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Home > General > The Geometrician; Containing Essays on Plane Geometry, and Trigonometry: With Their Application to the Solutions of a Variety of Problems ...
The Geometrician; Containing Essays on Plane Geometry, and Trigonometry: With Their Application to the Solutions of a Variety of Problems ...

The Geometrician; Containing Essays on Plane Geometry, and Trigonometry: With Their Application to the Solutions of a Variety of Problems ...


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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. 1775 Excerpt: ...229. as a Center, with a Radius == DF, describe a Circle FGE, and it will be that required. Demonstration. Let DE be J_ to BA, and DG J_ to AC; then the Z.s BED, BFD, being -Rt. z.s, are rr each other i and the z. EBD, = L. FBD by the Construction, and the Side BD common, v the As EBD, FBD, are--b each - 54, other in all Respects, and consequently ED n DF. By the same Reason DG-DF, . ED, DF, DG, are--each other, and consequently the Circle described about the Center D with the Radius DF, will pass thro' the Points FEG, or, in other Words, will touch the Sides of the given Triangle in the Points E, F, and G. E. D. 264. Problem 32. To inscribe a Square in a p VII given Circle ABCD. " F.'i. ' Construction. Through the Center E draw the Diameter AC, and C_L to it the Diameter AC, - 226. and join BA, AD, DC, BC, then is the rectilineal Figure ABCD the Square required. Demonstration. BE being--ED, AE common, and the z. AEB Z.AED, the Side AB a,4 will be '--Side AD; and, by the fame Reason, AB 58. == BC, and AD = DC v AB a = BC = AD = 45DC; that is, the rectilineal Figure ABCD is equilateral. And BD being a Diameter, the Z. BAD is N 2 an A Circle is said to be inscribed in a rectilineal Figure whea the Circumference touches each Side of the rectilineal-Figure. b l4g a.n L in a Semicircle, and v a Rt. i_: By the same Reason the z.s ABC, BCD, CDA, arr each of them Rt. z.s. Hence we have (hewn that the rectilineal Figure ABCD is equilateral, and its Z.S e 34. all Right 4.9. Consequently it is ac Square. Q_ E. Df PI. VII. 265. Problem 33. To describe a Square about a given Circle ABCD. Construction. Draw the Diameters AC, BD, 226. i at Rt. s to each other, and thro' the Points A, f ZS6. B, C, D, draw the Tangents GF, GH, HK, KF j then will t...


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Product Details
  • ISBN-13: 9781130613513
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 70
  • Spine Width: 4 mm
  • Weight: 141 gr
  • ISBN-10: 1130613518
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: With Their Application to the Solutions of a Variety of Problems ...
  • Width: 189 mm


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