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 |
Részletek a könyvből
1 - 5 találat összesen 78 találatból.
5. oldal
... obtained from those for internal section by changing the sign of the ratio ; that is , by changing m : + n into m : – n . In fact , in the case of internal section , PR and RQ are measured in the same direction , and their ratio ( Art ...
... obtained from those for internal section by changing the sign of the ratio ; that is , by changing m : + n into m : – n . In fact , in the case of internal section , PR and RQ are measured in the same direction , and their ratio ( Art ...
7. oldal
... obtained by expressing the perpendiculars from P on the original axes , in terms of the new coordinates and the old . Since PM - PQ sin PQM , we have PM = y sin w . But also PM = NR + PS = ON sin NOR + PN sin PNS . or Hence y sina X ...
... obtained by expressing the perpendiculars from P on the original axes , in terms of the new coordinates and the old . Since PM - PQ sin PQM , we have PM = y sin w . But also PM = NR + PS = ON sin NOR + PN sin PNS . or Hence y sina X ...
8. oldal
... obtained by adding x ' and y ' to the values for x and y given in the last article . Ex . 1. The coordinates of a point satisfy the relation x2 + y2 - 4x - 6y = 18 ; what will this become if the origin be transformed to the point ( 2 ...
... obtained by adding x ' and y ' to the values for x and y given in the last article . Ex . 1. The coordinates of a point satisfy the relation x2 + y2 - 4x - 6y = 18 ; what will this become if the origin be transformed to the point ( 2 ...
11. oldal
... obtain a result of the form xa , y = b , which , as was proved in the last chapter , represents a point . If the equations be of higher degree , they represent more points than one . For , eliminating y between the equations , we obtain ...
... obtain a result of the form xa , y = b , which , as was proved in the last chapter , represents a point . If the equations be of higher degree , they represent more points than one . For , eliminating y between the equations , we obtain ...
24. oldal
... obtain it in a form which is some- times more convenient , - - ( y ' — y ' ) x — ( x ' — x " ) y + x'y " — y'x " = 0 . The equation may also be written in the form ( x − x ′ ) ( y − y ′′ ) = ( x − x ' ) ( y — y ' ) . For this is the ...
... obtain it in a form which is some- times more convenient , - - ( y ' — y ' ) x — ( x ' — x " ) y + x'y " — y'x " = 0 . The equation may also be written in the form ( x − x ′ ) ( y − y ′′ ) = ( x − x ' ) ( y — y ' ) . For this is the ...
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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 bisectors centre chord of contact circumscribing coefficients common tangents condition conic having double conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal express find the equation find the locus fixed line fixed point foci focus four points geometrically given conic given line given point Hence hyperbola imaginary points 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 pole proved quadratic quadrilateral radical axis radius vector reciprocal rectangle right angles right line second degree sides square substituting tangential equation theorem transform trilinear coordinates values vanish vertex vertices
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