The Harmony of the World by Johannes Kepler, ed. trans. E. J. Aiton, A. M. Duncan & J.

By Johannes Kepler, ed. trans. E. J. Aiton, A. M. Duncan & J. V. Field

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Ill, p. 163). ” Kepler’s preference for the Greek terms may be due to the wish to avoid confusion when he considers the greater {major) and smaller {minor) parts formed by dividing a line, for instance in Sections XXVI, XXVII, and XXVIII below. That is, when its square is added to an expressible one the result is medial. 41 The resultants are the sum of the square of the lines and their rectangle. 42 That is, when its square is added to a medial one the result is medial. 43 Caspar notes (KGW 6, p.

101-102 (Definitions II) and p. 177 (Definitions III). That is, the sum of the lines. Euclid trans. Heath, vol. Ill, pp. 447-448. Euclid trans. Heath, vol. Ill, pp. 449-451. •’** Euclid trans. Heath, vol. Ill, pp. 212-215. In his translation of the Elements, Heath uses the expression “a first apotome,” and similarly for other apotomes and binomials. 34 B ook I What are the Terms of GO, afirst Apotome, I leavefor others tofind. ^^ XXIX Proposition Now when a division in proportional section is made on any line that is a Mizon; whose square is equal to the rectangle with length com­ pounded from a given expressible line and the line whose square is five fourths that of the given expressible line, and with breadth whose square is five fourths [of the same square]; then the smaller part will be an Elasson: where Elasson is a term not of comparison but denot­ ing quality: while the greater part will be another Mizon, [the term] again being understood qualitatively, whatever its Elements may be.

Therefore ZADC = ^ZDLC = i X 2 right angles. ■2 That is, the surface is not necessarily square itself but its area is equal to that of a square whose side is the diameter of the circle. C onstruction of R egular F igures 21 or more such parts. Such a line is called in Greek ^TjXT| giiKei, expres­ sible in length. Such an area is simply called pt|Tov, expressible. ’-^ We arrive at this degree of knowledge either by description and inscription; or alternatively by its relationship with some other quantity at which we arrive by those means.

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