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acting altitude axis ball base beam becomes body centre circle common consequently constant Corol curve denote descending described determine diameter direction distance divided draw earth effect elevation equal equation Exam example experiments expression fall feet figure fluent fluid fluxion force former given given plane gives gravity greatest half Hence horizontal horizontal plane inches increase length less manner means measure meet motion moving nearly parallel passing perpendicular plane position pressure PROBLEM produced projections proportion PROPOSITION quantity radius range ratio resistance respectively right angles roots rule sides sine solid space spherical square straight line strength supposed surface theorem tion triangle velocity vertical weight whole
141 ページ - ... powder, and that but a small one too ; so that all those nearly agree with the parabolic theory. Other experiments have also been carried on with the ballistic pendulum, at different times ; from which have been obtained some of the, laws for the quantity of powder, the weight and velocity of the ball, the length of the gun, &c. Namely, that the velocity of the ball varies as the square root of the charge directly, and as the square root of the weight of ball reciprocally ; and 'that, some rounds...
72 ページ - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
623 ページ - In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the O's...
240 ページ - Then say. As the weight lost in water, Is to the whole weight, So is the specific gravity of water, To the specific gravity of the body.
13 ページ - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
34 ページ - Two planes are said to have the same or a like inclination to one another which two other planes have, when the said angles of inclination are equal to one another.
207 ページ - Hence the magnitude of the whole body, is to the magnitude of the part immersed, as the specific gravity of the fluid, is to that of the body.
304 ページ - ... small parts, but as generated by continued motion, by means of which they increase or decrease ; as a line by the motion of a point ; a surface by the motion of a line ; and a solid by the motion of a surface.
380 ページ - ... it follows that, by means of it, any one of the three may be expelled out of the calculation, or else brought into it. Also, the momentum, or quantity of motion in a moving body, is qv^ the product of the velocity and matter. It is also to be observed, that the theorems equally hold good for the destruction of motion and velocity, by means of retarding forces, as for the generation of the same, by means of Accelerating forces . And to the following problems, which are all resolved by the application...