Mathematical Garden

On the month and its parts. Chapter 8.

What a lunar month is.

Solar month.

Common month.

A month is threefold, namely Lunar, Solar, and common. A Lunar month is the space of time in which the Moon, receding from the Sun, is joined to the same after completing its circle: and this by most is called a Lunar year, as was said above in the chapter on the year. A Solar month, however, is the space of time in which the Sun traverses any sign of the Zodiac. Months of this kind correspond almost in quantity with the months of the Calendar, although they have different beginnings. Common months, furthermore, are those that constitute the Calendar. Romulus, however, wanted there to be only ten months in the year, starting from March: but Numa Pompilius, seeing that the year was not well completed by ten months, added two at the beginning, namely January and February. You have the names of the months in the Calendar. But how many days each month has, although it appears in the Calendar, you will remember more easily by these verses:

June, April, September, and November have thirty.
Add one to the rest, February twenty-eight.
To which, if it is a leap year, one is added.

On the various accidents of the Moon. Chapter 9.

Having said above what a Lunar month is, and how it is understood: now we must speak of the various accidents of the Moon with the Sun. The Moon, therefore, when it increases, becomes horned, halved, swollen, full. By the same light it is also diminished, though with changed order, until it is intermenstrual and silent. The first day of the Moon, therefore, that is, when the Moon is first joined to the Sun, is called conjunction, coitus, Neomenia New Moon, synodos meeting, New Moon, interlunium, priming, congress, Silent, Intermenstrual Moon, or Intermenstruum; at Athens they call that day enen kai neanteianasos the day between the old and new. The first day, when it begins to appear, or, according to some, when it reaches the sextile of the Sun, is called menoeides crescent-shaped, horned, falcate, not yet half-full. The seventh is dichotomos cut in two, hemitomos half-cut, half-full, middle, halved. The eleventh is amphikyrtos convex on both sides, gibbous, turgid, swollen. The fifteenth is panselenos full moon, full moon, opposition, total moon, diameter, diametric radiation, full of light. Indeed, every lunation is divided into four quarters, by which four ages are distinguished by the philosophers, of which they assert the first to be hot and moist, the second hot and dry, the third cold and dry, and the fourth cold and moist. Furthermore, since one lunation, according to the calculation of the Hebrews, becomes...