An Elementary Treatise on the Differential Calculus: Containing the Theory of Plane Curves, with Numerous ExamplesLongmans, Green, 1873 - 367 sider |
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An Elementary Treatise on the Differential Calculus: Containing the Theory ... Benjamin Williamson Uten tilgangsbegrensning - 1873 |
An Elementary Treatise on the Differential Calculus: Containing the Theory ... Benjamin Williamson Uten tilgangsbegrensning - 1872 |
Vanlige uttrykk og setninger
accordingly angle asymptotes ax² axis centre circle conic conjugate point constant corresponding cubic cusp d²u d³u denote derived functions determined dF dF differential coefficient double point du du dv dv dx dx dx dy dx dx² dxdy dy dy dy dz dz dz easily seen ellipse equation Euler's Theorem evidently evolute EXAMPLES expansion expression finite formula fraction geometrical given curve Hence homogeneous function imaginary independent variables infinitely small intersection inverse Lagrange's Theorem limit maxima and minima minimum value negative nth degree origin osculating osculating circle parabola perpendicular point of contact point of inflexion positive preceding prove quadratic radii radius of curvature reciprocal polar represented result roots Salmon's substituting subtangent suppose tangent Taylor's Theorem triangle vanish y₁ zero аф
Populære avsnitt
Side 121 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Side 292 - The cycloid is the most important of transcendental curves, as well from the elegance of its properties as from its numerous applications in Mechanics. We shall proceed to investigate some of the most elementary properties of the curve.
Side 173 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Side 204 - ... divided at its point of contact into segments which are to each •other in a constant ratio. 6. Find the equation of the tangent at any point to the hypocycloid, «5 + yt - a* ; and prove that the portion of the tangent intercepted between the axes is of constant length.
Side 34 - Caeterum aequalia esse puto, non tantum quorum differentia est omnino nulla, sed et quorum differentia est incomparabiliter parva.
Side 204 - In the same curve prove that the portion of the tangent intercepted between the axes is divided at its point of contact into segments which are to each other in a constant ratio.
Side 205 - Cartesian oval is of the form r + kr' = a, where r and r' are the distances of any point on the curve from two fixed points, aud a, k are constants.
Side 202 - ... every right line drawn through the origin and terminated by the curve is divided into equal parts at the origin. This takes place for a curve of an even degree, when the sum of the exponents of x and y in each term is even ; and for a curve of an odd degree when the like sum is odd. Such a point is called the centrO* of the curve.
Side 205 - Prove that the locus of the foot of the perpendicular from the pole on the tangent to an equiangular spiral is the same curve turned through an angle.
Side 280 - ... passes through that point. 7. The locus of the centres of ellipses whose axes have a given direction, and which have a contact of the second order with a given curve at a common point, is an equilateral hyperbola passing through the point. 8.