019 - הִלְכוֹת קִדּוּשׁ הַחֹדֶשׁ פֵּרֶק יט

Laws of Sanctifying the New Moon, Chapter 19

1. Since the Sages said that among the matters with which they would examine the witnesses, they would ask them, “To which direction was the moon inclined?”—it is proper in my eyes to explain the method of calculating this matter. However, I will not be precise about it, since it is of no use for the actual sighting. The beginning of this calculation is to know the inclination of the constellations first.

2. The circle that passes through the middle of the constellations, along which the sun travels, does not pass through the center of the world from the midpoint of the east to the midpoint of the west. Rather, it is inclined above the equator that encircles the center of the world, toward the north and the south—half of it inclines toward the north, and half of it inclines toward the south.

3. There are two points on it where it intersects the circle of the equator that encircles the center of the world: one point is the beginning of the constellation Aries, and the other point opposite it is the beginning of the constellation Libra. Thus, six constellations incline toward the north, from the beginning of Aries until the end of Virgo; and six incline toward the south, from the beginning of Libra until the end of Pisces.

4. From the beginning of Aries, the constellations begin to incline gradually and to move away from the equator toward the north, until the beginning of Cancer; the beginning of Cancer is distant from the equator toward the north by approximately thirty-three and a half degrees. Then the constellations begin to approach the equator gradually, until the beginning of Libra, which is on the equator. From the beginning of Libra, they begin to incline and move away toward the south, until the beginning of Capricorn; the beginning of Capricorn is distant from the equator toward the south by thirty-three and a half degrees. Then the constellations begin to approach the equator gradually, until the beginning of Aries.

5. Thus, the beginning of Aries and the beginning of Libra revolve on the equator; therefore, when the sun is at these two points, it is not inclined either to the north or to the south, and it rises from the midpoint of the east and sets at the midpoint of the west, and the day and the night are equal in all inhabited places.

6. It has thus been clarified for you that each and every degree of the degrees of the constellations inclines either to the north or to the south, and its inclination has a measure; and the width of the inclination will not be more than thirty-three and a half degrees approximately.

7. These are the measures of their inclinations, according to the number of degrees of the constellations, beginning from the start of Aries:

Ten degrees—their inclination is four degrees;

Twenty degrees—their inclination is eight degrees;

Thirty degrees—their inclination is eleven and a half degrees;

Forty degrees—their inclination is fifteen degrees;

Fifty degrees—their inclination is eighteen degrees;

Sixty degrees—their inclination is twenty degrees;

Seventy degrees—their inclination is twenty-two degrees;

Eighty degrees—their inclination is thirty-three degrees;

Ninety degrees—their inclination is thirty-three and a half degrees.

8. If the number is not a multiple of ten, take its proportion between the two inclinations, as we explained regarding the sun and the moon. How so? Five degrees—their inclination is two degrees; and if the number of degrees is thirty-three, their inclination is nine degrees. And in this manner, for all numbers that are not multiples of ten.

Laws of Sanctifying the New Month, Chapter 19

9. Once you know the inclination of the degrees from one up to ninety, you will know the inclination of all of them in the same way that we have explained to you regarding the latitude of the moon: If the number is more than ninety up to one hundred and eighty, subtract it from one hundred and eighty; and if it is more than one hundred and eighty up to two hundred and seventy, subtract one hundred and eighty from it; and if it is more than two hundred and seventy up to three hundred and sixty, subtract it from three hundred and sixty. What remains is the inclination, and this is the inclination of that number in your hand, without any subtraction or addition.

10. If you wish to know how many degrees the moon inclines above the equator toward the north of the world or toward the south of the world, first determine the degree of inclination at the true position of the moon, and to which direction it inclines—north or south. Then recalculate and determine the first latitude of the moon, and see whether it is to the north or to the south. If both the latitude of the moon and the inclination of its degree are in the same direction, such as both being north or both being south, add them together. If they are in opposite directions, such as one being south and the other north, subtract the lesser from the greater, and the remainder is the distance of the moon above the equator in the direction of the greater of the two.

11. How is this? We want to know how much the moon inclines above the equator on the night of the sighting, which is the second of the month of Iyar of this year. You already know that the degree of the moon was nineteen in the constellation of Taurus, its inclination to the north was about eighteen degrees, and the latitude of the moon was to the south about four degrees. Subtract the lesser from the greater, and fourteen degrees remain. Thus, the moon is found to be fourteen degrees distant above the equator toward the north, since the greater number, which is eighteen degrees, was to the north. All of this calculation is approximate and not exact, since it is not necessary for the sighting.

12. If you wish to know toward which direction of the world the moon will appear to incline, calculate and determine its distance above the equator. If it is on the equator or within two or three degrees to the north or to the south, it will appear directly opposite the center of the west, and its defect will appear directly opposite the east of the world, evenly.

13. If it is distant above the equator toward the north of the world, it will appear between the west of the world and its north, and its defect will appear inclined from directly opposite the east of the world toward the south of the world.

14. If it is distant above the equator toward the south of the world, it will appear between the west of the world and its south, and its defect will appear inclined from directly opposite the east of the world toward the north of the world. The greater the distance, the greater the inclination.

15. From the questioning of the witnesses, when they are asked how high it was. This can be determined from the arc of vision: when the arc of vision is short, the moon appears as if it is close to the earth; when it is long, it appears high above the earth. According to the length of the arc of vision, so is its height above the earth as seen by the eyes.

16. We have now explained the calculations of all the methods needed for knowing the sighting and for the questioning of the witnesses, so that everything will be known to those who understand, and none of the ways of the Torah will be lacking, and they will not need to search for it in other books—"Seek out from the Book of the L‑rd and read; not one of them will be missing" (Yeshayahu 34:16).