One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 13
Sefer Zemanim · The working method for the true position of the sun: a course measured from the apogee, a table of seventeen angles that is added in one half of the circle and subtracted in the other, and an explicit ruling on how much precision to throw away
17
Table entries, from ten degrees to one hundred seventy
180
Degrees of course at which the correction vanishes
119
Minutes, the largest correction the sun ever needs
30
Minutes of course below which you round down
Part 1The three steps, and the sign of the correction
- Mean position, apogee, course. To know the true position of the sun on any day, first calculate its mean position by the methods already explained, then calculate the position of the apogee of the sun, then subtract the apogee from the mean position; the remainder is called the course of the sun. (13:1)
- Subtract below one hundred eighty, add above it. Calculate the angle determined by the course: if the course is less than 180 degrees the angle is subtracted from the mean position, and if the course is more than 180 degrees the angle is added, and the figure remaining is the true position. (13:2)
- At the two extremes there is no correction. If the course is an even 180 degrees or an even 360 degrees there is no angle to add or subtract at all, and the mean position is already the true position. (13:3)
- Both halves of the circle from one table. For a course greater than 180 degrees, subtract the course from 360 and take the angle of the remainder: a course of 200 leaves 160 and therefore 42 minutes, and a course of 300 leaves 60 and therefore 1 degree and 41 minutes. (13:5, 13:6)
RememberThe course is not where the sun is. It is how far the sun has moved from the point farthest from us.
Part 2The table, and the values between its rows
- The shape of the table. A course of ten degrees gives 20 minutes, twenty gives 40 minutes, thirty gives 58 minutes, forty gives 1 degree and 15 minutes, and sixty gives 1 degree and 41 minutes. (13:4)
- The peak sits at ninety and then unwinds. Ninety degrees of course give 1 degree and 59 minutes, the largest angle in the table; one hundred already gives 1 degree and 58 minutes, one hundred fifty gives 1 degree and 1 minute, one hundred seventy gives 21 minutes, and one hundred eighty has no measure. (13:4)
- Interpolate a minute to the degree. A course of 65 degrees sits between 60, whose angle is 1 degree and 41 minutes, and 70, whose angle is 1 degree and 51 minutes; ten minutes across ten degrees means a degree brings a minute, so 65 gives 1 degree and 46 minutes. (13:7)
- The same procedure for units and tens. A course of 67 degrees gives 1 degree and 48 minutes, and the identical procedure is followed for any course carrying both units and tens, for the calculations regarding the moon as well as the sun. (13:8)
RememberThe whole difference between the even sun and the sun we see is under two degrees, and at two points it is nothing.
Part 3A worked date, and what he tells you to discard
- A real date, carried through. For the beginning of Friday night, the fourteenth of Tammuz of that year, the mean position of the sun is 105 degrees 37 minutes 25 seconds and the apogee is 86 degrees 45 minutes 23 seconds, leaving a course of 18 degrees 52 minutes 2 seconds. (13:9)
- Round the course to a whole degree. With regard to the course the minutes are of no consequence: less than thirty and they are disregarded entirely, more than thirty and they count as an additional degree, so this course is treated as 19 degrees and its angle works out to 38 minutes. (13:9)
- Subtract, then read the constellation. Since the course is less than 180 degrees the 38 minutes are subtracted from the mean position, leaving 104 degrees 59 minutes 25 seconds, which places the sun fifteen degrees less 35 seconds into Cancer; seconds need no attention at all in any sighting calculation, and thirty or more are simply counted as a minute. (13:10)
- The method runs in both directions. Since the location of the sun can now be calculated for any date desired, the true date of any equinox or solstice can be calculated too, whether it falls after the established starting point or in years already past. (13:11)
RememberHe built the table to the minute and then ruled, in writing, which of your digits are not allowed to matter.