Barrow, Isaac, 1630-1677, Child, J. M. (James Mark), tr · Chicago, London : The Open court publishing company · leaf 161
ws,reference being made to the figure on the left-hand side. I40 BARROWS GEOMETRICAL LECTURES Let the curve VXY be such that, if EA produced meets itin Y, then always EA : AD = AY : R. Divide the arc EV intoan infinite number of parts at F, L, . . . , and draw FBX,LCX, . . ., parallel to HD,… … Then AY . AD. BD = R . EA . BD =^ R . (EA . AD - EA . AB),and BX . AD . BD = R . FB . AD - R . (EA . AD - IJ . AD); hence, if XW is drawn parallel to VD, cutting AY in W, thenWY . AD^ - WY. AD . BD = R . (IJ . AD - EA. AB).But EA:AT=IJ:AB, or EA.AB-IJ.AT;WY . AD2 - R . (IJ . AD - IJ . AT) = R . IJ…
Geometry
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