Quadrivium Miscellany with Rithmomachia

...and the cathetus original: kathet.; from the Greek kathetos, a geometric term for a line falling perpendicularly to another.—that is, the line lying across and the line hanging downwards—meeting together, they form a right angle. This is all regarding the surface where I distinguish the mark itself. Indeed, I wish to assign that length to the gnomon The part of an astronomical instrument that casts a shadow or serves as a pointer. according to the size of the instrument. From that mark, I draw a perpendicular line downwards, parallel to the cathetus. It should be of such length as the size of the hanging instrument requires.

Next, I place the ruler at the aforementioned center—point V or angle X—and at the first degree I described on the arc of the quadrant A quarter-circle used for measuring angles. which I had made. I place it here clearly to the side. Where the ruler touches the perpendicular line I mentioned above, I designate that mark. And so, descending downwards through each of the following degrees in order, I place the ruler, fixed at the very clear angle X. At each position, I note where the ruler touches that line in sequence, marked up to the sixty-sixth degree. Through this, the instrument’s length is lost original: longitudo deperdit; likely referring to the way the linear scale expands as the angle increases, eventually extending beyond the physical edge of the tablet., taking a deeper downward length for each of the zodiac signs and establishing how many degrees the sun reaches at the end of each hour.