A Course of Mathematics for the Use of Academies: As Well as Private Tuition, 第 2 巻


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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...
94 ページ - D'Alembert, was the Precession of the equinoxes and the Nutation of the earth's axis, according to the theory of gravitation.
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...