An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 1-5 of 40
Page x
... similarly situated to each other , in- PAGE 88 17 . 18 . tersect in the same two points in the line at infinity Radical axis of two similar and similarly situated Conics Property of the nine - point Circle 89 · ib . . 91 19 . Equation ...
... similarly situated to each other , in- PAGE 88 17 . 18 . tersect in the same two points in the line at infinity Radical axis of two similar and similarly situated Conics Property of the nine - point Circle 89 · ib . . 91 19 . Equation ...
Page xii
... similarly situated curves 154 ib . 17 . 18 . These projections may be effected in an infinite number of ways Any two intersecting conics may be projected into hyperbolas of any assigned eccentricity ib . ib . 19 . 20 . • 21 . 22 . • Any ...
... similarly situated curves 154 ib . 17 . 18 . These projections may be effected in an infinite number of ways Any two intersecting conics may be projected into hyperbolas of any assigned eccentricity ib . ib . 19 . 20 . • 21 . 22 . • Any ...
Page 1
... similarly for B and y . It thus 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 ...
... similarly for B and y . It thus 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 ...
Page 2
... Similarly bß twice the area of PCA , = cy twice the area of PAB . = Adding these equations , we get ax + bB + cy = 2A . Next , suppose P to lie between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be ...
... Similarly bß twice the area of PCA , = cy twice the area of PAB . = Adding these equations , we get ax + bB + cy = 2A . Next , suppose P to lie between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be ...
Page 6
... Similarly 2A 2A a2 = -l ; a2bc 4A2 ab2c m = - 4A2 , abc2 n = - 4A ** abc Hence r2 4A2 - { a ( B1 — B2 ) ( Y1 — Y2 ) + 6 ( Y1 − Y2 ) ( α2 — α2 ) + c ( α , -α ) ( B1- B2 ) } . -- - This is one form of the expression for . It may also be ...
... Similarly 2A 2A a2 = -l ; a2bc 4A2 ab2c m = - 4A2 , abc2 n = - 4A ** abc Hence r2 4A2 - { a ( B1 — B2 ) ( Y1 — Y2 ) + 6 ( Y1 − Y2 ) ( α2 — α2 ) + c ( α , -α ) ( B1- B2 ) } . -- - This is one form of the expression for . It may also be ...
Other editions - View all
Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα