Smart, Edward Howard · London : Macmillian and Co. · leaf 163
rbola, cutting the asymptotes at L, L,M, M (Fig 71), and one another at T. Then LF=FL and MQ = QM. CARNOTS THEOREM 135 Also, since the opposite angles at T are equal, ALTM _ TL.TM _(PL+PT)(QM - QT)tUTTM ~ A LTMALTM-ALTM (PL-PT)(QM + QT)2(PT.QM-QT.PL) ALTM (PL-PT)(QM+QT) Now when P moves up to Q, PT… … Fio. 71, Hence ACMIVI = ACLL, and any tangent cuts off from theasymptotes a triangle of constant area. To find this constant,consider the triangle cut off by the tangent at A; the area ofthis is (by IV.) AC. BC. Ex. Verify that the two expressions found for this constant area agree. § 6. Properties…
Geometry, Projective
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
