A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - Broj stranica: 399 |
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Rezultati 1 - 5 od 69.
Stranica 3
... give the principal formulæ in their most general form . Suppose , in the last figure , the angle YOX oblique and = w , then and PSQ = 180 ° -w , PQ2 = PS " + QS - 2PS . QS.cos PSQ , or , PQ2 = ( y ' — y ' ' ) 2 + ( x ′ — x " ) 2 + 2 ( y ...
... give the principal formulæ in their most general form . Suppose , in the last figure , the angle YOX oblique and = w , then and PSQ = 180 ° -w , PQ2 = PS " + QS - 2PS . QS.cos PSQ , or , PQ2 = ( y ' — y ' ' ) 2 + ( x ′ — x " ) 2 + 2 ( y ...
Stranica 7
... give a separate figure . To transform from a system of rectangular axes to a new rectangular system making an angle 0 with the old . Here we have a = 0 , B = 90 + 0 , a ' = 90-0 , B ' - 0 ; and the general formulæ become y = X sin0 + Y ...
... give a separate figure . To transform from a system of rectangular axes to a new rectangular system making an angle 0 with the old . Here we have a = 0 , B = 90 + 0 , a ' = 90-0 , B ' - 0 ; and the general formulæ become y = X sin0 + Y ...
Stranica 29
... gives us the equation x cos ay sina - p = ± ( x cos B + y sin ẞ −p ' ) , since each side of this equation denotes the length of one of those perpendiculars ( Art . 34 ) . If the equations had been given in the form Ax THE RIGHT LINE . 29.
... gives us the equation x cos ay sina - p = ± ( x cos B + y sin ẞ −p ' ) , since each side of this equation denotes the length of one of those perpendiculars ( Art . 34 ) . If the equations had been given in the form Ax THE RIGHT LINE . 29.
Stranica 30
... give the constant terms opposite signs , we shall have the equation of the bisector of the supplemental angle . Ex . 1. Reduce the equations of the bisectors of the angles between two lines to the form x cos a + y sin a = p . Ans . x ...
... give the constant terms opposite signs , we shall have the equation of the bisector of the supplemental angle . Ex . 1. Reduce the equations of the bisectors of the angles between two lines to the form x cos a + y sin a = p . Ans . x ...
Stranica 31
... give their areas Y 21 different signs ; and the quadrilateral space included by the four points is the sum instead of the difference of the two triangles . COR . 1. Double the area of the triangle formed by the lines joining the points ...
... give their areas Y 21 different signs ; and the quadrilateral space included by the four points is the sum instead of the difference of the two triangles . COR . 1. Double the area of the triangle formed by the lines joining the points ...
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Ostala izdanja - Prikaži sve
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Pregled nije dostupan - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Pregled nije dostupan - 2016 |
Uobičajeni izrazi i fraze
anharmonic ratio asymptotes ax² axes bisected by² centre chord of contact circumscribing coefficients coincide common tangents condition conic having double conic section conic touching conjugate diameters coordinates corresponding denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points given conic given line given point harmonic Hence hyperbola imaginary points infinite distance inscribed intercept last Article line at infinity line joining line meets meet the curve middle points mẞ 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 represents right angles right line second degree sides square substituting tangential equation theorem trilinear coordinates values vanish vertex vertices
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