. 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. 100 THE ELEMENTS Book III. cause EBD is a right angle; therefore the rectangle AD, DC,U-.^—^ together with the square of EB, is equal to the squares of EB,BD : take away the common square of EB ; therefore the re-maining rectangle AD, DC is equal to the square of , if from any point, &c. Q. E.
. 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. 100 THE ELEMENTS Book III. cause EBD is a right angle; therefore the rectangle AD, DC,U-.^—^ together with the square of EB, is equal to the squares of EB,BD : take away the common square of EB ; therefore the re-maining rectangle AD, DC is equal to the square of , if from any point, &c. Q. E. D. Cor. If from any point without a A circle, there be drawn two straightlines cutting it, as AB, AC, the rect-angles contained by the whole linesand the parts of them without thecircle, are equal to one another, rectangle B A, AE to the rectan-gle CA, AF : for each of them isequal to the square of the straightline AD which touches the PROP. XXXVII. THEOR. See U. IF from a point without a circle there be drawntwo straight lines, one of which cuts the circle, andthe other meets it; if the rectangle contained by thewhole line which cuts the circle, and the part of itwithout the circle be equal to the square of the linewhich meets it, the Jine which meets shall touch thecircle. a 17. 18. 3. c 36. 3. Let any point D be taken without the circle ABC, and from itlet two straight lines DCA and DB be drawn, of which DCAcuts the circle, and DB meets it; if the rectangle AD, DC 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 th
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
