The Mathematical Principles of Natural Philosophy, Band 3Sherwood, Neely, and Jones, 1819 |
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Seite 100
... cycloid ALI . Which done , take GK to the perimeter GEFG of the wheel , in the ratio of the time in which the body proceeding from A defcribed the arc AP , to the time of a whole revolu- tion in the ellipfis . Erect the perpendicular KL ...
... cycloid ALI . Which done , take GK to the perimeter GEFG of the wheel , in the ratio of the time in which the body proceeding from A defcribed the arc AP , to the time of a whole revolu- tion in the ellipfis . Erect the perpendicular KL ...
Seite 132
... cycloid or epicycloid ) , will be to dou- ble the verfed fine of half the arc which fince that time has touched the globe in passing over it , as the fum of the dia- meters of the globe and the wheel to the femidiameter of the globe ...
... cycloid or epicycloid ) , will be to dou- ble the verfed fine of half the arc which fince that time has touched the globe in passing over it , as the fum of the dia- meters of the globe and the wheel to the femidiameter of the globe ...
Seite 132
... cycloid without the globe , the other in the latter propofition the cycloid within the globe , for diftinction fake . COR . 1. Hence if there be defcribed the entire cycloid ASL , and the fame be bifected in S , the length of the part ...
... cycloid without the globe , the other in the latter propofition the cycloid within the globe , for diftinction fake . COR . 1. Hence if there be defcribed the entire cycloid ASL , and the fame be bifected in S , the length of the part ...
Seite 135
... cycloid , continuing straight . Then will the weight T ofcillate in the given cycloid QRS . Q.E.F. For , let the thread PT meet the cycloid QRS in T , and the circle QOS in V , and let CV be drawn ; and to the rectilinear part of the ...
... cycloid , continuing straight . Then will the weight T ofcillate in the given cycloid QRS . Q.E.F. For , let the thread PT meet the cycloid QRS in T , and the circle QOS in V , and let CV be drawn ; and to the rectilinear part of the ...
Seite 136
... cycloid QRS ; I fay , that all the ofcil- lations , how unequal foever in themselves , will be performed in equal times . For upon the tangent TW infinitely produced let fall the perpendicular CX , and join CT . Because the centripetal ...
... cycloid QRS ; I fay , that all the ofcil- lations , how unequal foever in themselves , will be performed in equal times . For upon the tangent TW infinitely produced let fall the perpendicular CX , and join CT . Because the centripetal ...
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The Mathematical Principles of Natural Philosophy Sir Isaac Newton,Andrew D 1734 Motte,William 1771-1807 Davis Keine Leseprobe verfügbar - 2021 |
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ABFD abfolute accelerative alfo alſo angle VCP apfides apfis arife attracting body axis becauſe bifected body revolving cafe caufes cauſe centre of force centre of gravity centripetal force circle common centre conic fection corpufcle curve line cycloid decreaſe defcend defcribed demonftrated diminiſhed diſtance drawn duplicate ratio ellipfis equal fecond feveral fhall fhould fides figure fimilar fince firft firſt fituate focus folid fome fquare fubduplicate ratio fuch fuperficies fuppofe fyzygies given by pofition given ratio globe greateſt half-fheets hyperbola immoveable increaſed infinitum interfections inverſely laſt latus rectum lefs LEMMA let fall motion move obferved ofcillate orbit paffing parabola parallel parallelogram particles perpendicular plane principal vertex prop proportional PROPOSITION quadratures quantity radius reafon reciprocally rectangle reft right line SCHOLIUM ſpace ſphere tangent thefe themſelves THEOREM theſe thofe thoſe trajectory triangles velocity whofe Widegate