An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page ix
... Determinant 59 3-6 . Law of Formation of Determinants 60 7 . Signs of the several Terms of a Determinant 65 8 . Sign changed by interchange of Two Consecutive Lines or Co- lumns 9 . Multiplication of a Determinant by a given Quantity ...
... Determinant 59 3-6 . Law of Formation of Determinants 60 7 . Signs of the several Terms of a Determinant 65 8 . Sign changed by interchange of Two Consecutive Lines or Co- lumns 9 . Multiplication of a Determinant by a given Quantity ...
Page xiv
... determinants is a determinant Property of the co - ordinates of three points , forming a cón- jugate triad 171 • · 173 · 18 . 19 . Envelope of a side of an inscribed triangle whose other sides pass each through a fixed point , Locus of ...
... determinants is a determinant Property of the co - ordinates of three points , forming a cón- jugate triad 171 • · 173 · 18 . 19 . Envelope of a side of an inscribed triangle whose other sides pass each through a fixed point , Locus of ...
Page 59
... Determinants ( the second edition of which will be found in Crelle's Journal , t . 51 , pp . 209 , 328 ) , and to the ori- ginal memoirs communicated to various scientific Journals by Messrs Boole , Sylvester , Cayley , and others . 2 ...
... Determinants ( the second edition of which will be found in Crelle's Journal , t . 51 , pp . 209 , 328 ) , and to the ori- ginal memoirs communicated to various scientific Journals by Messrs Boole , Sylvester , Cayley , and others . 2 ...
Page 60
... determinant of the given system of equations . We proceed to investigate the law of its formation . 3. First , suppose we have two equations , а1x12 + α2x12 = 0 , b1x1 + b1x1 = 0 . Multiply the first by b2 , the second by a ,, and ...
... determinant of the given system of equations . We proceed to investigate the law of its formation . 3. First , suppose we have two equations , а1x12 + α2x12 = 0 , b1x1 + b1x1 = 0 . Multiply the first by b2 , the second by a ,, and ...
Page 61
... b2 ( c , α ̧ — câα2 ) b ,, b3 Ca Ca + b1 Cq , Ca ag , ag + c1 ( a , b , - ab2 ) b2 , b + c12 -b2 ag , as Ca Ca Ca Ca ag as + c1 b1 , b2 bq , b g It will be seen that the above process is really DETERMINANTS OF THREE ROWS . 61.
... b2 ( c , α ̧ — câα2 ) b ,, b3 Ca Ca + b1 Cq , Ca ag , ag + c1 ( a , b , - ab2 ) b2 , b + c12 -b2 ag , as Ca Ca Ca Ca ag as + c1 b1 , b2 bq , b g It will be seen that the above process is really DETERMINANTS OF THREE ROWS . 61.
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Common terms and phrases
angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ centre Chap chord co-ordinates coefficients common tangents conic section determinant directrix find the equation fixed point fixed straight line follows four points given conic given point given straight line given triangle Hence investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides parabola Pascal's Theorem perpendicular point f points at infinity points of contact points of intersection PQRS prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree shewn similar and similarly sin POS tangents drawn term a,b,c theorem three points three straight lines triangle of reference ua² uf+w'g+v'h ux² V'ca va² Vb² vß² W'ab whence wy² λα