. 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. parallel meets the dia-meter is given; and the rectangle contained by the t^\ oparallels is given. In BC the diameter of the circle ABC given in position, orin BC produced, let the given point D be taken, and from Dlet a straight line DA be drawn to any point A in the circum-ference, and let AE be drawn 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. parallel meets the dia-meter is given; and the rectangle contained by the t^\ oparallels is given. In BC the diameter of the circle ABC given in position, orin BC produced, let the given point D be taken, and from Dlet a straight line DA be drawn to any point A in the circum-ference, and let AE be drawn at right angles to DA, and fromthe f>oint E where it meets the circumference again let EF bedrawn parallel to DA meeting BC in F; the point F is given, asalso the rectangle AD, EF. Produce FF to the circumference in G, and join AG : be-cause GEA is a right angle, the straight line AG is ^ the dia-a Cor, of the circle ABC ; and BC is also a diameter of U ;*•therefore the point H where they meet is the centre of thecircle, and consequently H is given : and the point D is given,wherefore DH is given in magnitude: and because AD is pa- *^^ EUCLIDS b4 6. rallel to FG, and GH equal to HA ; DH is equal *> to HF, andAD equal to GF : and DH is given, therefore HF is given ia A A. inagnitude ; and it is also given in position, and the point H isc 30. dat. given, therefore ^ the point F is givt-n. And because the straight line KFG is drawn from a given point F without or v^iihin the circle ABC given in position,d JS. or therefore *i the rectangle EF, FG is given : and GF is equal to96. dat. ^Q^ wherefore the x-ectangle AD, EF is given. 4 PROP. c. IF from a given point in a straight line given in posi-tion, a straight line be drawn to any point in the circum-ference of a circle given in position; and from this pointa straight line be drawn making Avith the first an angleequal to the difference of a right angle and the anglecontained by the straight line given in position, an
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
