An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xi
... Corresponding Points and Lines . The angle between the radius vector and tangent in any curve is equal to the cor- responding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic . Double application of the Method of ...
... Corresponding Points and Lines . The angle between the radius vector and tangent in any curve is equal to the cor- responding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic . Double application of the Method of ...
Page 33
... corresponding to certain special forms of the equation . PROP . Every curve represented by an equation of the second ... correspond ; whence it appears that the straight line and the curve cut one another in two real , coincident , or ...
... corresponding to certain special forms of the equation . PROP . Every curve represented by an equation of the second ... correspond ; whence it appears that the straight line and the curve cut one another in two real , coincident , or ...
Page 47
... right - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . Suppose them to be PQ and RS . The intersection .CONDITION OF TANGENCY . 47 16 Condition of Tangency.
... right - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . Suppose them to be PQ and RS . The intersection .CONDITION OF TANGENCY . 47 16 Condition of Tangency.
Page 56
... correspond- ing value of a may be ascertained by substitution in the equation to be ax + bB + cy = 2A - -2aA 4k bc - a These values all become infinite when 4k bc = a2 , as mani- festly ought to be the case , since , as has been shewn ...
... correspond- ing value of a may be ascertained by substitution in the equation to be ax + bB + cy = 2A - -2aA 4k bc - a These values all become infinite when 4k bc = a2 , as mani- festly ought to be the case , since , as has been shewn ...
Page 61
... corresponding member of ( C ) we get 30 or - - a ̧ ( b ̧ ¢ ̧ − b ̧c2 ) + b ̧ ( c‚a ̧− c ̧α ) + c1 ( ab ̧ — a , b ) , - а1 аg , ag ხ ,, ხე , ხვ C1 , bg C2 , C3 = α1 = a1 - = α1 ( b ̧ ¢ ̧− b2c1 ) + b2 ( c , α ̧ — câα2 ) b ,, b3 Ca ...
... corresponding member of ( C ) we get 30 or - - a ̧ ( b ̧ ¢ ̧ − b ̧c2 ) + b ̧ ( c‚a ̧− c ̧α ) + c1 ( ab ̧ — a , b ) , - а1 аg , ag ხ ,, ხე , ხვ C1 , bg C2 , C3 = α1 = a1 - = α1 ( b ̧ ¢ ̧− b2c1 ) + b2 ( c , α ̧ — câα2 ) b ,, b3 Ca ...
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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