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" ... time. Subduct from both sides the subduplicate ratio of the latus rectum, and there will remain the sesquiplicate ratio of the greater axis, equal to the ratio of the periodic time. QED COR. Therefore the periodic times in ellipses are the same as... "
The First Three Sections of Newton's Principia: With Copious Notes and ... - עמוד 41
מאת Isaac Newton - 1826 - 183 דפים
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 494 דפים
...ratio of the greater axis, equal to the ratio of the periodick time. Cor. 1. Therefore the periodick times in ellipses, are the same, as in circles, whose...diameters are equal to the greater axes of the ellipses. Cor. 2. And the periodick times in ellipses, are in a sesquiplicate ratio of the mean distances of...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 494 דפים
...ratio of the greater axis, equal to the ratio of the periodick time. Cor. 1. Therefore the periodick times in ellipses, are the same, as in circles, whose diameters are equal to the greater axea of the ellipses. Cor. 2. And the periodick times in ellipses, are in a sesquiplicate ratio of...
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The Three First Sections and Part of the Seventh Section of Newton's ...

Sir Isaac Newton - 1850 - 163 דפים
...rectum, and the ratio of the periodical time. Subduct from both sides the subduplicate ratio of the latus rectum, and there will remain the sesquiplicate ratio...diameters are equal to the greater axes of the ellipses. 2CB = ^2AC .JK. .: 2 AC. 2CB =2AC. V2 AC . V K.\ but 2 AC . 2 CB oc period i , time , .-. 2 AC! V K....
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Newton's Principia: Sections I. II. III.

Sir Isaac Newton - 1863 - 288 דפים
...BG, the periodic time, which varies as the area divided by QT. SP, « AC*. COB. Hence the periodic times in ellipses are the same as in circles whose diameters are equal to the major axes of the ellipses. Observations on the preceding Propositions. 177. Prop. xiv. and its Corollary...
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The True Doctrine of Orbits: An Original Treatise on Central Forces

H. G. Rush - 1887 - 135 דפים
...area, the conclusion which Newton states in one of his corollaries is unavoidable, viz : " the periodic times in ellipses are the same as in circles whose diameters are equal to the major axis of the ellipses. " The major axis of the ellipse alone will not enable us to determine its...
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Principia: First Book. sections I, II, III

Isaac Newton - 1900 - 292 דפים
...BC, the periodic time, •which varies as the area divided by QT.SP, oc AC*. COR. Hence the periodic times in ellipses are the same as in circles whose diameters are equal to the major axes of the ellipses. Observations on the preceding Propositions. 212. Prop. XIV. and Cor. may...
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The Philosophy of Physics

Roberto Torretti - 1999 - 512 דפים
...times in the ellipses are as the 4th power of their greater axes" (Prop. XV). "Therefore, the periodic times in ellipses are the same as in circles whose...diameters are equal to the greater axes of the ellipses" (1726, p. 61; cf. Prop. IV and its Cor. 6). In the middle sections of Book I, Newton proves a series...
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