 | Charles Davies - 1836 - 296 דפים
...have, after passing to the limit, ds = and by substituting for dz its value (Art. 128), we have whence, the differential of a surface of revolution is equal to the circumference of a circle perpendicular to the axis, into the differential of the arc of the meridian curve. Remark.... | |
 | Charles Davies - 1838 - 300 דפים
...to the limit, and by substituting for dz its value (Art. 128), we have ds = 2*y Vda? + dy2 : whence, the differential of a surface of revolution is equal to the circumference of a circle perpendicular to the aaris, into the differential of the arc of the meridian curve. / / B... | |
 | Albert Ensign Church - 1842 - 330 דפים
...Since the second members of both the above inequalities reduce hence DIFFERENTIAL CALCULUS. du = + df ; that is, the differential of a surface of revolution is equal to the circumference of a circle perpendicular to the axis, multiplied by the differential of the arc of the generating curve.... | |
 | Albert Ensign Church - 1851 - 374 דפים
...-i*iî. + PA + Р'Л8) -/l + (P + P'A) members of both the above inequalities reduce when A = 0, we must have that is, the differential of a surface of revolution is equal to the circumference of a circle perpendicular to the axis, multiplied by the differential of the arc of the generating curve.... | |
 | Elias Loomis - 1851 - 296 דפים
...co-ordinates is placed on the circumference, is y— V2rx—x', 188 PROPOSITION X. — THEOREM. (255.) The differential of a surface of revolution, is equal to the circumference of a circle perpendicular to the axis, multiplied by the differential of the arc of the generating curve.... | |
 | Albert Ensign Church - 1859 - 360 דפים
...the extremity of the radius y. Therefore 2«yJdjc'-i-\-dy* is the differential in question. In words, The differential of a surface of revolution is equal to the circumference of a circle perpendicular to the axis, into the differential of the arc of the meridian curve. Our first... | |
 | Catherinus Putnam Buckingham - 1875 - 374 דפים
...circle will be an ordinate of the directing curve and the differential of the curve will t'e V <ix*+dys (Art. 34); and hence calling the surface of revolution...in terms of a single independent variable. EXAMPLE i. (67) To find the differential of the surface of a cone. In this case the revolving line is straight,... | |
 | William Kent - 1902 - 1204 דפים
...ordinate of the extreme point. The curve is therefore quadrable. Quadrature of surfaces of revolution.— The differential of a surface of revolution is equal to the circumference of a circle perpendicular to the axis into the differential of the arc of the meridian curve. in which... | |
 | William Kent - 1923 - 1450 דפים
...ordinate of the extreme point. The curve is therefore quadrable. Quadrature of Surfaces of Revolution. — The differential of a surface of revolution is equal to the circumference of a circle perpendicular to the axis into the differential of the arc of the meridian curve. ds = 2тгу\/й£2+й1/г;... | |
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... the differential of a surface of revolution is equal to the circumference of a circle perpendicular to the axis, into the differential of the arc of the meridian curve. 