. Elements of geometry : containing books I to III. Let 0 be a pt. in the © A B( from which more than two OA, OB, OC, drawn to the Oce, are equal. Then must Oh th centre of the 0. Join AB, BC, and draw OD, OE ± to AB, I OB. and OD i Then in the right-angled as AOD, BOD, .-. AD=DB;.. the centre ( the • is in it may be shown th i the centre of the <3 is tiO;,*. U in the centre of the ©. I. E. Cor. p. 1. Q. E. D Book PROPOSITIOX X. \%% Proposition X. Theorem. Tim circles cannot luce more then two joints common toboth, without coim If it be possib
. Elements of geometry : containing books I to III. Let 0 be a pt. in the © A B( from which more than two OA, OB, OC, drawn to the Oce, are equal. Then must Oh th centre of the 0. Join AB, BC, and draw OD, OE ± to AB, I OB. and OD i Then in the right-angled as AOD, BOD, .-. AD=DB;.. the centre ( the • is in it may be shown th i the centre of the <3 is tiO;,*. U in the centre of the ©. I. E. Cor. p. 1. Q. E. D Book PROPOSITIOX X. \%% Proposition X. Theorem. Tim circles cannot luce more then two joints common toboth, without coim If it be possible, let ABC and ABE be two ©s which havemore than two pts. in common, as A, B, C. Join AB, BC. Then v AB is a chord of each circle, .. the centre of each circle lies in the straight line, whichbisects AB at right angles ; III. 1. and V BC is a chord of each circle, .*. the centre of each circle lies in the straight line, -whichbisects BC at right angles. III. 1. .. the centre of each circle is the point, in which the twostraight lines, which bisect AB and BC at right angles, meet, .. the ©s ABC, ADE have a common centre, which isimpossible ; III. 5 and (J. .. two ©s cannot have more than two pts. common to both. Q. E. D. Note. We here insert two Propositions, EucL III. 25 andiv. 5, which are closely connected with Theorems i. and x. ofthis book. The learner should compare with this portion ofthe subject the note on Loci, p. 103. IU : nrs ELEMENTS. [Book III. Proposition- A. PROBLEM. (Eucl. Hi. 25, )„ „,-. of at ?? ?. >? < the ci -de of i it is a par
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