An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 37
... parabola . 5. To determine the condition that a given straight line may touch the conic . If the conic be touched by the straight line ( 7 , m , n ) , the two ... Parabola 5 Condition of Tangency Every Parabola touches the Line Infinity 6.
... parabola . 5. To determine the condition that a given straight line may touch the conic . If the conic be touched by the straight line ( 7 , m , n ) , the two ... Parabola 5 Condition of Tangency Every Parabola touches the Line Infinity 6.
Page 40
... ( see p . 32 ) . We have then to find the equations of BH , CI , which , by their in- tersection , determine 0 . B H Fig . 16 . Let f , g , h , be the co 40 MODERN GEOMETRY . 8 Position of the Centre Condition for a Parabola 16.
... ( see p . 32 ) . We have then to find the equations of BH , CI , which , by their in- tersection , determine 0 . B H Fig . 16 . Let f , g , h , be the co 40 MODERN GEOMETRY . 8 Position of the Centre Condition for a Parabola 16.
Page 42
... parabola . For the centre of a parabola is in- finitely distant , its co - ordinates must therefore satisfy the alge- braical relation whence we get aa + bB + cy = 0 , Lbc + Mca + Nab = 0 , L M N or + a ō tē = = 0 , as the required ...
... parabola . For the centre of a parabola is in- finitely distant , its co - ordinates must therefore satisfy the alge- braical relation whence we get aa + bB + cy = 0 , Lbc + Mca + Nab = 0 , L M N or + a ō tē = = 0 , as the required ...
Page 49
... parabola satisfies the analytical condition of touching the line aa + bB + cy = 0 , the required condition becomes a2 72 + + L2 M2 N2 = = 0 . 18. To find the co - ordinates of the centre . Let B , B , be the points in which the conic is ...
... parabola satisfies the analytical condition of touching the line aa + bB + cy = 0 , the required condition becomes a2 72 + + L2 M2 N2 = = 0 . 18. To find the co - ordinates of the centre . Let B , B , be the points in which the conic is ...
Page 55
... parabola touching AB , AC in B , C , is a2a2 = 4bc By . 27. To find the centre of the conic . Since the conic touches AB , AC in BC , it follows that the straight line drawn through A , and the middle point of BC , will pass through the ...
... parabola touching AB , AC in B , C , is a2a2 = 4bc By . 27. To find the centre of the conic . Since the conic touches AB , AC in BC , it follows that the straight line drawn through A , and the middle point of BC , will pass through the ...
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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