An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page x
... Corresponding Points and Lines . The angle between the radius vector and tangent in any curve is equal to the correspond- ing angle in the Reciprocal Curve 113 22 . Co - ordinates of the foci of a Conic · 115 EXAMPLES 116 23 . Double ...
... Corresponding Points and Lines . The angle between the radius vector and tangent in any curve is equal to the correspond- ing angle in the Reciprocal Curve 113 22 . Co - ordinates of the foci of a Conic · 115 EXAMPLES 116 23 . Double ...
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
... the triangle of reference be right - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . ( L2M " — L2M2 ) * B = ( CONDITION OF TANGENCY . 47 16 Condition of Tangency.
... the triangle of reference be right - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . ( L2M " — L2M2 ) * B = ( CONDITION OF TANGENCY . 47 16 Condition of Tangency.
Page 56
... correspond- ing value of a may be ascertained by substitution in the equation aa + bB + cy = 2A to be -2aA 4k bc - a · " These values all become infinite when 4k bca " , 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 aa + bB + cy = 2A to be -2aA 4k bc - a · " These values all become infinite when 4k bca " , as mani- festly ought to be the case , since , as has been shewn ...
Page 60
... corresponding member of ( C ) we get or - a , ( b , c – bạc , ) + b , ( ca – ca ) + c ( a , b – a , b ) , - b1 , bg , b 19 27 C1 C2 C3 = a ] ხ ,, ხვ 27 C2 , C3 bạ , bạ 27 - ≈α1 ( b ̧¤ ̧ — b ̧¤ ̧ ) + b1 ( c2α ̧ → с ̧α2 ) b2 [ + ] 1 ...
... corresponding member of ( C ) we get or - a , ( b , c – bạc , ) + b , ( ca – ca ) + c ( a , b – a , b ) , - b1 , bg , b 19 27 C1 C2 C3 = a ] ხ ,, ხვ 27 C2 , C3 bạ , bạ 27 - ≈α1 ( b ̧¤ ̧ — b ̧¤ ̧ ) + b1 ( c2α ̧ → с ̧α2 ) b2 [ + ] 1 ...
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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