A Collection of Problems and Theorems, with Hints, Results, and Occasional Solutions, Forming Examples in the Methods of Modern Geometry: Especially Trilinear Coordinates (1865)
A Collection of Problems and Theorems, with Hints, Results, and Occasional Solutions, Forming Examples in the Methods of Modern Geometry: Especially Trilinear Coordinates (1865)
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. 1865 Excerpt: ...= 0. or, in its rational state, fa + mp + -V 2mn07-2nk, a-2Zma/3 = 0. 232. The equation to the inscribed circle is (--a) 7 + (--6) 7a + (--c) ap = 0, or fa cotiA + iacotiB+ "Pcot%C=0. 233. The general equation of a parabola touching the three sides of the triangle ABC is Ifkf + nfia-(I + n) ap = 0. 234. The equation to ...
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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. 1865 Excerpt: ...= 0. or, in its rational state, fa + mp + -V 2mn07-2nk, a-2Zma/3 = 0. 232. The equation to the inscribed circle is (--a) 7 + (--6) 7a + (--c) ap = 0, or fa cotiA + iacotiB+ "Pcot%C=0. 233. The general equation of a parabola touching the three sides of the triangle ABC is Ifkf + nfia-(I + n) ap = 0. 234. The equation to the circumscribing circle will be acf + frfi + cV-2&V/37-2cW7- 2o6'a/3 = 0, CHAPTER IV. QUADEILINEAB, COORDINATES. 238. If a', fi, Y, & be the perpendiculars from any point on the four sides of a quadrilateral, they are connected by the relations W + mP + w( + ri' = 0, ad + bpf + ci + #' = s, where I, m, n, r, a, b, c, d are constant functions of the sides and angles of the quadrilateral. 239. Shew that quadrilinear equations may be reduced to trilinear, by eliminating one of the variables; for instance S =-(a + /3 +. 7). What inference is to be derived from this transformation? 240. Shew that the general equation of the second degree? may be of the form Xap + 'i + pay 4-p'pS + vai + 1/7-0. 241. The straight line at infinity in its more general form has for its equation A + -) O + (B + ") 0 + (C+ K)7 + (D + K) = 0. 242. Let ABCB be a quadrilateral of reference, the equations to whose sides AB, BC, CD, DA are respectively o = 0, /3 = 0, 7 = 0, 3 = 0; constructing the figure as in the diagram, we have, for the three diagonals SB ( a+" = l "?::: -. -.; i: -. R Also for OJS.. AR. several interesting properties may be deduced from these equations, such as follow: viz. OF and BQ produced will meet on the line AR produced, OE and CR will intersect on BQ, OE and DQ will meet on AR, OF and CR will meet on DQ. 243. The general form for the equation to the conic circumscribing t...
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