 | Edmond Halley, Royal Society (Great Britain) - 1705 - 390 pages
...of the leaft Vibrations of a Pendulum, to be to the Time of the Fall of a Body, from the hcighth of half the length of the Pendulum^ as the Circumference of a Circle to its Diameter j whence, as a Corollary, it follows, th.3t as the Square of the Diameter to the Square of... | |
 | Royal Society (Great Britain) - 1722 - 722 pages
...of the leaft Vibrations of a Pundulum, to be to the Time of the Fall of a Body, from the Height of Half the Length of the Pendulum, as the Circumference of a Circle to its Diameter : YVhence, ts a Corollary, it follows, That as the Square of the Diameter to the Square of... | |
 | Jacques Rohault - 1723 - 358 pages
...equal to each other ; and have very nearly the fame Ratio to the Time of the perpendicular Fall through half the Length of the Pendulum ; as the Circumference of a Circle has to its Diameter. Coroll. i. Hence alfo appears a Method of determining the Space through which... | |
 | Thomas Simpson - 1740 - 164 pages
...barelypb*\ which is to the Time, wherein a Body freely descending from Reft,, would fall thro' CB, Half the Length of the Pendulum, as the Circumference of a Circle, to its Diameter. CORO LV MOREOVER, when only -1 is = o, or the Refiftance uniform, the Vibrations will, alfo,... | |
 | John Rowning - 1744 - 470 pages
...large or fmall, will be perform'd in the fame Time. Q^ ED Time in which a Body would fall freely thro1 half the Length of the Pendulum, as the Circumference of a Circle is to its Diameter (£). PR OB. (b) To demonftrate this, the following Lemma's will be of Ufe. LEMMA... | |
 | John Keill - 1745 - 352 pages
...Cycloid, is to the Time of the perpendicular Fall through the Axis of that Cycloid, that is, through half the Length of the Pendulum, as the Circumference of a Circle to its Diameter. And it hence follows, that the Time of any the fmalleft Ofcillation is to the Time of the Fall through... | |
 | Benjamin Martin - 1747 - 398 pages
...of the Times of their Vibrations. (5.) The Time of one Vibration -is to the Time of Defcent through half the Length of the Pendulum, as the Circumference of a Circle to its Diameter. (6.) Whence the Length of a Pendulum vibrating Seconds will be found 39 Inches nearly ; and... | |
 | Royal Society (Great Britain) - 1749 - 674 pages
...of the leaft Vibrations of a Pendulum, to be to riae Time of the Fall of a Body, from the Height of Half the Length of the Pendulum, as the Circumference of a Circle to its Diameter : whence, as a Corollary^ it follows, That as the Square of the Diameter to the Square of... | |
 | John Rowning - 1753 - 476 pages
...Cycloid, will be to the time a Body take? up in falling perpendicularly through a fpace equal to IK, (half the length of the Pendulum ;) as the Circumference of a Circle to its Diameter, and confequently it will always be the fame. They that would fee a Demonftration of this and feveral other... | |
 | William Emerson - 1758 - 410 pages
...cycloid ; the time of one vibration, is 55. to the time of a bodfs falling perpendicularly through half the length of the pendulum ; as the circumference of a circle to the diameter. Let ADa be the cycloid, FD its axis, FGD the generating circle. Let the body defcend... | |
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CIRCULAR arcs, is to the time down half the length of the pendulum, as the circumference of a circle to its diameter ; and therefore, within moderate limits, the time will be the same, whether the arc of vibration be larger or smaller. 
