. 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. I. PROB. IN a given circle to place a straight line, equal toa given straight line not greater than the diameter ofthe circle. Let ABC be the given circle, and D the given straight line,not greater than the diameter of the circle. Draw BC the diameter of the circle ABC ; then, if BC isequal to D, th
. 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. I. PROB. IN a given circle to place a straight line, equal toa given straight line not greater than the diameter ofthe circle. Let ABC be the given circle, and D the given straight line,not greater than the diameter of the circle. Draw BC the diameter of the circle ABC ; then, if BC isequal to D, the thing required is done ; for in the circle ABCa straight line BC is placedequal to D ; but, if it is not, BCis greater than D ; make CEequal»to D, and from the cen-tre C, at the distance CE, de-scribe the circle AEF, and joinCA; therefore, because C isthe centre of the circle AEF,CA is equal to CE ; but D isequal to CE; therefore D isequal to CA : wherefore, in the circle ABC, a straight line is placed equal to the given straightline D, which is not greater than the diameter of the was to be a PROP. II. PROB. IN a given circle to inscribe a triangle equiangularto a given triangle. 104 THE ELEMENTS Book IV. a 17. c 32. 3. Let ABC be the given circle, and DEF the given triangle ; itis required to inscribe in the circle ABC a triangle equiangularto the triangle DEF. Draw a the straight line GAH touching the circle in the pointA, and at the point A, in the straight line AH, make the angleHAC equal to the angle DEF; and at the point A, in the straightline AG, make the an-gle GAB equal to the ^ ^-^^ Aangle DFE, and joinBC : therefore becauseHyVG touches the cir-cle ABC, and AC isdrawn from the pointof contact, the anglePL\C is equal c to theangle ABC in the alter-nate segment of the cir-cle : but HAC is equal to the angle DEF ; therefore also the an-gle ABC is equal to DEF : for the same reason, the angle ACBis equal to the angle DFE ; therefore
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
