Analytical View of Sir Isaac Newtons Principia
Analytical View of Sir Isaac Newtons Principia
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Again, since dv x xv* v -- v -- . Ax m ma d v x d x v + ~~ ma integrating throughout the motion So that if the spaces described are taken in Arithmetical Progression, the velocities augmented by a certain given quantity will be in Geometrical Progression. This is Newton's twelfth proposition. And by eliminating v be- tween the two equations, we can find x in terms of t. But the result is complicated and of little value.
Secondly. Let us proceed to the more general case : we have dv _ x x v z d ...t m m ' a NEWTON'S PRINCIPIA. 207 dv k dt for the sake of brevity, put > and integrating, we get, after correction, log this will enable us to find / in terms of v, and, by solving the equation, v in terms- of t.
If the particle be moving in the direction opposite to that in which f acts, and if, also the above integral becomes imaginary ; the true expression will manifestly be, if Again, we have dv x K v z v -7 f v . - ax m m a for the sake of brevity put o 2 mfa.
c T+ ~^~ 4 x 208 NEWTON'S PRINCIPIA.
What to read after Analytical View of Sir Isaac Newtons Principia?
You can find similar books in the "Read Also" column, or choose other free books by Henry Brougham Brougham And Vaux to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Again, since dv x xv* v -- v -- . Ax m ma d v x d x v + ~~ ma integrating throughout the motion So that if the spaces described are taken in Arithmetical Progression, the velocities augmented by a certain given quantity will be in Geometrical Progression. This is Newton's twelfth proposition. And by eliminating v be- tween the two equations, we can find x in terms of t. But the result is complicated and of little value.
Secondly. Let us proceed to the more general case : we have dv _ x x v z d ...t m m ' a NEWTON'S PRINCIPIA. 207 dv k dt for the sake of brevity, put > and integrating, we get, after correction, log this will enable us to find / in terms of v, and, by solving the equation, v in terms- of t.
If the particle be moving in the direction opposite to that in which f acts, and if, also the above integral becomes imaginary ; the true expression will manifestly be, if Again, we have dv x K v z v -7 f v . - ax m m a for the sake of brevity put o 2 mfa.
c T+ ~^~ 4 x 208 NEWTON'S PRINCIPIA.
What to read after Analytical View of Sir Isaac Newtons Principia?
You can find similar books in the "Read Also" column, or choose other free books by Henry Brougham Brougham And Vaux to read onlineMoreLess
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