. Elements of geometry : containing books I to III. Let D be any pt. \\ ithout the 0 ABC, and let the st. lines DBA, DCbe drawn to cut and touch the 0. TJo D, DB=sq. on DC. I. ... 0, the centre, draw OM bisecting AB in JI, and join OB, OC, v AB is bisected in M and produced to D,.: rect. AD, DB with sq. on MB=eq. on MD. II. to each the sq. on MO,rect. AD, DB with sqq. on MB, MO=sqq. on MD, the any!. 1 Care rt. 1 B : III. 3 and 18. .. rect. _4D, _Di>* with sq. on OB=m\. on 0J5;.*. rect. -iD. DF with sq. on OB=sqq. on OC, DC. 1. sq. on Of> = »q. on OC;. rect.
. Elements of geometry : containing books I to III. Let D be any pt. \\ ithout the 0 ABC, and let the st. lines DBA, DCbe drawn to cut and touch the 0. TJo D, DB=sq. on DC. I. ... 0, the centre, draw OM bisecting AB in JI, and join OB, OC, v AB is bisected in M and produced to D,.: rect. AD, DB with sq. on MB=eq. on MD. II. to each the sq. on MO,rect. AD, DB with sqq. on MB, MO=sqq. on MD, the any!. 1 Care rt. 1 B : III. 3 and 18. .. rect. _4D, _Di>* with sq. on OB=m\. on 0J5;.*. rect. -iD. DF with sq. on OB=sqq. on OC, DC. 1. sq. on Of> = »q. on OC;. rect. Ah. DU=sq. on .DC. Q. e. d. Ir IDS ELEMEXTS. [Book III. Proposition XXXVII. , from << i oint without circle, then In <!, ? night of which cuts tlo circle, and the <»///./? meett it : ifdangle contained by th whole line which cuts the iand th pari of if without the circle, be equal to th waich meets it, the lint which meets must touci therircl*. Let A be a pt. without the • B( D, of which 0 is the centraFrom .1 lei two >t. lines ACD, AB be drawn, of whichACD ruts the • and .1 /• meets it. Then ifrect. DA, AC=sq. on .!/•. \l must touch the All touching the • in /:,, and joip OB, OA, . .1 l> ruts the and .1 /. .-. rect. DA, 4C=sq on .!/:. III. 36. But net. DA, 4C=sq. on AB; Hyp, .•. sq. ..u I /; sq, ii A E ;.-. I/; AE. • OAB, .!/•:.V OH ?--!:, and I La en,mm:,, and Al\=AE, ABO- AEO. Bui .1 EO is a rt, z ;I /. is a rt. L .Now BO, if produced, i a diameter of the © ;.?. AB touches the ©. III. 18. III. E. D. Book IIL] M7SCELLAXEOUS EXERCISES. 169 Miscellaneous Exercises on Book III. 1. The segments, into which a circle is cut by any strline, contain angles, v hose difference is equal to the inclinationto each other of the straight lines touching the circle at the ex-tremities of the straight line which divides the circle. 2. If from the point in which a number of circles
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