... Art . 199 . Ex . 5. If from a fixed point O , OP be drawn to a given circle , and the angle TPO be constant , the en- velope of TP is a conic ... equations xy = k2 or px = y2 , it is the same as if we say that , " given two tangents to a ...
A Treatise on the Analytic Geometry of Three Dimensions
... equations of the focal conics , & c . 227. We have seen ( Art . 211 ) that ... projectively by substituting any fixed conic for the imaginary circle at ... equation of a sphere , in rectangular coordinates , is written down at once by ...
A Treatise on the Analytic Geometry of Three Dimensions
... equations of the focal conics , & c . 218. We have seen ( Art . 202 ) that ... projectively by substituting any fixed conic for the imaginary circle at ... equation of a sphere , to rectangular co - ordinates , is written down at once by ...
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on Conic Sections
... equations of this form ( see Art . 149 ) . 145. Instead of projecting the point of inflexion to infinity , we might so project ... conic , must , since these three points of it are in a right line , be for all these curves this same right ...
A Treatise on the Higher Plane Curves: intended as a sequel to a treatise on Conic Sections
... equations of this form ( see Art . 149 ) . 145. Instead of projecting the point of inflexion to infinity , we might so project ... conic , must , since these three points of it are in a right line , be for all these curves this same right ...
A Treatise on the Analytic Geometry of Three Dimensions
... project into three bitangents which , with that at infinity , form a set of four bitangents whose points of contact lie on a conic . For if xw is a line on the surface and O is the point xyz the equation ... Art . 354 . But one of these pairs ...
... LESSON XII . LINEAR TRANSFORMATIONS . Invariance of discriminants Number of ... 120 119 120 121 122 123 Method by symmetric functions Concomitants which ... degree has an invariant of the 4th order 124 125 126 127 127 129 129 129 ...
A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods
... ( Arts . 134 and 240 ) . Now , although the roots of this equation are in both cases imaginary , yet they are in both ... conics only differ in the constant terms , since the co - ordinates of the centre do not contain F ( Art . 138 ) , the ...
A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods
... done wrong in using a second appellation when a name to which there was no ... linear system was made simultaneously by Euler ( Berlin Memoirs , 1764 ) and ... equations in Poisson's ( see Journal de l'Ecole Polytechnique , Cahier XI ...
... Algebra . The differential equation , Art . 56 , is an application of the ... done wrong in using a second appellation when a name to which there was no ... linear system was made simultaneously by Euler ( Berlin Memoirs , 1764 ) and ...
A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods
... ( Arts . 134 and 240 ) . Now , although the roots of this equation are in both cases imaginary , yet they are in both ... conics only differ in the constant terms , since the co - ordinates of the centre do not contain F ( Art . 138 ) , the ...
A Treatise on the Higher Plane Curves: Intended as a Sequel to a Treatise on Conic Sections
... conic passing through the two points ; and when the three conics are circles , the Jacobian conic is the circle which cuts them at right angles ( Conics , Art . 388 , Ex . 3 ) . The Jacobian being a determinant , the Jacobian of aU + BV ...
A Treatise on the Analytic Geometry of Three Dimensions
... conics are focal conics ; that the locus of the vertices of right cones which stand on a given conic is a conic of ... Art . 126 ) that if a quadric circumscribe a surface of revolution , the cone enveloping the former whose vertex is a ...
... cone . 126. The reciprocal of a sphere with regard to any point is a surface generated by the revolution of a conic round the transverse axis . This may be proved as at Conics , Art . 308 . It is easily proved that if we have any two ...
... ( Conics , Art . 78 ) only three con- ditions are necessary in order that an equation of the third degree , containing nine independent constants , should represent a system of three lines involving only six constants . It may be verified ...
A Treatise on the Analytic Geometry of Three Dimensions
... mx ; z = − c , y == and the conditions of the problem give or - ( z −c ) 2 + mx , = ( ≈ + c ) 2 + ( y + mx ) 2 1 + m2 ( y - mx ) 2 1 + m2 cz ( 1 + m2 ) + mxy = 0 . The locus is therefore a hyperbolic paraboloid . If the shortest ...
Non-miraculous Christianity: And Other Sermons Preached in the Chapel of Trinity College, Dublin
... your thoughts dwell on such a model , you will not be indulging in unprofitable dreamings on a picture of your own imagination , not even in ideal . reproduction of the historical past . It is permitted you to hold real communion with ...
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