A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - 399 oldal |
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1 - 5 találat összesen 86 találatból.
4. oldal
... written the coordinates with their proper signs , he is careful to take for PS and QS the algebraic difference of the corresponding pair of coordinates . - Ex . 1. Find the lengths of the sides of a triangle , the coordinates of whose ...
... written the coordinates with their proper signs , he is careful to take for PS and QS the algebraic difference of the corresponding pair of coordinates . - Ex . 1. Find the lengths of the sides of a triangle , the coordinates of whose ...
9. oldal
... written y sin = L , x sin ∞ = M sin ∞ - - L cos w ; whence But sin2w ( x2 + y2 + 2xy cos w ) = ( L2 + M2 ) sin2w . L2 + M2 = X2 + y2 + 2XY cos ( a - ẞ ) , and a- · β = ΧΟΥ . 11. The degree of any equation between the coordinates is ...
... written y sin = L , x sin ∞ = M sin ∞ - - L cos w ; whence But sin2w ( x2 + y2 + 2xy cos w ) = ( L2 + M2 ) sin2w . L2 + M2 = X2 + y2 + 2XY cos ( a - ẞ ) , and a- · β = ΧΟΥ . 11. The degree of any equation between the coordinates is ...
23. oldal
... written in the form y - y ' = my x - x where m is indeterminate . But since the line must also pass through the point x " y " , this equation must be satisfied when the coordinates " , y " , are substituted for x and y ; hence y " -y ...
... written in the form y - y ' = my x - x where m is indeterminate . But since the line must also pass through the point x " y " , this equation must be satisfied when the coordinates " , y " , are substituted for x and y ; hence y " -y ...
24. oldal
... written in the form ( x − x ' ) ( y − y ′′ ) = ( x − x ' ' ) ( y — y ' ) . - - For this is the equation of a right line , since the terms xy , which appear on both sides , destroy each other ; and it is satisfied either by making = x ...
... written in the form ( x − x ' ) ( y − y ′′ ) = ( x − x ' ' ) ( y — y ' ) . - - For this is the equation of a right line , since the terms xy , which appear on both sides , destroy each other ; and it is satisfied either by making = x ...
31. oldal
... . This may be otherwise written , - - x ̧ ( ÿ2 −у „ ) + x ̧ ( ÿ ̧− Y1 ) + x ̧ ( Y ̧ − Y2 ) + ...... .xm ( Y1 — Yμ - 1 ) , or else - - Y1 ( x − x2 ) + Y2 ( x , − x ̧ ) + Y2 ( x , − x ̧ ) + ... ..Y „ ( X „ -1 −X2 ) . - - - - Ex . 1 ...
... . This may be otherwise written , - - x ̧ ( ÿ2 −у „ ) + x ̧ ( ÿ ̧− Y1 ) + x ̧ ( Y ̧ − Y2 ) + ...... .xm ( Y1 — Yμ - 1 ) , or else - - Y1 ( x − x2 ) + Y2 ( x , − x ̧ ) + Y2 ( x , − x ̧ ) + ... ..Y „ ( X „ -1 −X2 ) . - - - - Ex . 1 ...
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Más kiadások - Összes megtekintése
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Nincs elérhető előnézet - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Nincs elérhető előnézet - 2016 |
Gyakori szavak és kifejezések
anharmonic ratio asymptotes ax² axes bisected bisector centre chord of contact circumscribing coefficients common tangents condition conic having double conic section conic touching conjugate diameters corresponding denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points geometrically given conic given line given point harmonic Hence hyperbola infinite distance inscribed intercept last Article line at infinity line joining line meets meet the curve middle points origin parabola parallel Pascal's theorem perpendicular point of contact point x'y points at infinity points of intersection polar polar equation pole proved quadratic quadrilateral radical axis radius vector reciprocal rectangle right angles right line second degree sides square substituting tangential equation theorem trilinear coordinates values vanish vertex vertices µß
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