## A treatise on the integral calculus and its applications1857 |

### From inside the book

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Page 90

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**tractory**; on account of the radi- cal , there are two values of x for every value of У less than c , these two values being numerically equal , but of opposite signs . There is a cusp at the point for which x = 0 and y = c ; and the ... Page 101

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**Tractory**measured from the cusp is determined by s = c log . 3. Shew that the Cissoid is rectifiable . 4. Shew that the whole length of the curve whose equation is 4 ( x2 + y2 ) — a2 = 3a1y * is equal to 6a . It - 2 að may be proved ... Page 137

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**tractory**, the axis of y , and the asymptote is πο 4 ( See Art . 100 ) . 14. Find the area of the loop of the curve y2 ( a2 + x2 ) = x2 ( a2x2 ) . Result . ( π − 2 ) . 15. Find the area of the loop of the curve ab Result . 30 ' 16a1y2 ... Page 141

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**tractory**round the axis of x is 4πc2 . 52. A sphere is pierced perpendicularly to the plane of one of its great circles by two right cylinders , of which the diameters are equal to the radius of the sphere and the axes pass through the ...### Other editions - View all

### Common terms and phrases

Application c² sin² Cambridge circle cloth co-ordinates constant cos² cos³ Crown 8vo curve cycloid definite integral denote differential coefficient double integral dx dx dx dy dz dy dx dz dx element ellipse equal Eulerian integral example expression Fcap Fellow of St Find the area find the volume formula function Hence indefinitely Integral Calculus integrate with respect intrinsic equation John's College latus rectum length limits M.A. Fellow MACMILLAN & CO.'S numerous obtain ordinate parabola partial fractions perpendicular plane positive preceding article radius vector result revolution revolve round round the axis shew sin² solid suppose surface tangent tion tractory transformed integral Trinity College unity vanishes variables vertex x₁ Y₁ πα аф

### Popular passages

Page 13 - Prize Essay for 1877. 8vo. 8.r. 6V. SMITH— Works by the Rev. BARNARD SMITH, MA, Rector of Glaston, Rutland, late Fellow and Senior Bursar of St. Peter's College, Cambridge. ARITHMETIC AND ALGEBRA, in their Principles and Application ; with numerous systematically arranged Examples taken from the Cambridge Examination Papers, with especial reference to the Ordinary Examination for the BA Degree.

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