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

### From inside the book

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Page 78

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**radius vector**and perpendicular . 85. Let be the angle between the**radius vector**r of any point of a curve and the tangent at that point ; then dr ( Dif . Cal . Art . 310 ) . Let p be the perpendicular cos = ds " from the pole on the ... Page 101

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**radius vector**at the point of contact . EXAMPLES . 1. For what values of m and n are the curves a " y " = x " rectifiable ? ( See Art . 14. ) n m + n n 1 Result . If or 2m is an integer , 2m 2 2. Shew that the length of the arc of a ... Page 113

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**radius vector**SA drawn to a fixed point A , and the**radius vector**SP , then ( Dif . Cal . Art . 313 ) Hence 2 dA _ { $ ( 0 ) } * ̧ de 2 A = { $ ( 0 ) } 2 do . + [ { $ Let ( 0 ) be the integral of { $ ( 0 ) } 2 then " 2 A = √ ( 0 ) + C ... Page 115

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**radius vector**which is inclined to the initial line at a right angle ; 8-2 AREAS OF PLANE CURVES AND OF SURFACES . 115. Page 120

... area is to be evaluated which is bounded by these arcs and the straight lines BC and be ; then the area is ± √ ( r , 2 — r ̧2 ) d0 , where r2 denotes any

... area is to be evaluated which is bounded by these arcs and the straight lines BC and be ; then the area is ± √ ( r , 2 — r ̧2 ) d0 , where r2 denotes any

**radius vector**of the exterior arc 120 AREAS OF PLANE CURVES AND OF SURFACES .### 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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