. Elements of geometry : containing books I to III. Let ABC be a ©, of which the centre is O, and the diameter Through B draw DE at right angles to A OB. I. must DE bt a tangent to th ? .Take any point P in DE, and join , V _ OBP is a right angle,.. _ OPB is less than a right angle, I. 17. and .-. OP is greater than OB. I. 10. Hence P is a point withou th • ABC. F - Tn th^ same wav it may be shewn that every point in 7or U2£ produced in tither direction, except the point B, \\-?without the • : DE is a tangent to the r . Di f. &; O. E. D. !44 El CI IPS , [Book III. Propo
. Elements of geometry : containing books I to III. Let ABC be a ©, of which the centre is O, and the diameter Through B draw DE at right angles to A OB. I. must DE bt a tangent to th ? .Take any point P in DE, and join , V _ OBP is a right angle,.. _ OPB is less than a right angle, I. 17. and .-. OP is greater than OB. I. 10. Hence P is a point withou th • ABC. F - Tn th^ same wav it may be shewn that every point in 7or U2£ produced in tither direction, except the point B, \\-?without the • : DE is a tangent to the r . Di f. &; O. E. D. !44 El CI IPS , [Book III. Proposition XVII. draw a straight line from a given point, either withoutor on the circumference, which shall loach a given Let A be the given pt., without the • />< 0 the centre of © BCD, and join OA in E, and with centre Sand radius EO describe© ABOD, cutting the given • in B and /. Join AB, AD. Tins, an tangents ? the 0 £0, ££.Then v E=BE, .: l 0BE= l BOE ; I. a. .-. z AEB=tmcei OBfi ; I. 32. and v AE BE, .-. - .17;/;= ^BAE: 1. \..-. OEB«twice i ABE ; I. 32. .•. sum of a I/.7., OEB- twice stun ofzs 0£i?, ABE,that is, two righl angles=twicer 02L4 ; .. /..I is a right angle,and .. AH is a tangent to the • BCUi ill. it may be Bhewn that .1/ is a tangent to © , l be described about a that the sum of AB equal to the sum o
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