An Elementary Treatise on the Differential Calculus: Containing the Theory of Plane Curves, with Numerous Examples

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Longmans, Green, 1873 - 367 pàgines
 

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Pàgina 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.
Pàgina 304 - 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.
Pàgina 185 - 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.
Pàgina 216 - ... 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.
Pàgina 34 - Caeterum aequalia esse puto, non tantum quorum differentia est omnino nulla, sed et quorum differentia est incomparabiliter parva.
Pàgina 216 - 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.
Pàgina 217 - 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.
Pàgina 214 - ... 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.
Pàgina 217 - 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.
Pàgina 292 - ... 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.

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