A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - 399 páginas |
Dentro del libro
Resultados 1-5 de 84
Página 7
... manner ẞ + B ' = w . The formulæ of transformation are most easily obtained by expressing the perpendiculars from P on the original axes , in terms of the new coordinates and the old . Since PM = PQ sin PQM , we have PM = y sin w . But ...
... manner ẞ + B ' = w . The formulæ of transformation are most easily obtained by expressing the perpendiculars from P on the original axes , in terms of the new coordinates and the old . Since PM = PQ sin PQM , we have PM = y sin w . But ...
Página 9
... manner in general that x2 + y2 + 2xy cosxOy = X2 + Y2 + 2XY cos XOY . If we write X sina + Ý sin ß = Ĺ , X cos a + Y cos ẞ = M , the expressions in Art . 9 may be written y sin ∞ = L , x sin ∞ = M sin ∞ - L cos ; whence But sin2 ( x2 ...
... manner in general that x2 + y2 + 2xy cosxOy = X2 + Y2 + 2XY cos XOY . If we write X sina + Ý sin ß = Ĺ , X cos a + Y cos ẞ = M , the expressions in Art . 9 may be written y sin ∞ = L , x sin ∞ = M sin ∞ - L cos ; whence But sin2 ( x2 ...
Página 11
... manner , is the point whose coordinates are x = α , y = ẞ1 , & c . y = B1 . = x = Ex . 1. What point is denoted by the equations 3x + 5y = 13 , 4x - y = 2 ? Ans . x 1 , y = 2 Ex . 2. What points are represented by the two equations x2 + ...
... manner , is the point whose coordinates are x = α , y = ẞ1 , & c . y = B1 . = x = Ex . 1. What point is denoted by the equations 3x + 5y = 13 , 4x - y = 2 ? Ans . x 1 , y = 2 Ex . 2. What points are represented by the two equations x2 + ...
Página 13
... manner , ano- ther series of points , p ' , q ' , r ' , whose co- ordinates satisfy the equation . So again , if we assume x = a " or x = a " , & c . Now , if x be supposed to take successively all a a а " u ' possible values , the ...
... manner , ano- ther series of points , p ' , q ' , r ' , whose co- ordinates satisfy the equation . So again , if we assume x = a " or x = a " , & c . Now , if x be supposed to take successively all a a а " u ' possible values , the ...
Página 14
... manner , the equation y = b represents a line PN parallel to the axis OX , and meeting the axis OY at a distance from the origin ON = b . If we suppose b to be equal to nothing , we see that the equation y = 0 denotes the axis OX ; and ...
... manner , the equation y = b represents a line PN parallel to the axis OX , and meeting the axis OY at a distance from the origin ON = b . If we suppose b to be equal to nothing , we see that the equation y = 0 denotes the axis OX ; and ...
Contenido
96 | |
99 | |
103 | |
105 | |
116 | |
121 | |
129 | |
136 | |
146 | |
153 | |
159 | |
166 | |
168 | |
173 | |
181 | |
192 | |
199 | |
201 | |
206 | |
208 | |
214 | |
217 | |
220 | |
222 | |
225 | |
231 | |
295 | |
301 | |
314 | |
320 | |
326 | |
332 | |
337 | |
343 | |
347 | |
353 | |
359 | |
362 | |
369 | |
377 | |
379 | |
383 | |
389 | |
391 | |
393 | |
394 | |
395 | |
396 | |
399 | |
4 | |
Otras ediciones - Ver todas
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 15 - Other Worlds than Ours ; The Plurality of Worlds Studied under the Light of Recent Scientific Researches.
Página 12 - TREASURY OF KNOWLEDGE AND LIBRARY OF REFERENCE. Comprising an English Dictionary and Grammar, Universal Gazetteer, Classical Dictionary, Chronology, Law Dictionary, &c.
Página 20 - INSECTS AT HOME : A Popular Account of British Insects, their Structure, Habits and Transformations.
Página 8 - Huth. — THE MARRIAGE OF NEAR KIN, considered with Respect to the Law of Nations, the Result of Experience, and the Teachings of Biology. By ALFRED HENRY HUTH. Royal 8vo.
Página 2 - THE HOUSE OF WALDERNE. A Tale of the Cloister and the Forest in the Days of the Barons
Página 7 - GEORGE). THE SEA AND ITS LIVING WONDERS. With 12 Plates and 303 Woodcuts. 8vo., 71.
Página 2 - A General History of Greece from the Earliest Period to the Death of Alexander the Great, with a sketch of the subsequent History to the present time. New Edition. Crown 8vo. Cloth, price js. 6d. Tales of Ancient Greece.
Página 1 - History of Civilisation in England and France, Spain and Scotland. By HENRY THOMAS BUCKLE. 3 vols. crown 8vo. 24*.
Página 9 - CRITIQUE OF PRACTICAL REASON, AND OTHER WORKS ON THE THEORY OF ETHICS.
Página 15 - New Star Atlas for the Library, the School, and the Observatory, in 12 Circular Maps.