. Elements of geometry : containing books I to III. chord FD, dividing the ©into segments FCD, mud z DFB= z in segment F,and 1 DFA= z in segment F draw the chord EC ±.to AB. Then FC is a diameter of the • , III. 19. Take any pt. E in the arc FED, and join FE, ED. Di I. DFB=sum of z s .F£D, .FCD ;and z iii; has been proved = z .FCD ; :.lDFA= lEED,that is, z DFA= z in segment .FED. Q. E. u. Ex. The chord joining the points of contact of para II gents is a diameter, r64 EUCLIDS ELEMENTS. [Book III. Proposition XXXIII. a given straight line to describt a a ..xxt of a c
. Elements of geometry : containing books I to III. chord FD, dividing the ©into segments FCD, mud z DFB= z in segment F,and 1 DFA= z in segment F draw the chord EC ±.to AB. Then FC is a diameter of the • , III. 19. Take any pt. E in the arc FED, and join FE, ED. Di I. DFB=sum of z s .F£D, .FCD ;and z iii; has been proved = z .FCD ; :.lDFA= lEED,that is, z DFA= z in segment .FED. Q. E. u. Ex. The chord joining the points of contact of para II gents is a diameter, r64 EUCLIDS ELEMENTS. [Book III. Proposition XXXIII. a given straight line to describt a a ..xxt of a circlemtaining ? a : ?i,J^c-. Lei AB be .In- given st. line, and C the given is required / describi ?> .1/- a w »< «/ a 9 tofttcfc*/iaW contain am l = 0. A- pt. .1 in st. line AB make z B4D= t C. I. 23Draw .1 E to ,f /. and 1From F draw IGi to J /-, meeting A E in (/. Join OB. Then in a . B#F ;•.? J /? /;/?, and i <: is eomn i I FG . ; OA //;. i. i. With 0 as centre and GJ as radius d is a tangent to the • Al [II. Ift Aiil . the chord .!/• is drawn from the pt of contact A,.-. z /;J7>= z in segmi nl ABB, III. 32. that gmenf .1///. contains nn i — . <. :iti•! it ia d( 3d ibi d < was r< qd. q. K. I . 1. Two circles intersect in A, and through I is drawnighl line meeting th< fain in /.,. Prove thai the angle between the tangents ;u / and Q is equal bietween t I 2. From two given points n the Baroe Bide of a straight
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