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 7
... Hence y sin∞ = X sina + Y sin ß . In like manner x sin∞ = X sina ' + Y sinß ' ; x sin∞ = X sin ( -a ) + Y sin ( w - B ) . In the figure the angles a , B , w are all measured on the same side of Ox ; and a ' , B ' , w , all on the ...
... Hence y sin∞ = X sina + Y sin ß . In like manner x sin∞ = X sina ' + Y sinß ' ; x sin∞ = X sin ( -a ) + Y sin ( w - B ) . In the figure the angles a , B , w are all measured on the same side of Ox ; and a ' , B ' , w , all on the ...
Página 12
... the line MK , but its position in that line would not be determined . Hence the line MK is the locus of all the points represented by the equation x = a , since , whatever point we take on the line MK 12 THE RIGHT LINE .
... the line MK , but its position in that line would not be determined . Hence the line MK is the locus of all the points represented by the equation x = a , since , whatever point we take on the line MK 12 THE RIGHT LINE .
Página 20
... Hence we learn , that B are re- A and √ ( A2 + B2 ) √ ( A2 + B2 ) spectively the cosine and sine of the angle which the per- pendicular from the origin on the line ( Ax + By + C = 0 ) makes with the axis of x , and that perpendicular ...
... Hence we learn , that B are re- A and √ ( A2 + B2 ) √ ( A2 + B2 ) spectively the cosine and sine of the angle which the per- pendicular from the origin on the line ( Ax + By + C = 0 ) makes with the axis of x , and that perpendicular ...
Página 37
... hence the equa- tion becomes p ( cose cosa + sine sina ) = p ; or , as we got before , An equation of the form p cos ( 0 ― a ) = p . p ( 4 cose + B sin 0 ) = C can be ( as in Art . 23 ) reduced to the form p cos ( -a ) = p , by dividing ...
... hence the equa- tion becomes p ( cose cosa + sine sina ) = p ; or , as we got before , An equation of the form p cos ( 0 ― a ) = p . p ( 4 cose + B sin 0 ) = C can be ( as in Art . 23 ) reduced to the form p cos ( -a ) = p , by dividing ...
Página 48
... Hence , if the equation of a right line contain an indeterminate quantity in the first degree , the right line will always pass through a fixed point . Ex . 1. Given vertical angle of a triangle and the sum of the reciprocals of the ...
... Hence , if the equation of a right line contain an indeterminate quantity in the first degree , the right line will always pass through a fixed point . Ex . 1. Given vertical angle of a triangle and the sum of the reciprocals of the ...
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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