Mathematical Garden

...of time, from the point of the sky from which it set out, to which it returns. And this revolution, according to the Alphonsine calculation, is completed in 365 days, five hours, 49 minutes, and almost sixteen seconds.

Lunar year. The Lunar year, however, is understood in three ways. In the first way, the Lunar year is the space of time in which the Moon, by its own motion, according to its even course, circles the entire Zodiac, which is accomplished, according to Alphonsus, in 27 days, 7 hours, 44 minutes, and almost five seconds. Whence the verses:

The Moon traverses its cycle in twenty
Seven days, and over that, eight hours.

In the second way, the Lunar year is the space of time intercepted between one conjunction of the Moon with the Sun and another; this space contains 29 days, 12 hours, 44 minutes, 3 seconds.

Kinds of Lunar year. In the third way, the Lunar year is called the space of twelve lunations in a common year, and thirteen in an embolismic one. Therefore, the Lunar year containing twelve such lunations contains 354 days. From this it is clear that the common Solar year exceeds this Lunar year by almost eleven days, which excess causes the age of the Moon to vary each year in the calendars of the months: so that in this year (for example) the first is in the calends of a certain month, in the following it will be the twelfth, and for that reason, the Epact the age of the moon at the beginning of the year was discovered.

Embolismic year. The embolismic year, however, contains 384 days. Therefore, it exceeds the Solar year by 19 days. And they say that this year was divinely revealed to the holy Moses. But since in our recently reformed calendar, the lunations found by the Golden Number correspond exactly to the celestial motion, we omit the explanation of embolisms as it is of little relevance here.

Great year. The Great year, however, is the space of the revolution of the Auges apsides of the orbits, and it is completed in 49 thousand Roman years, or (as some assert) 36 thousand; and this is called by some the Platonic year.

Discrete year. There is, moreover, a year that is called discrete, because it can be applied to all planets according to their own course, and it is the space of time in which each of the planets completely traverses the entire Zodiac, as we will recount below in the third treatise, chapter one.

Emergent year. Furthermore, besides the usual or common year, there is another year, which is called emergent: namely, when some notable event emerges and the subsequent time is calculated from it: just as the Greeks calculated time from the first Olympiad; and Christians, from the first Sunday of the Incarnation; and the monks of Mount Olivet, from the beginning of their congregation, which was in the year 1300; and so on for others, as we will discuss below under the title concerning eras.