. Elements of geometry : containing books I to III. n from theextremity of the I Ex. 5. If, from the extremit;es of any diameter of a givencircle, perpendiculars be drawn to any chord of the circleis not parallel to the diameter, the Less p rpendiculat shall beequal to that segment of the greater, which is contained betweenthe circumference and the chord. Ex i. If two circles cut one another, and from either pointif intersection diameters be drawn, the extremities of thesediameters and the other point of intersection lie in the samestraight line. 7. Draw a straight line cutting two concen
. Elements of geometry : containing books I to III. n from theextremity of the I Ex. 5. If, from the extremit;es of any diameter of a givencircle, perpendiculars be drawn to any chord of the circleis not parallel to the diameter, the Less p rpendiculat shall beequal to that segment of the greater, which is contained betweenthe circumference and the chord. Ex i. If two circles cut one another, and from either pointif intersection diameters be drawn, the extremities of thesediameters and the other point of intersection lie in the samestraight line. 7. Draw a straight line cutting two concentric circles,co that tin- part of it which is intercepted by the circumferenceof the greater may be twice the part intercepted by the circum-ference of the L Book III.] PROrOSlTTOX XXXII. 163 Proposition XXXil. a straight li e towh a circle, and from th oint of contacta straight Urn bi drawn fitting On circle, th angles made bythis line urith th liiu Urn ? ??< equal to the angles, which an in th al cmate segments of the Let the st. line AB touch the 9 CDEF in the 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 descr
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