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
6 - 10 találat összesen 82 találatból.
xiv. oldal
... Chord is a given Line 340 Equation of Asymptotes of Conic given by Trilinear Equation • 340 Condition that a Triangle self - conjugate with regard to one Conic should be inscribed or circumscribed about another Six vertices of two self ...
... Chord is a given Line 340 Equation of Asymptotes of Conic given by Trilinear Equation • 340 Condition that a Triangle self - conjugate with regard to one Conic should be inscribed or circumscribed about another Six vertices of two self ...
80. oldal
... chord becomes x " y - y ' x2 + x2 == x - x ' y ' + y ' And if we now make x ' = x " and y ' = y " , we find for the equation of the tangent y - y ' x ' y ' ' 12 X - X or , reducing , and remembering that " + y " = r2 , we get finally xx ...
... chord becomes x " y - y ' x2 + x2 == x - x ' y ' + y ' And if we now make x ' = x " and y ' = y " , we find for the equation of the tangent y - y ' x ' y ' ' 12 X - X or , reducing , and remembering that " + y " = r2 , we get finally xx ...
81. oldal
... chord joining two points on the curve may be written - a ( x − x ' ) ( x − x ′′ ) + 2h ( x − x ' ) ( y − y ′′ ) + b ( y − y ' ) ( y — y ′′ ) = --- · ax2 + 2hxy + by * + 2gx + 2fy + c . For the equation represents a right line , the ...
... chord joining two points on the curve may be written - a ( x − x ' ) ( x − x ′′ ) + 2h ( x − x ' ) ( y − y ′′ ) + b ( y − y ' ) ( y — y ′′ ) = --- · ax2 + 2hxy + by * + 2gx + 2fy + c . For the equation represents a right line , the ...
89. oldal
... chords of a given circle drawn parallel to a given line . Let the equation of any of the parallel chords be cosa + y sin a − p = 0 , - where a is , by hypothesis ... chord will ( Art . 7 ) be ( x THEOREMS AND EXAMPLES ON THE CIRCLE . 89.
... chords of a given circle drawn parallel to a given line . Let the equation of any of the parallel chords be cosa + y sin a − p = 0 , - where a is , by hypothesis ... chord will ( Art . 7 ) be ( x THEOREMS AND EXAMPLES ON THE CIRCLE . 89.
90. oldal
... chord will ( Art . 7 ) be ( x + x " ) , or , from the theory of equations , will = p cos a . In like manner , the y of the middle point will equal p sin a . Hence the equation of the locus is y = x tan a , that is , a right line drawn ...
... chord will ( Art . 7 ) be ( x + x " ) , or , from the theory of equations , will = p cos a . In like manner , the y of the middle point will equal p sin a . Hence the equation of the locus is y = x tan a , that is , a right line drawn ...
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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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