶחְסְרוּ דֶּרֶךְ מִדַּרְכֵי הַתּוֹרָה וְלֹא יְשׁוֹטְטוּ לְבַקֵּשׁ אַחֲרֶיהָ בִּסְפָרִים אֲחֵרִים. (ישעיה לד טז) "דִּרְשׁוּ מֵעַל סֵפֶר ה'" וְקִרְאוּ, אַחַת מֵהֵנָּה לֹא נֶעְדָּרָה: סָלִיק הִלְכוֹת קִדּוּשׁ הַחֹדֶשׁ
כסף משנה