The Philosophical magazine; a journal of theoretical, experimental and applied physics . rties afford constructions by means of which,having given the straight lines KA, KB, KC, KD, or the pointsA, B, C, D in a straight line, the value of \ may be found; or,having given \ and three of the straight lines KA, KB, KC, KD,or-three of the points A, B, C, D, the fourth may be found. 14. Let the points D, E, F, G, no three of which are in onestraight line, be the gnomouic projections of four poles thesymbols of which arc known- To find the symbol of any pole Pgiven in position. Let uvw be the symbol
The Philosophical magazine; a journal of theoretical, experimental and applied physics . rties afford constructions by means of which,having given the straight lines KA, KB, KC, KD, or the pointsA, B, C, D in a straight line, the value of \ may be found; or,having given \ and three of the straight lines KA, KB, KC, KD,or-three of the points A, B, C, D, the fourth may be found. 14. Let the points D, E, F, G, no three of which are in onestraight line, be the gnomouic projections of four poles thesymbols of which arc known- To find the symbol of any pole Pgiven in position. Let uvw be the symbol of P. Since thesymbols of D, E, F, G are given, the symbol of the lines joiningthem two by two may be found by (?;). By equating thevalue of sin EDF sin GDP : sin GDF sin EDP, obtained byconstruction, with its value as given by (/u.) in terms of theindices of DE, DG, F, P, an equation is obtained of the formff/«4-6v 4-cw = 0, where a, b, c are integers. By equating thevalue of sinDEG isin KKl: sin FEGsinDEP obtained by con-struction, with Its value n\ terms of the uidices of DE, FE,. 4-4 Prof. Miller on the employment of the Gnomonic G, P, a second equation is obtained of the same form as the pre-ceding. From tliesc two equations the ratios of u, v, w may befound. When P is in one of the linesthrough two of the points D, E, F, G,the equation (77), w^hich expresses thiscondition, may be used in the place ofone of the preceding equations invol-ving u, V, w. 15. Let the points D, E, F, G, nothree of which are in one straight line,be the gnomonic projections of fourpoles the symbols of which are findP, having given its symbol uviv. Since u, v, w, the indices of P, are given, as well as the indicesof ])E, DG, F, \, the numerical value of sin EDF sin GDP : EDP may be found. Hence DE, DF, DG being given,and the value of X, DP may be constructed. Tn the same manner,with ED, EG, EF, and the numerical value of sin DEG sin FEP :sin FEG sin DEP, EP may be constructed.
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