Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids : to which are added, Elements of plane and spherical geometry (1826)
Playfair, John, 1748-1819, Euclid · Philadelphia : Marot & Walter · leaf 145
to the squareCB, the rectangle DF is equal to CB. Takeaway the common part CE from each, andthe remainder FB is equal to the remainderDE. But FB is the rectangle contained byFE and EB, that is, by AB and BE; and DEis the square upon AE; therefore AE is amean proportional between AB and BE (17.6.),… … Otherwise: Let AB be the given straight line; it is required to cut it in ex-treme and mean ratio. Divide AB in the point C, so that the rectangle contained by AB, BC be equal to the square of AC (11.2.): . Then because the rectanijleABBC is equal A C ft to the square of AC, as BA to AC, so is AC…
Euclid's Elements · Geometry · Trigonometry
Internet Archive · Public Domain Mark 1.0. Free to use for anything.
