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Home > Biographies & Memoire > Biography and non-fiction prose > Anthologies: general > Geometrical Analysis; Or the Construction and Solution of Various Geometrical Problems from Analysis, by Geometry, Algebra, and the Differential Calculus; Also, the Geometrical Construction of Algebraic Equations, and a Mode of Constructing Curves
Geometrical Analysis; Or the Construction and Solution of Various Geometrical Problems from Analysis, by Geometry, Algebra, and the Differential Calculus; Also, the Geometrical Construction of Algebraic Equations, and a Mode of Constructing Curves

Geometrical Analysis; Or the Construction and Solution of Various Geometrical Problems from Analysis, by Geometry, Algebra, and the Differential Calculus; Also, the Geometrical Construction of Algebraic Equations, and a Mode of Constructing Curves


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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. 1872 Excerpt: ... to DE, and through G, where the circumference cuts AO, draw HG PI perpendicular to BC or DE; then GI is the diameter of AIEGD; DP = PE, arc DG = GE, and OG x GA = HG GI. Whence this Construction.--On the given tangent DE (III. Prob. 16) describe a circle such that the segment DAE shall contain the given III. 33. angle. Bisect DE by the diameter IPG, which produce until PH= the given radius. Draw BHG parallel to DE. On A'O' (Fig. 2), equal to the given line AO, describe a semicircle of which if is the centre; draw the radius MJperpendicular to A'O'; lay MN a mean proportional between HG and G1. Draw NKparallel to A'O', and KG'parallel to MJ; then A'O' x G'O, = G'K2 = MN2HG x GI. Apply G'O' from G to O in BG, and produce OG to meet the circumference in A. Draw ADB, AEG; let fall the perpendicular OF on DE, and with centre 0 and radius OF describe the circle O, FL, to which the line DFE will be tangent. Demonstration.--It remains to show only that AG--A'G'. Join AI; then, in similar triangles GAI and GHO, GH: GO:: GA: GI; hence GO x GA (or G'O' X 0.4) = 0/ X 0#= (by construction) (c)'0' x G'A'. Hence 0.4 = G'A' and 0.4 = 0M'. Galculation.--OH = v'. OG'--GH2 = PF. By similar triangles GHO and OFR, GH: GO:: 02: 0i?, and G#: HO:: OF: FR. Whence BP, RE, DR, and AR become known; and by similar triangles, J!0, 0C, and BG also. Then in triangles ABG and.4C0 we have, Case 2, AB and AG; and thence, by similar triangles, we have AD and AE. Scholium.--If the point 0 comes between DE and the arc DGE, we must produce A'O' to G" (IV. Prob. 4) so that the rectangle 4/0" X G"O' = GHx.HI--MN2, and proceed in every other respect as already directed. (See Problem XXXII. of "The Circle.") II. Prob. 11. Problem XXIX.--From a given point within a given semic.


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Product Details
  • ISBN-13: 9781130252446
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 66
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1130252442
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 136 gr


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Geometrical Analysis; Or the Construction and Solution of Various Geometrical Problems from Analysis, by Geometry, Algebra, and the Differential Calculus; Also, the Geometrical Construction of Algebraic Equations, and a Mode of Constructing Curves
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Geometrical Analysis; Or the Construction and Solution of Various Geometrical Problems from Analysis, by Geometry, Algebra, and the Differential Calculus; Also, the Geometrical Construction of Algebraic Equations, and a Mode of Constructing Curves
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