. The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected. PROP. XXXVL THEOR. IF from any point without a circle two straightlines be drawn, one of which cuts the circle, and theOther touches it; the rectangle contained by the wholeUne which cuts the circle, and the part of it withoutthe circle, shall be equal to the square of the ^which touches it. OF EUCLID
. The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected. PROP. XXXVL THEOR. IF from any point without a circle two straightlines be drawn, one of which cuts the circle, and theOther touches it; the rectangle contained by the wholeUne which cuts the circle, and the part of it withoutthe circle, shall be equal to the square of the ^which touches it. OF EUCLID* n. c 47. J. Let D be any point without the circle ABC, and I>CA, DB Book straight lines drawn from it, of which DCA cuts the circle, Vi^^—^and DB touches the same : the rectangle AD, DC is equal to thesquare of DB. Either DCA passes through the centre, or it does not; first,let it pass through the centre E, and join EB ; therefore the an-gle EBD is a right * angle t and be- a 18. 3»cause the straight line AC is bisectedin E, and produced to the point D, therectangle AD, DC, together with the Square of EC, is equal ^ to the square / C b 6. 2. of ED, and CE is equal to EB : there-fore the rectangle AD, DC, togetherwith the square of EB, is equal to thesquare of ED : but the square of ED isequals to the squares of EB, BD, be-cause EBD is a right angle : thereforethe rectangle AD, DC, together withthe square of EB, is equal to the squaresof EB, BD : take away the commonsquare of EB ; tljerefore the remain-ing rectangle AD, DC is equal to thesquare of the tangent DB. But if DCA
Size: 1246px × 2004px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
