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

### From inside the book

Results 11-15 of 21

Page 101

...

...

**tangent**to a curve in space , then the equation ds r dr √ ( 22 — p2 ) which was proved for a plane curve in Art . 85 will still hold . For each member of the equation expresses the secant of the angle which the**tangent**makes with ... Page 112

...

...

**tangent**at its extremity ; hence the area included be- tween the curve , the axis of x , and an ordinate at the point for which = c , is C sin w [ ° √ ( 4α'x ) dx = · 0 4 sin o va ' c2 W 3 9 that is two - thirds of the parallelogram ... Page 122

...

...

**tangent**at the latter point ; then the sine of the angle between this**tangent**and the corresponding radius vector is r de ds ( Dif . Cal . Art . 310 ) ; also P is another expression for this sine ; hence , ra = 2 . Let A denote the area ... Page 130

...

...

**tangent**plane to the surface at p to be inclined to the plane of ( x , y ) at an angle y , then it is known from solid geometry that 2 dz dz sec y = + + dx ) dy dz dx dz dy where and must be found from the known equation to the surface ... Page 131

...

...

**tangent**plane at p of which PQ is the projection is Ax Ay sec y . We shall assume that the limit of the sum of such terms as Ax Ay secy for all values of x and y comprised between assigned limits is the area of the surface corresponding ...### 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.

Page 8 - Essays, Biographical and Critical; chiefly on the English PoetS. By DAVID MASSON, MA Professor of English Literature in University College, London.

Page 16 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.

Page 4 - Law," in which a comparison is occasionally made between the Roman Laws and those of England, by Samuel Hallifax, late Lord Bishop of St.

Page 15 - The fitness of Holy Scripture for Unfolding the Spiritual Life of Man : Christ the Desire of all Nations ; or, the Unconscious Prophecies of Heathendom.

Page 2 - The Evidences of Christianity as Exhibited in the Writings of its Apologists down to Augustine. An Essay which obtained the Hulsean Prize for the Year 1852. By WJ BOLTON, of Gonville and Caius College, Cambridge. 8vo. cloth, 6s.

Page 2 - W. ARCHER BUTLER, late Professor of Moral Philosophy in the University of Dublin. Edited, from the Author's Manuscripts, by WILLIAM HEPWORTH THOMPSON, MA Regius Professor of Greek in the University of Cambridge.

Page 4 - FROST.— The First Three Sections of Newton's Principia. With Notes and Problems in illustration of the subject. By PERCIVAL FROST, MA late Fellow of St. John's College, Cambridge, and Mathematical Lecturer of Jesus College. Crown 8vo. cloth, 10s.

Page 12 - PUCKLE.— An Elementary Treatise on Conic Sections and Algebraic Geometry. With a numerous collection of Easy Examples progressively arranged, especially designed for the use of Schools and Beginners. By G. HALE PUCKLE, MA, Principal of Windermere College.