An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page v
... appears to justify the publication of a treatise devoted exclusively to these branches of Mathe- matics . 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 Mathe- matics . 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 important 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 important relation ...
Page 16
... appears , that by making the ratios : m : n suf- ficiently nearly equal to the ratios a : bc , the values of q and r may be made as great as we please , in other words , that the straight line ( l , m , n ) may be removed as far as we ...
... appears , that by making the ratios : m : n suf- ficiently nearly equal to the ratios a : bc , the values of q and r may be made as great as we please , in other words , that the straight line ( l , 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 point 0 ...
... 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 point 0 ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²