. 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. beequal to the square of DB, DB touches the circle. Draw a the straight line DE touching the circle ABC, findits centre F, and join FE, FB, FD ; then FED is a right •> an-gle : and because DE touches the circle ABC, and DCA cutsit, the rectangle AD, DC is equal ^ to the square of DE: butthe rectangle A
. 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. beequal to the square of DB, DB touches the circle. Draw a the straight line DE touching the circle ABC, findits centre F, and join FE, FB, FD ; then FED is a right •> an-gle : and because DE touches the circle ABC, and DCA cutsit, the rectangle AD, DC is equal ^ to the square of DE: butthe rectangle AD, DC is, by hypothesis, equal to the square ofDB : therefore the square of DE is equal to the square of DB ;And the straight line DE equal to the straight line DB ; and OF EUCLID. 101 FE is equal to FB, wherefore DE, EF are equal to DB, BFj Book III. and the base FD is common to the ~ two triangles DEF, DBF; therefore the angle DEF is equal ^ to the angle /1 \ d DBF; but DEF is a right angle, therefore also DBF is a right angle: and FB, if produced, is a diameter, and the straight line which is drawn at right angles to a diameter, from the extremity of it, touches ^ the circle: i / ^i^ \ g 16. 3. therefore DB touches the circle ABC. Wherefore, if from a point, &c. Q. E. fHE ELEMENTS OF EUCLID, BOOK IV. DEFINITIONS. SeeN.
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
