A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 pages |
À l'intérieur du livre
Résultats 1-5 sur 23
Page 3
... radius vector of the point P , and POX the vectorial angle . 7. The position of any point might be expressed by positive values of the polar co - ordinates and r , since there is here no ambiguity corresponding to that arising from the ...
... radius vector of the point P , and POX the vectorial angle . 7. The position of any point might be expressed by positive values of the polar co - ordinates and r , since there is here no ambiguity corresponding to that arising from the ...
Page 4
... radius vector is a 4 -- negative quantity , we measure it on the same line as if it had been a positive quantity but in the opposite direction from 0 . Hence if ẞ represent any angle and c any length the same point is determined by the ...
... radius vector is a 4 -- negative quantity , we measure it on the same line as if it had been a positive quantity but in the opposite direction from 0 . Hence if ẞ represent any angle and c any length the same point is determined by the ...
Page 84
... radius of the circle ; a , b the co- ordinates of C ; x , y the co - ordinates of P. Draw CN , PM parallel to OY , and CQ parallel to OX . Then that is , or CQ2 + PQ2 = CP2 ; ( x − a ) 2 + ( y — b ) 2 = c2 - - ( 1 ) , x2 + y2 — 2ax ...
... radius of the circle ; a , b the co- ordinates of C ; x , y the co - ordinates of P. Draw CN , PM parallel to OY , and CQ parallel to OX . Then that is , or CQ2 + PQ2 = CP2 ; ( x − a ) 2 + ( y — b ) 2 = c2 - - ( 1 ) , x2 + y2 — 2ax ...
Page 86
... radius . III . If A2 + B2 −4C be positive , we see by comparing equation ( 2 ) with equation ( 1 ) of the preceding article that it represents a circle , such that the co - ordinates of its centre are B and its radius ( 42 + B2 − 4 C ...
... radius . III . If A2 + B2 −4C be positive , we see by comparing equation ( 2 ) with equation ( 1 ) of the preceding article that it represents a circle , such that the co - ordinates of its centre are B and its radius ( 42 + B2 − 4 C ...
Page 96
... radius of the circle ; a , b the co - ordinates of C ; x , y the co - ordinates of P. Draw CN , PM parallel to OY , and CQ parallel to OX . Then CP2 = CQ2 + PQ2 - 2CQ . PQ cos CQP = CQ2 + PQ2 + 2CQ . PQ cos w ; that is , ( x − a ) 2 + ...
... radius of the circle ; a , b the co - ordinates of C ; x , y the co - ordinates of P. Draw CN , PM parallel to OY , and CQ parallel to OX . Then CP2 = CQ2 + PQ2 - 2CQ . PQ cos CQP = CQ2 + PQ2 + 2CQ . PQ cos w ; that is , ( x − a ) 2 + ...
Autres éditions - Tout afficher
A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and ... Isaac Todhunter Affichage du livre entier - 1862 |
Expressions et termes fréquents
a²b² a²b³ a²y abscissa asymptotes ax² axes axis of x b²x² bisects centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant Crown 8vo cy² denote directrix distance Edition ellipse equa equal Examples external point find the equation find the locus fixed point focal chord focus given lines given point Hence the equation inclined latus rectum Let the equation line drawn line joining lines meet lines which pass major axis meet the curve middle point negative normal ordinate origin parabola parallel perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article proposition radical axis radius ratio rectangular required equation respectively right angles shew shewn sides Similarly student suppose tangent tion triangle vertex x₁ y₁
Fréquemment cités
Page 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 304 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Page 25 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Page 141 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Page 189 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.