apotome (apotome)

[NL., Apotomes are of six incommensurable cla es. To define these, let o denote the length of the minuend line, called by Euclid the whole, and let denote the length of the subtrahend line, called by Euclid the adapted line (προσαρμόζουσα). The apotome is o-w. It is a first apotome if o and 102-π2 are commensurable with the unit line. It is a second apotome if yo2-2 is commensurable with o and is commensurable with the unit line. It is a third apotome if yo2-2 is commensurable with o, but neither o noris commensurable with the unit line. It is a fourth apotome if o is incommensurable with 02-72, but is commensurable with the unit line. It is a fifth apotome if V02-2 is incommensurable but commensurable with the unit line. It is a sixth apotome if neither 102-12, o, nor is commensurable with unity. The first apotome of a medial line is the difference of two medial lines, com. mensurable in power only, whose rectangle is a rational The second apotome of a medial line is the difference of two medial lines, commensurable in power only, whose rectangle is a medial area. area. 2. In the Pythagorean musical system, the greater of the two half steps or semitones into which the whole step or whole tone is divided. Its vibration-ratio is.