Elementary Illustrations of the Celestial Mechanics of Laplace Part the First
Elementary Illustrations of the Celestial Mechanics of Laplace Part the First
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209. Theorem. The fluxion of the cycloidal arc is to that of the basis, as the evolved radius to the diameter of the generating circle.
For the increment GI=:2BK, and BK : BL'. '. BG : BC, and 2BK : BL: : FG ; BC, which is therefore the ratio of the fluxions.
Scholium. If the fluxion of the base be constant' that of the curve will vary as the distance of the describing point from the point of contact.
OF THE PROPERTIES OF CURVES. 51 210. Definition. If the absciss be equal to the arc of a given... circle, and the perpendicular ordinate to the corresponding sine, the curve will be a figure of sines.
211. Definition. If a second figure of sines be added, by taking ordinates equal to the cosines, the pair may be called conjugate figures of sines.
212. Theorem. The radius of curvature of the figure of sines at the vertex is equal to the ordinate.
For the fluxion of the base becoming ultimately equal to that of tlie absciss in the corresponding circle, while the ordinates are also equal, tlic curve ultimately coincides witli a portion of tliat circle.
What to read after Elementary Illustrations of the Celestial Mechanics of Laplace Part the First?
You can find similar books in the "Read Also" column, or choose other free books by Pierre Simon Laplace to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
209. Theorem. The fluxion of the cycloidal arc is to that of the basis, as the evolved radius to the diameter of the generating circle.
For the increment GI=:2BK, and BK : BL'. '. BG : BC, and 2BK : BL: : FG ; BC, which is therefore the ratio of the fluxions.
Scholium. If the fluxion of the base be constant' that of the curve will vary as the distance of the describing point from the point of contact.
OF THE PROPERTIES OF CURVES. 51 210. Definition. If the absciss be equal to the arc of a given... circle, and the perpendicular ordinate to the corresponding sine, the curve will be a figure of sines.
211. Definition. If a second figure of sines be added, by taking ordinates equal to the cosines, the pair may be called conjugate figures of sines.
212. Theorem. The radius of curvature of the figure of sines at the vertex is equal to the ordinate.
For the fluxion of the base becoming ultimately equal to that of tlie absciss in the corresponding circle, while the ordinates are also equal, tlic curve ultimately coincides witli a portion of tliat circle.
What to read after Elementary Illustrations of the Celestial Mechanics of Laplace Part the First?
You can find similar books in the "Read Also" column, or choose other free books by Pierre Simon Laplace to read onlineMoreLess
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