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

### From inside the book

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**tangent**at P. Let ACY = 0 and CY = p ; then it may be proved that PY - AP = a ( 1 — e2sin20 ) do ; this may be proved in the same manner as the corresponding result of the preceding article ; we may either make the requisite changes of ... Page 91

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**tangent**at the variable extremity to the**tangent**at some fixed point of the then the equation which determines the relation between 8 and is called the intrinsic equation to the curve . In some investigations , especially those relating ... Page 92

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**tangent**at that point ; from the given equation we have dy dx = f ' ( x ) = 1 tan & by hypothesis ; thus x is known in terms of tan o , say x = F ( tan 4 ) ; then dx аф ds also dx = F ' ( tan ) sec ; = cosec & ; therefore ds аф = = F ... Page 93

... obviously sap . 109. The equation to the catenary is с y + c = = ( e + e x the origin being on the curve . Hence x с dy = } ( e - e ̈3 ) , s = ( e2 - e ̈13 ) ; dx - thus if be the angle which the

... obviously sap . 109. The equation to the catenary is с y + c = = ( e + e x the origin being on the curve . Hence x с dy = } ( e - e ̈3 ) , s = ( e2 - e ̈13 ) ; dx - thus if be the angle which the

**tangent**at any LENGTHS OF CURVES . 93. Page 94

Isaac Todhunter. thus if be the angle which the

Isaac Todhunter. thus if be the angle which the

**tangent**at any point makes with the**tangent**at the origin s = c tan p . 110. We have seen in Art . 86 , that for the epicycloid dy dx a + b Cos COS 0 b sin a + b tan & suppose , 0 - sin ...### 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

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