This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1885 Excerpt: ...of 12 T to F, as Pl and Q. Let ff, be greater than On FPl make ify = FQ, and with centre Z, and radius Plql describe the circle qjI. Determine the point f as in Case 1, and with centre f and radius FQ draw the circle G1F. Determine Fl, the centre of a circle touching r/JI externally and GH internally. F, will be the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1885 Excerpt: ...of 12 T to F, as Pl and Q. Let ff, be greater than On FPl make ify = FQ, and with centre Z, and radius Plql describe the circle qjI. Determine the point f as in Case 1, and with centre f and radius FQ draw the circle G1F. Determine Fl, the centre of a circle touching r/JI externally and GH internally. F, will be the second focus. Proof. Fl-FlP, = Fql + qj-Ff, = I-(Ff, -qf, ) = FQ-FlQ =fFl, as in Case 1. Problem 108. To describe an hyperbola, a focus F, a point P on the curve, and two tan-gents TQ, TR being given (Fig. 102). Fig.102. F and P must be either both on the same side or both on opposite sides of each tangent. If F and P are on the same side of each tangent, the necessary condition for a possible solution has been explained in the corresponding problem for the ellipse, Prob. 78, p. 127, and the solution given. If they are on opposite sides, as in fig., draw FYf perpendicular to QT meeting it in Y, and FY.f. perpendicular to RT meeting it in Yi, and make Yf= IT and YJ = T, F. With centre P and radius PF describe a circle FG, and find F. the centre of a circle to touch FG and to pass through f and f. Prob. 27. Since f and f will necessarily lie within the circle FG, two solutions can generally be obtained. Proof. If Fl is the second focus, fFl =flFl the transverse axis = FP--FlP, which by construction it does. Problem 109. To describe an hyperbola, a focus F and three tangents PT, QT and RS being given (Fig. 103). F must not lie within the triangle formed by the tangents. From F drop perpendiculars FYf, FYlf, FY f on the given tangents, meeting them respectively in Y, Yl and Y3, and make Yf=YF, TA-TlF, and TJ3 = Y3F; then, as//, and/ must all be equidistant from the second focus (p. 153), and the problem therefore reduces to finding the centre (FJ
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Add this copy of Constructive Geometry of Plane Curves... to cart. $29.98, very good condition, Sold by Ebooksweb rated 3.0 out of 5 stars, ships from Bensalem, PA, UNITED STATES, published 2011 by Nabu Press.
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