An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page v
... appears to justify the publication of a treatise devoted exclusively to these branches of Mathematics . This remark applies more especially to the method of Trilinear Co - ordinates , which forms the subject of the greater part of the ...
... appears to justify the publication of a treatise devoted exclusively to these branches of Mathematics . This remark applies more especially to the method of Trilinear Co - ordinates , which forms the subject of the greater part of the ...
Page 1
... appears that the trilinear co - ordinates of any point within the triangle of reference are all positive ; while no point has all its co - ordinates negative . 2. Between the trilinear co - ordinates of any point an im- portant relation ...
... appears that the trilinear co - ordinates of any point within the triangle of reference are all positive ; while no point has all its co - ordinates negative . 2. Between the trilinear co - ordinates of any point an im- portant relation ...
Page 16
... appears , that by making the ratios 7 : m : n suf- ficiently nearly equal to the ratios ab : c , the values of q and may be made as great as we please , in other words , that the straight line ( 7 , m , n ) may be removed as far as we ...
... appears , that by making the ratios 7 : m : n suf- ficiently nearly equal to the ratios ab : c , the values of q and may be made as great as we please , in other words , that the straight line ( 7 , m , n ) may be removed as far as we ...
Page 24
... appears , from the above proposition , that if a pencil be cut by two distinct transversals in P , Q , R , S and P , Q , R , S ' respectively , the anharmonic ratio of the range P , Q , R , S will be equal to that of the range P ' , Q ...
... appears , from the above proposition , that if a pencil be cut by two distinct transversals in P , Q , R , S and P , Q , R , S ' respectively , the anharmonic ratio of the range P , Q , R , S will be equal to that of the range P ' , Q ...
Page 25
... appears that if PQ = QR , PS = ∞ . Hence , if PR be bisected in Q , the fourth har- monic to the range P , Q , R is infinitely distant . Or , as it may otherwise be stated , if PR be bisected in Q , and P , Q , R be joined with any ...
... appears that if PQ = QR , PS = ∞ . Hence , if PR be bisected in Q , the fourth har- monic to the range P , Q , R is infinitely distant . Or , as it may otherwise be stated , if PR be bisected in Q , and P , Q , R be joined with any ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα