. Elements of geometry : containing books I to III. Then if /•:/; be joined, t DBE i is a facl from which we can work backward,and deducethe necessary construction ; thus: Big l/»i\ the straight line BE, meeting AC in E Draw ED and EF parallel to /.and AB DBFE is the rhombus required. (See Ex. 4, p. 59.) Books t 6 II] ? ? </ < TlOtf OP J-KOBLEMS. to; Ex. 3. To determine the joint in a given straight line, atwhich straight lines, drawn front two given points, on tin sameside of tin given line, make equal angles with it. Let CD be the given line, and A and B the
. Elements of geometry : containing books I to III. Then if /•:/; be joined, t DBE i is a facl from which we can work backward,and deducethe necessary construction ; thus: Big l/»i\ the straight line BE, meeting AC in E Draw ED and EF parallel to /.and AB DBFE is the rhombus required. (See Ex. 4, p. 59.) Books t 6 II] ? ? </ < TlOtf OP J-KOBLEMS. to; Ex. 3. To determine the joint in a given straight line, atwhich straight lines, drawn front two given points, on tin sameside of tin given line, make equal angles with it. Let CD be the given line, and A and B the given points. Suppose the problem to be effected, and P to be the We then reason thus : If BP were produced to some point A , L CPA, being= z BPD, will be= L , if PA be made equal to PA, AA will be bisected by CP at right angles. Tliis is a fact from which we can work backward, and findthe steps necessary for the solution of the problem ; thus : From A draw iOi to CD. Produce AO to A, making OA=OA. Join BA, cutting CD in P. Then P is the point required. Note 10. On Symmetry. The problem, which we have just been considering, suggeststhe following remarks : If two points, A and A, be so situa ed with respect to astraight line CD, that CD bisects at right angles the straightline joining A and A, then A and A are said to be symmetricalwith regard to CD. The importance of symmetrical relations, as suggestive ofmethods for the solution of problems, cannot be fully shewn 108 EUCLIDS ELEMENTS. [Books I. & IL to a learner, who is unacquainted with the properties of thecircle. The following example, however, will illustrate thispart of the subjec
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