A Treatise on Algebraic Geometry |
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Common terms and phrases
algebraic algebraic curves Algebraic Geometry asymptote axes of co-ordinates axis of x Ay² B²x² bisected coefficient coincide conjugate diameters corresponding curvature cx² cycloid determine directrix distance dx² dy dx eliminated ellipse or hyperbola epitrochoid equa equal equation becomes expressed extremity find the equation find the locus focus formula geometry given angle given point given right line Given the base gives Hence the equation hypocycloid intercepted Let the co-ordinates Let the equation line be drawn locus sought logarithmic spiral meet the curve negative ordinates origin osculating circle parabola parallel parameter passing perpendicular plane point of contact point of intersection polar equation polar subtangent PROP rectangle represented result roots second degree segment sides spiral square substituted subtangent tang tangent tion touches tractrix transverse axis triangle values variables vertex vertical
Popular passages
Page 403 - G, the distance of the centre of gyration from the axis of motion, t, the time the force acts, v the velocity acquired by the revolving body in that time.
Page 106 - ... made to move always parallel to itself with one end touching a circle, the other end will describe a circle equal in every respect to the first.
Page xxvii - Gregory with one another, and with copies of some of them taken in the hand of Mr. Collins; and have extracted from them what relates to the matter referred to us, all which extracts herewith delivered to you, we believe to be genuine and authentic ; and by these letters and papers we find, 1st, That Mr.
Page 475 - Patris veluti imago, et ab illo ut lumen a lumine emanans, eidem ор.оаиа-ч>; existit qualiscunque adumbratio. Aut, si mavis, quia curva nostra mirabilis in ipsa mutatione semper sibi constantissime manet similis et numero eadem, poterit esse, vel fortitudinis et constan ti;i...
Page xxviii - That the differential method is one and the same with the method of Fluxions, excepting the name and mode of notation ; Mr.
Page xxviii - Fluxions, and marking them witli the letter d, a mark not used by Mr. Newton. And therefore we take the proper question to be, not who invented this or that method, but who was the first inventor of the method.
Page 466 - The two problems of the duplication of the cube and the trisection of an angle...
Page 109 - Given the base and the sum of the sides of a triangle to find the locus of the centre of the circle touching the base, and the prolongation of the other two sides.
Page xxxviii - Lloyd, singly and unassisted, conceived and executed the most important and rapid revolution ever effected in the details of a great public institution.
Page 195 - Since for each value of x there are two equal values of y, with...