Barrow, Isaac, 1630-1677, Child, J. M. (James Mark), tr · Chicago, London : The Open court publishing company · leaf 144
lastly, and more particularly, for its own intrinsicmerits, as stated below. Barrows enunciation and proofare as follows :— Example 5. Let DEB be a quadrant of a circle, towhich BX is a tangent; then let the line AMO be suchthat, if in the straight line AV any part AP is taken equalto the arc BE,… … K L A Fig. 120. Then, since CE : EK = arc EF : LK = QP : LK ; thereforer \ g = e \\X, ox LK = gelr, and CL = f+geir; hence alsoLF = J{r^ -P - 2fgelr) = ^(^-2 _ ^f^.j^y But CL: LF = CB : BH,or/+^^/r:^(^2 _ 2/^^/^) = ^.,,, _ ^^and squaring, we have /^ + ^fS^I^ • S^ - ^fg^l^ = ^^ : ^fi^ - 2ma.Hence,…
Geometry
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