Apotome

Definitions

  • Webster's Revised Unabridged Dictionary
    • Apotome (Math) The difference between two quantities commensurable only in power, as between √2 and 1, or between the diagonal and side of a square.
    • Apotome (Mus) The remaining part of a whole tone after a smaller semitone has been deducted from it; a major semitone.
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Century Dictionary and Cyclopedia
    • n apotome In mathematics, a term used by Euclid to denote a straight line which is the difference between two straight lines that are rational (in Euclid's sense, that is, are either commensurable with the unit line, or have their squares commensurable with the square on the unit line) and that are commensurable in power only (that is, have their squares commensurable, but are themselves incommensurable). Apotomes are of six incommensurable classes. To define these, let o denote the length of the minuend line, called by Euclid the whole, and let π; denote the length of the subtrahend line, called by Euclid the adapted line (προσαρμόςουσ, σ1α). The apotome is ο—π. It is a first apotome if ο and are commensurable with the unit line. It is a second apotome if is commensurable with ο and π is commensurable with the unit line. It is a third apotome if is commensurable with ο, but neither ο nor π is commensurable with the unit line. It is a fourth apotome if ο is incommensurable with , but is commensurable with the unit line. It is a fifth apotome if is incommensurable but π commensurable with the unit line. It is a sixth apotome if neither , ο, nor π is commensurable with unity. The first apotome of a medial line is the difference of two medial lines, commensurable in power only, whose rectangle is a rational area. The second apotome of a medial line is the difference of two medial lines, commensurable in power only, whose rectangle is a medial area.
    • n apotome 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 2187/2048.
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Etymology

Webster's Revised Unabridged Dictionary
Gr. a cutting off, fr. to cut off; from + to cut