A system of mechanics, being the substance of lectures upon that branch of natural philosophy / By T. Parkinson.

  • Parkinson, Thomas, 1745-1830.
Date:
1785
Catalogue details

Licence: Public Domain Mark

Credit: A system of mechanics, being the substance of lectures upon that branch of natural philosophy / By T. Parkinson. Source: Wellcome Collection.

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    629. Cor. 2. If the velocity of projection be the fame; the pa« rameter belonging to DO will be the fame, whatever be the angle4 of projection; for the projeftile velocity and G being given, DE» w DEZ ERS and confequently -g-g-, or the parameter,, are given. . 630, Cor. 3. Let T be the fpace through which* body falls from reft, when acted upon by the conftant force G, to acquire a * velocity, equal to that in any point D of the jmrve, and let y-> be the velocity acquired in falling from E to R, by the aCtion of; fame force G, and V % v :: DE : 2 ER (106): but TiER :: Vz \ v* DEZ (526) :: D E*: 4 E R2, and 24= ~ ith of ;the parameter be?» - longing to DO* , FIG. CLXX. Vl *» * v- <■ > «. ' • . # , ' , , ? ' 63 tv Cor. 4. If G be the force .of gravity, 4he axrs and alf dia-v meters of the parabola,,are perpendicular to the horizon; the ve- locities are equal at eqqaldiftances from the principabvertex; tht time of arriving at the vertex of the axis, or at the greateft alti^* iude, is equal to half thectima oLthe. flight; the/p^rabola cuts the , horizon, and all lines parallel to the horizon, in equal angles; and v, D£, which ?is parallel to the, ordinate OR} is a tangent’to the. parabola, at D.; 632. Cor. 5. The-velocity in different points varies in- a fubi- duplicate ratio of the parameter belonging to thofe points, or, if JX be the diredlrix and DI perpendicular to it, in a fubduplicate. ratio of DI or D,S being, the.focus, or, in the fame parabola, as the perpendicular S T upon the tangent DT. The horizontal, velocity DHi determined by; drawing, perpendiculars, from the body upon the horizon, varies as DE, and is confequently uni- form; and the velocity,.therefore, in any point D, being as DE, is as the fecant of the angle of elevation ; and at the principal vertex, the velocity in the curve and the horizontal velocity, are equal. 633. Prop.