Barrow, Isaac, 1630-1677, Child, J. M. (James Mark), tr · Chicago, London : The Open court publishing company · leaf 120
en LG will touch thecurve LGO. For, if the two curves XEM, YFN areboth convex to the line VP,since HM = NO, and HI = KL, KO>NO>HM>HI>KL;hence the curve lies altogether above thelineGL If both curves are concave to VP, theargument is similar, but now ZGO fallsaltogether below the line GL… … 100 BARROWS GEOMETRICAL LECTURES common tangent KF. Let now the third curve be z{j(o;then, since LO = IM + KN, and L^ = IM - KN, therefore ^0is always equal to 2KN; hence, by § 3 above, the curveszQiOj ZGO also touch, and LG is the common tangent.Therefore the construction holds in this case also.…
Geometry
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