The Philosophical magazine; a journal of theoretical, experimental and applied physics . w (v). sinPKQ sinRKS _ PQ RS _ ehjrfk + g[ ^u-\-qv + rwsinRKQ ilTPKS ~ RQ PS ~ p/i + qk + Yl eu + (v + g 19. Let the symbols of thefaces represented by the lines AB, AC, BC, DE be given, andlet uviv be the symbol of theface represented by the lineMN. By equating the value ofAD . BM : BD . AM, as given byconstruction, with its value asgiven by (v) in terms of the indices of the points A, B, andthose of the lines DE, MN, an equation is obtained of the formau + bv + cw = 0, where a, b, c are integers. The com
The Philosophical magazine; a journal of theoretical, experimental and applied physics . w (v). sinPKQ sinRKS _ PQ RS _ ehjrfk + g[ ^u-\-qv + rwsinRKQ ilTPKS ~ RQ PS ~ p/i + qk + Yl eu + (v + g 19. Let the symbols of thefaces represented by the lines AB, AC, BC, DE be given, andlet uviv be the symbol of theface represented by the lineMN. By equating the value ofAD . BM : BD . AM, as given byconstruction, with its value asgiven by (v) in terms of the indices of the points A, B, andthose of the lines DE, MN, an equation is obtained of the formau + bv + cw = 0, where a, b, c are integers. The comparison ofthe value of AE . CN : CE. AN, as obtained by construction, withits value as given by [y) in terms of the indices of A, C, DE, MN,yields a similar equation. By elimination between these twoequations the ratios of u, v, iv may be found. 20. Let the symbols of the faces represented by the lines AB, AC, BC, DE be given, and let u, v, w, the indices of a face to berepresented by a line MN, be given. The numerical value ofAD . BM : BD . AM can be found by (v); knowing this, and the 46
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