@book{ brougham_analytical_2012,
  title = {Analytical View of Sir Isaac Newton's Principia},
  volume = {1},
  isbn = {978-12-3634-281-2},
  publisher = {General Books},
  author = {Brougham, Henry and Routh, Eduard John},
  month = {May},
  year = {2012},
  note = {This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1855 Excerpt: ‥.) W y e V m V cos a/ put {NA} = f, N P = n (my. {CM}–(=)'"!–/ {COS} a-, T where a =–V. X cos p This is a very simple form of the equation to the curve and enables us to investigate many of its properties with ease. We learn that if the successive values of N A are in geometric progression those of N P will be in arithmetical progression. This is Newton's second corollary. It is also manifest from the manner in which we eliminated t, that we have or the particle moves in such a manner that its distance from O A, measured parallel to any fixed straight line, varies as the time. This is Newton's first corollary. Since O B. cos a = O C, and {OC}={TMV} cos {OB}=-V; X and since any point may be considered as the origin of projection, we learn that the velocity at P is always proportional to the tangent {PT}. This is Newton's sixth corollary. If / be the latus rectum of the parabola that would be described under the same circumstances of projection, if the medium offered no resistance, then 2 V2 cos2 a 3. Problem. To determine the motion of a particle moving in a straight line in a medium resisting in the ratio of the square of the velocity and acted on by a uniform force. Let the symbols V, v, x, m, t, x, have the same meaning that they had in the corresponding problem in which the resistance varied as the velocity. Then the whole moving force upon the particle will clearly be mf–x v also we have the accelerating force on a particle moving in any manner equal to-r-; which, since v =–, may also at d t be put under the form v j-. Taking both these forms, we have m–= mf–x v2 d t J dv m v-j-= mf–x ' which are identical equations. The first equation gives v in terms of t, the second v in terms of x. First. Suppose / = 0, or that the body moves by its ‥.}
}

{"_id":"APfCoYQtPj3voqZbw","authorIDs":[],"author_short":["Brougham, H.","Routh","John, E."],"bibbaseid":"brougham-routh-john-analyticalviewofsirisaacnewtonsprincipia-2012","bibdata":{"author":["Brougham, Henry","Routh","John, Eduard"],"author_short":["Brougham, H.","Routh","John, E."],"bibtex":"@book{ brougham_analytical_2012,\n title = {Analytical View of Sir Isaac Newton's Principia},\n volume = {1},\n isbn = {978-12-3634-281-2},\n publisher = {General Books},\n author = {Brougham, Henry and Routh, Eduard John},\n month = {May},\n year = {2012},\n note = {This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1855 Excerpt: ‥.) W y e V m V cos a/ put {NA} = f, N P = n (my. {CM}–(=)'\"!–/ {COS} a-, T where a =–V. X cos p This is a very simple form of the equation to the curve and enables us to investigate many of its properties with ease. We learn that if the successive values of N A are in geometric progression those of N P will be in arithmetical progression. This is Newton's second corollary. It is also manifest from the manner in which we eliminated t, that we have or the particle moves in such a manner that its distance from O A, measured parallel to any fixed straight line, varies as the time. This is Newton's first corollary. Since O B. cos a = O C, and {OC}={TMV} cos {OB}=-V; X and since any point may be considered as the origin of projection, we learn that the velocity at P is always proportional to the tangent {PT}. This is Newton's sixth corollary. If / be the latus rectum of the parabola that would be described under the same circumstances of projection, if the medium offered no resistance, then 2 V2 cos2 a 3. Problem. To determine the motion of a particle moving in a straight line in a medium resisting in the ratio of the square of the velocity and acted on by a uniform force. Let the symbols V, v, x, m, t, x, have the same meaning that they had in the corresponding problem in which the resistance varied as the velocity. Then the whole moving force upon the particle will clearly be mf–x v also we have the accelerating force on a particle moving in any manner equal to-r-; which, since v =–, may also at d t be put under the form v j-. Taking both these forms, we have m–= mf–x v2 d t J dv m v-j-= mf–x ' which are identical equations. The first equation gives v in terms of t, the second v in terms of x. First. Suppose / = 0, or that the body moves by its ‥.}\n}","bibtype":"book","id":"brougham_analytical_2012","isbn":"978-12-3634-281-2","key":"brougham_analytical_2012","month":"May","note":"This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1855 Excerpt: ‥.) W y e V m V cos a/ put NA = f, N P = n (my. CM–(=)'\"!–/ COS a-, T where a =–V. X cos p This is a very simple form of the equation to the curve and enables us to investigate many of its properties with ease. We learn that if the successive values of N A are in geometric progression those of N P will be in arithmetical progression. This is Newton's second corollary. It is also manifest from the manner in which we eliminated t, that we have or the particle moves in such a manner that its distance from O A, measured parallel to any fixed straight line, varies as the time. This is Newton's first corollary. Since O B. cos a = O C, and OC=TMV cos OB=-V; X and since any point may be considered as the origin of projection, we learn that the velocity at P is always proportional to the tangent PT. This is Newton's sixth corollary. If / be the latus rectum of the parabola that would be described under the same circumstances of projection, if the medium offered no resistance, then 2 V2 cos2 a 3. Problem. To determine the motion of a particle moving in a straight line in a medium resisting in the ratio of the square of the velocity and acted on by a uniform force. Let the symbols V, v, x, m, t, x, have the same meaning that they had in the corresponding problem in which the resistance varied as the velocity. Then the whole moving force upon the particle will clearly be mf–x v also we have the accelerating force on a particle moving in any manner equal to-r-; which, since v =–, may also at d t be put under the form v j-. Taking both these forms, we have m–= mf–x v2 d t J dv m v-j-= mf–x ' which are identical equations. The first equation gives v in terms of t, the second v in terms of x. First. Suppose / = 0, or that the body moves by its ‥.","publisher":"General Books","title":"Analytical View of Sir Isaac Newton's Principia","type":"book","volume":"1","year":"2012","bibbaseid":"brougham-routh-john-analyticalviewofsirisaacnewtonsprincipia-2012","role":"author","urls":{},"downloads":0,"html":""},"bibtype":"book","biburl":"http://bibbase.org/zotero/valy8851","creationDate":"2014-10-20T03:49:00.464Z","downloads":0,"keywords":[],"search_terms":["analytical","view","sir","isaac","newton","principia","brougham","routh","john"],"title":"Analytical View of Sir Isaac Newton's Principia","year":2012,"dataSources":["A4EkMccS6ypgD6dWJ"]}