An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... Inter- section of Two given Straight Lines Condition that Three Points may lie in the same Straight Line Condition that Three Straight Lines may intersect in a Point . Condition that Two Straight Lines may be parallel to one another ...
... Inter- section of Two given Straight Lines Condition that Three Points may lie in the same Straight Line Condition that Three Straight Lines may intersect in a Point . Condition that Two Straight Lines may be parallel to one another ...
Page xii
... inter- section be real , and two imaginary , one vertex only is real . If the four points of intersection be all real , all the common chords are real ; if not , one pair only is real Invariants of two Conics ON PROJECTIONS . 9 ...
... inter- section be real , and two imaginary , one vertex only is real . If the four points of intersection be all real , all the common chords are real ; if not , one pair only is real Invariants of two Conics ON PROJECTIONS . 9 ...
Page 22
... inter- sect in one point . 7. From the vertices of a triangle ABC , three straight lines AP , BQ , CR are drawn to pass through one point , and three straight lines AP ' , BQ ' , CR ' to pass through another point , the points P , P ...
... inter- sect in one point . 7. From the vertices of a triangle ABC , three straight lines AP , BQ , CR are drawn to pass through one point , and three straight lines AP ' , BQ ' , CR ' to pass through another point , the points P , P ...
Page 27
... inter- secting straight lines . Let AB , AD , AC be three given intersecting straight lines , and let it be required to find a straight line AE , such that AB , AD , AC , AE shall form an harmonic pencil . Fig . 12 . B Through D , any ...
... inter- secting straight lines . Let AB , AD , AC be three given intersecting straight lines , and let it be required to find a straight line AE , such that AB , AD , AC , AE shall form an harmonic pencil . Fig . 12 . B Through D , any ...
Page 28
... point ; and AD , sect BC in D ; If ABC be a given triangle , P any given the fourth harmonic to AB , AP , AC , inter- BE , the fourth harmonic to BC , BP , BA , intersect CA in E ; CF , the fourth harmonic 28 TRILINEAR CO - ORDINATES .
... point ; and AD , sect BC in D ; If ABC be a given triangle , P any given the fourth harmonic to AB , AP , AC , inter- BE , the fourth harmonic to BC , BP , BA , intersect CA in E ; CF , the fourth harmonic 28 TRILINEAR CO - ORDINATES .
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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