An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xiii
... constant • PAGE 158 · • • • 25 . Any system of points in involution projects into a system in involution , and the foci of one system project into the foci of the other • ib . 26 . · 27 . A system of Conics , passing through four given ...
... constant • PAGE 158 · • • • 25 . Any system of points in involution projects into a system in involution , and the foci of one system project into the foci of the other • ib . 26 . · 27 . A system of Conics , passing through four given ...
Page 10
... constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by qß , ry , and the area of QAR by A .. gr bc Hence 2qr qB + ry = bc gr = ( ax + bB + cy ) . bc This is the equation of the ...
... constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by qß , ry , and the area of QAR by A .. gr bc Hence 2qr qB + ry = bc gr = ( ax + bB + cy ) . bc This is the equation of the ...
Page 11
... f B - g $ y - h = bn = ст cl . an am — bl ' - Hence , the ratio of Pm to Pn is constant EQUATION OF THE FIRST DEGREE . 11 Every Equation of the First Degree represents a Straight Line Point of Intersection of Two Straight Lines.
... f B - g $ y - h = bn = ст cl . an am — bl ' - Hence , the ratio of Pm to Pn is constant EQUATION OF THE FIRST DEGREE . 11 Every Equation of the First Degree represents a Straight Line Point of Intersection of Two Straight Lines.
Page 12
... constant , whatever point on the locus P may represent . This can only be true when that locus is a straight line . 9. To find the co - ordinates of the point of intersection of two given straight lines . Let the equations of the two ...
... constant , whatever point on the locus P may represent . This can only be true when that locus is a straight line . 9. To find the co - ordinates of the point of intersection of two given straight lines . Let the equations of the two ...
Page 13
... constant . For this equation is satis- fied when the equations of the given straight lines are both satisfied , and , being of the first degree , it represents a straight line . It is therefore the equation of a straight line passing ...
... constant . For this equation is satis- fied when the equations of the given straight lines are both satisfied , and , being of the first degree , it represents a straight line . It is therefore the equation of a straight line passing ...
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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