An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page x
... Locus of the intersection of two Tangents at right angles to PAGE 87 18 . To find the magnitudes of the axes of the Conic 89 19 . To find the area of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola EXAMPLES ཉ་ྲ ...
... Locus of the intersection of two Tangents at right angles to PAGE 87 18 . To find the magnitudes of the axes of the Conic 89 19 . To find the area of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola EXAMPLES ཉ་ྲ ...
Page 3
... locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for example , and this may be made homo- geneous in a , ß , y by multiplying each term by ax + bB + cy 2A raised to a ...
... locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for example , and this may be made homo- geneous in a , ß , y by multiplying each term by ax + bB + cy 2A raised to a ...
Page 10
... locus of a point which moves in such a manner , that the sum of the areas of the triangles PAQ , PAR is constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by qß , try , and the ...
... locus of a point which moves in such a manner , that the sum of the areas of the triangles PAQ , PAR is constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by qß , try , and the ...
Page 11
... locus of the equation , a , ß , y those of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendi- cular to AB . Also draw Dm , Dn , perpendicular respectively to PM , PN . Then Pm - B - g , Pn - y - h . = Also , since f , g ...
... locus of the equation , a , ß , y those of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendi- cular to AB . Also draw Dm , Dn , perpendicular respectively to PM , PN . Then Pm - B - g , Pn - y - h . = Also , since f , g ...
Page 12
... 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 straight lines be la + mB + ny = 0 ...
... 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 straight lines be la + mB + ny = 0 ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα