An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xii
... EXAMPLES MISCELLANEOUS EXAMPLES ib . 150 CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION OF A xii CONTENTS .
... EXAMPLES MISCELLANEOUS EXAMPLES ib . 150 CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION OF A xii CONTENTS .
Page 3
... 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 suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF REFERENCE . 3.
... 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 suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF REFERENCE . 3.
Page 4
... examples may familiarize the reader with this system of co - ordinates . 1. Prove that the co - ordinates of the middle point of the A line BC are 0 , C • 2. The co - ordinates of the centre of the circumscribed circle are R cos A , R ...
... examples may familiarize the reader with this system of co - ordinates . 1. Prove that the co - ordinates of the middle point of the A line BC are 0 , C • 2. The co - ordinates of the centre of the circumscribed circle are R cos A , R ...
Page 21
... EXAMPLES . 1. Find the equation of the straight line joining the middle points of two sides of the triangle of reference ; and thence prove that it is parallel to the third side . 2. Find the equations of the straight lines , drawn ...
... EXAMPLES . 1. Find the equation of the straight line joining the middle points of two sides of the triangle of reference ; and thence prove that it is parallel to the third side . 2. Find the equations of the straight lines , drawn ...
Page 56
... EXAMPLES . 1. A triangle is inscribed in a conic ; prove that the points , in which each side intersects the tangent at the opposite angle , lie in a straight line . 2. A triangle is described about a conic ; prove that the straight ...
... EXAMPLES . 1. A triangle is inscribed in a conic ; prove that the points , in which each side intersects the tangent at the opposite angle , lie in a straight line . 2. A triangle is described about a conic ; prove that the straight ...
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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