. Trigonometria. aufe the fides E D and D B are Radii, and the an-gles at their bafesX and B, E and Bare equal, by the %\ef ike firfi Bool^of Suclid, and the angleat B common to both, therefore the triangles EXB and E D B are equiangled, and their fidesproportional; that is, D B. E B:: E B. X B. and X B the difference between the DiameterC B and C X, the fide of a Decangle, being multiplied by D B Radius, is equal to the fquare ofE B,thc fide of a Pentagon, as was to be proved; finfeclary. The fide of a Decangle being given, the fide of a Pentagon is alfo given; for, bv this Propo-fition, C X
. Trigonometria. aufe the fides E D and D B are Radii, and the an-gles at their bafesX and B, E and Bare equal, by the %\ef ike firfi Bool^of Suclid, and the angleat B common to both, therefore the triangles EXB and E D B are equiangled, and their fidesproportional; that is, D B. E B:: E B. X B. and X B the difference between the DiameterC B and C X, the fide of a Decangle, being multiplied by D B Radius, is equal to the fquare ofE B,thc fide of a Pentagon, as was to be proved; finfeclary. The fide of a Decangle being given, the fide of a Pentagon is alfo given; for, bv this Propo-fition, C X the fide of a Decangle being fubtra£ted from the Diameter C B, the difference X Bmultiplied by DB Radius, is the fquare of EB, the fide of a Pentagon, whofe fquare root isthefideitfclr. 10 The fubtenfe of 24 degrees is the fide of a Quindecangle, or a right line infcribed be-tween the bafis of a triangle and a Quinquangle, one of the angles in each figure meeting inthe fame point of the Circumference* D fcemon-*. 10 Triw/winctr/a o ■ontmimcti Vemonfimioto In the annexed Diagram D H is the bafe of an equilateral triangle, E G Mu J bate of a Quinquangle. Now then DB being the third part, or five 15 of*a circle, and BNEfix 1 > , it followed^, that D £ is one 15 part ofthe fame circumference inferibed between thebate of the triangle D H, and of the quinquangleE G, both figures having an angle in the famepoint B, as was to be proved. CenfeHary. Therefore the fides of a triangle and a quin-quangle being given, the fide of a qnindecangleis alto given : For if D K H the fide of a trianglebe , as by the 6th. £LG, the fide of a quinquangle, 1175s-* 4946, as by the laft aforegoing, DK,thei of DH will be , andE L the 7 of E G will be ,andtheir difference is D I 278 5. A K the co-fine of DK will be AL the co-fine of £L will be £ 574947, and their difference is KL, or I
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Keywords: ., bookcentury1600, bookdecade1650, bookidtrigonometri, bookyear1658
