A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, Reader, and Dyer, 1869 - 377 páginas |
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Página xiv
... reduces to two coincident Lines · Equation of Circle cutting three Circles orthogonally 347 347 Condition that a line should be cut in involution by three Conics Invariants of a system of three Conics Condition that they should have a ...
... reduces to two coincident Lines · Equation of Circle cutting three Circles orthogonally 347 347 Condition that a line should be cut in involution by three Conics Invariants of a system of three Conics Condition that they should have a ...
Página 17
... reduced to the form y = mx + b , since it is equivalent to A C y X- B Bi this equation therefore always represents a ... reduce it , as in the last Article , to the form y = mx + b , and we find that A B = sina sinẞ ' or if the axes be ...
... reduced to the form y = mx + b , since it is equivalent to A C y X- B Bi this equation therefore always represents a ... reduce it , as in the last Article , to the form y = mx + b , and we find that A B = sina sinẞ ' or if the axes be ...
Página 18
... NM ' ; x У a b = 1 represents M'N ' . By dividing by the constant term , any equation of the first degree can evidently be reduced to some one of these four forms . Ex . 1. Examine the position of the following lines 18 THE RIGHT LINE .
... NM ' ; x У a b = 1 represents M'N ' . By dividing by the constant term , any equation of the first degree can evidently be reduced to some one of these four forms . Ex . 1. Examine the position of the following lines 18 THE RIGHT LINE .
Página 20
... reduce the equation Ax + By + C = 0 ( referred to oblique co - ordinates ) to the form x cosa + y cosẞ = p . = Let us suppose that the given equation when multiplied by a certain factor R is reduced to the required form , then RA cosa ...
... reduce the equation Ax + By + C = 0 ( referred to oblique co - ordinates ) to the form x cosa + y cosẞ = p . = Let us suppose that the given equation when multiplied by a certain factor R is reduced to the required form , then RA cosa ...
Página 21
... reduced to either of the forms - x cosa + y cosẞ− p = 0 , x cos ( a + 180 ° ) + y cos ( B + 180 ° ) + p = 0 . 25. To find the angle between two lines whose equations with regard to rectangular co - ordinates are given . The angle ...
... reduced to either of the forms - x cosa + y cosẞ− p = 0 , x cos ( a + 180 ° ) + y cos ( B + 180 ° ) + p = 0 . 25. To find the angle between two lines whose equations with regard to rectangular co - ordinates are given . The angle ...
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Términos y frases comunes
anharmonic ratio asymptotes ax² axes bisected bisectors chord of contact circumscribing coefficients common tangents condition conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the co-ordinates find the equation find the locus fixed lines fixed point foci focus four points given circles given line given point Hence hyperbola imaginary points infinite distance inscribed intercept joining the points last Article length 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 rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices