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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. 1726 Excerpt: ...Ax. 1. E. D. If the. Secant DA pafs not thro' the Cerner E. PREPARATION. From the Center E, to the Point of Conta& B, draw E B, which (18.) will be perpendicular to the Tangent DB; alfo draw EC. ED, and EF cutting D A, at Right-angles, which 0.) will Bifc t CA in the Point F. Prop, xxxvn. If the ReBangle contained under the Secant D A, and its external Part D C, be equal to the Square of a Line D B, meeting the Circumference of a Circle F, thai Line D touches tlx Circle. PREPARATION. From tht Point D, draw (17.) a Tangent D F; alfo from the Center, draw EB, ED, EF. I fay, (c) touting tije Cwcfe DEMONSTRATION. DAxDC = DF#. 36. DAxDC = DB?. Hyp. DYqz=DBtq. Ax. 1. DF = DB. Ax. 10. EF = EB. Def. 16. 1. E'D is common. DF = DB, EF = EB, ED is common. EFD = EBD. 8. i. EFD is a xL. 18. EBD is a xL (c)35 toudjeg tfce Cfrcle, . Cer. Q. E. D, EUCLID'S ELEMENTS, Demonftraced after a New, Plain, and Eafie METHOD. Ai the Line AB. a totQtoMfoeo f wtt it fatb to be tnfcvibeu in CiVCle, when the Vertex of each of its A Angles touches the Circumference of the Circle it is inferibed in. Thus the Triangle ABC is inferibed in the B Circlc ABC. L 1 ci r a Circle ist to be oefcribeo about eb ifigure, when its Circumference panes thro' the Vertex of each Angle of the Figure it is faid to be circumfcribed about. Thus the Circle ABC is defcribed about the Triangle ABC figure i$ rtato to be oefcribca a bOUt a Circle, when all the Sides of the Figure which: is circumfcrjbed, touch the Periphery of JD the Ciicle. Thus the Triangle EDF, is delcribed about the Circle G H I. a Ci

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