. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . must intersect the line Vp insome point nearer to the initial point P than p. If the elevationbe diminished, the curve of trajectory will touch the parabola C Sin some point below/>, and will therefore intersect Pp in somepoint nearer to P than/». The times of describing any given portions Vp .pp of thecurve are as the corresponding parts P m. m m, Fig. 3364, ofthe tangent or the intercepted parts C/.//of the directrix;for according to the original suppo
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . must intersect the line Vp insome point nearer to the initial point P than p. If the elevationbe diminished, the curve of trajectory will touch the parabola C Sin some point below/>, and will therefore intersect Pp in somepoint nearer to P than/». The times of describing any given portions Vp .pp of thecurve are as the corresponding parts P m. m m, Fig. 3364, ofthe tangent or the intercepted parts C/.//of the directrix;for according to the original supposition í. P p = ¿. P m andtpp — tmm ; and because the directrix cuts the three parallelsVG .pm .p in, P m I min .. Cf . ff. So far the subject maybe most clearly illustrated under the form of geometrical rea-soning ; but in order to deduce practical formulae adapted toactual calculation and comparison, we must again avail ourselvesof the facilities afforded by the rudimental portion of the differential and integral calculus ; forindependently of the necessity of constructing algebraical formulae adapted to practical purposes, a. 1758 GÜNNEEY. process of reasoning and a consequent result can be thus exhibited under the form of a few well-knovm symbols, which would require pages of geometrical reasoning to demonstrate. Take the parabolic curve A D K, Fig. 3365, of which A K is the base and D B the axis, torepresent the trajectory of a shot discharged from the point A with a given initial velocity. Letthe ordinate M P be perpendicular to the horizontal base A K, M T a tangent to the curve at thepoint M. Take M P = ?/, A P = ^, and A the origin of the co-ordinates. From any point K inthe ordinate M P draw the perpendicular R S to the tangent M T ; draw R T perpendicular to theordinate to meet the tangent in T, the triangle M T R may be taken to represent the differentialtriangle. Then the force / in the direction M P is to the effect in the direction R S perpendicularto the t
Size: 1548px × 1614px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1870, bookidsp, booksubjectengineering
