Arithmetic calendar.

Chapter 5: Introduction.

Laws 1-2: Introduction; discrepancy with observations: -1…+1 day (+1 - very rare).
Law 2: Fixed Rosh Hodesh: sighting of the Moon can be +/- 1 day; +2 - extremely rare.
Law 3: When started.
Laws 4-12: Second day of festivals.
Law 13: Conclusion.

Chapter 6: Conjunction. Lunar month and year. Leap year cycle.

Law 1: "Molad" - approximate conjunction (Sun. Moon and Earth on the same line).
Law 2: day = 24 hours; 1 hour = 1080 parts.
Law 3: Lunar month (between conjunctions) = 29d12h793p.
Law 4: Lunar year (12 lunar months) = 354d8h876p = 354d8h48m40s; Leap lunar year (13 lunar months) = 383d21h589p; Solar year = 365d6h (see also 9:1, 10:6); longer than the lunar year by 10d21h204p.
Law 5: Lunar month % 7 = 1d12h793p; lunar year % 7 = 4d8h876p; leap year % 7 = 5d21h589p.
Law 7: if molad Nisan - Sunday, 5h107p after sunrise, next month - Iyar: Tuesday night, 5h900p.
Law 8: First conjunction - Tishrei, year #1: Monday, 5h204p (just subtract % from the next one :)) Conjunction of Rosh Hashono of Adam's creation (year #2, see Shmita and Yovel 10:2): Friday, 6h.
Law 9: We do not need the number of days, just the remainders.
Law 10: 19 year cycle (12+7 leap); because the difference between 19 solar years and the cycle is less than a day: 1h485p.
Law 11: Leap years: 3,6,8,11,14,17,19.
Law 12: cycle % 7 = 2d16h595p.

Chapter 7: New Year corrections.

Law 1: Rosh Hashono gets pushed off from Sunday, Wednesday, Friday.
Law 2: Gets pushed off if molad is after noon (Molad Zoken).
Law 3: ADU applies after noon push-off also.
Law 4: Non-leap year, if molad is at night of the 3rd day after 9h204p: push off to Thursday (or the year willbe too long).
Law 5: Year after leap one, Monday, after 5h589p: push to Tuesday.
Law 7: ADU - why?

Chapter 8: TODO

Law 1: -> 6.3
Law 2: Month - 29 or 30 days.
Laws 5-6: Same?
Law 7: TODO
Law 8: TODO

Chapter 9: Seasons.

Law 2: 1/4 of the year between seasons (91d 7.5h).
Law 3: Nisan (Spring) - Aries; Tammuz - Cancer; Tishrei - Libra; Teves - Cap.? Vernal equinox of year #1 = 7d9h642p before conjunction of Nisan. Notes 5,7 in Moznaim edition. Every year seasons move 30h; in 28 years - in the same place.
Law 5: Vernal equinox, year 4930: midnight, 5th day, 8th of Nisan.
Laws 6-8: Simplified procedure.
Law 7: Real seasons - 2 days before average ones. Note 5: 1st hour of the 4th day of creation; 1st vernal equinox. Autumnal: Wednesday, 3 hours after daybreak, 1d23h before conjunction of Tishrei.

Chapter 10: More precise length of the year. Seasons.

Law 1: More precise length of a solar year. Moments.
Law 2: Seasons for this year length.
Law 3: Vernal equinox of year #1 - 9h642p before conjunction of Nisan. (Differenbt from 9:3: Rav Ada follows Rabbi Yehoshua - world created in Nisan; Shmuel (9:3) follows Rabbi Eliezer - world created in Tishrei.) Every first year of the 19-year cycle.
Law 4: 1/4 of the year between seasons (91d7h519p31m).
Law 5: Simplified procedure.
Law 6: This more precise calculation of seasons was used by Sanhedrin to leap the year because of the spring equinox.
Law 7: Real vernal equinox approximately 2 days before either of these calculations.