An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 6-10 of 13
Page 39
... positively and one negatively . For , if they be taken otherwise , the left - hand member of the equation of the conic will become a perfect square , as may be ascertained by sub- stitution , and the conic will degenerate into a ...
... positively and one negatively . For , if they be taken otherwise , the left - hand member of the equation of the conic will become a perfect square , as may be ascertained by sub- stitution , and the conic will degenerate into a ...
Page 65
... positive coefficient . Now every other term may be formed from this by making such suffix change places with either of its adjacent suffixes a sufficient number of times . Thus the term a , b , c , is produced by simply making the ...
... positive coefficient . Now every other term may be formed from this by making such suffix change places with either of its adjacent suffixes a sufficient number of times . Thus the term a , b , c , is produced by simply making the ...
Page 92
... positive ; or according as Ua2 + Vb2 + We + 2 U'bc + 2 V'ca + 2 W'ab is positive or negative . 1 . EXAMPLES . Each angular point of a triangle is joined with each of two given points ; prove that the six points of intersection of the ...
... positive ; or according as Ua2 + Vb2 + We + 2 U'bc + 2 V'ca + 2 W'ab is positive or negative . 1 . EXAMPLES . Each angular point of a triangle is joined with each of two given points ; prove that the six points of intersection of the ...
Page 120
... positive , and from C to B negative , it will readily be seen that 오 γ = a2 Since this is a relation between the co - ordinates of any line passing through the point D , it may be considered as the equation of the point D. == If D be ...
... positive , and from C to B negative , it will readily be seen that 오 γ = a2 Since this is a relation between the co - ordinates of any line passing through the point D , it may be considered as the equation of the point D. == If D be ...
Page 121
... positive , sin p == AO ' sin ( AOB - 0 ) = 30 BO ' ՈՐ sin ( COA− + 0 ) = co or sin ( COA + 0 ) = CO ' These equations may be written p + AO sin 0 Դ CO • = 0 , = 0 , q + BO cos A OB.sin 0 — BO sin A OB . cos 0 = 0 , r + CO cos COA ...
... positive , sin p == AO ' sin ( AOB - 0 ) = 30 BO ' ՈՐ sin ( COA− + 0 ) = co or sin ( COA + 0 ) = CO ' These equations may be written p + AO sin 0 Դ CO • = 0 , = 0 , q + BO cos A OB.sin 0 — BO sin A OB . cos 0 = 0 , r + CO cos COA ...
Other editions - View all
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