Law 1

The mean rate of movement of the sun in one day (that is, twenty four hours) is fifty nine minutes and eight seconds, in symbols - 59′8″. It follows that its movement in ten days is nine degrees fifty one minutes and twenty three seconds, in symbols - 9°51′23″. It also follows that its movement in a hundred days is ninety eight degrees thirty three minutes and fidty three seconds, in symbols - 98°33′53″. It also follows that remainder of its movement in a thousand days, after you subtract all [multiples of] 360° (as was explained) is two hundred sixty five degrees thirty eight minutes and fifty seconds, in symbols - 265°38′50″. It also follows that the remainder of its movement in ten thousand days is one hundred thirty six degrees twenty eight minutes and twenty seconds, in symbols - 136°28′20″.

And in this way you can multiply and calculate its movement for any number [of days] that you want. Similarly, if you want to make known to you values of its movement for two days, three, four and so on to ten - do it. Similarly, if you want for to have known and ready values of its movement for twenty days, thirty, fourty and so on to a hundred - do it. This is clear and known once you know its movement in 1 day.

And you should have ready and known to you mean movement of the Sun for twenty nine days and for three hundred and fifty four (which is the number of days in the lunar year when its months are "regular" (TODO link), and it is called "regular year"). The reason is: if you have those movement values ready, this calculations of the visibility of the moon will be easy, because there are twenty nine complete days from the night of observation to the night of observation of the following month, and so it is every month: no less than twenty nine days and no more. Since our sole desire in all those calculations is exclusively to determine visibility [of the moon]. And between the night of sighting of this month and night of sighting of the same month next year there is either a regular year or a year and 1 day; and the same every year. Mean movement of the Sun in twenty nine days is twenty eight degrees thirty five minutes and one second, in symbols - 28°35′1″. Its movement in a regular year is three hundred forty eight degrees, fifty five minutes and fifteen seconds, in symbols - 348°55′15″.