Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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MATHEMATICA. LIB. I. CAP. XIX.
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xml:space
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">Ponamus Cycloïdem ADB, inverſam, cujus axis ſit verticalis, & </
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ex A deſcendere, demonſtrandum anguliut d DE, aut BEL , coſinum
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portionalem eſſe radici quadratæ altitudinis FL , id eſt proportionem
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qui chordæ FE cujus quadratum ad inſtar altitudinis FL augetur & </
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fig. 5.</
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tur . </
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<
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<
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circuli ſit F, & </
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<
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">quod in omnibus punctis cycloïdis Io-
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cum habet, manente eodem radio FB.</
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">Linea ergo celerrimi deſcenſus, à puncto ad punctum, eſt Cycloïs inverſa, cu-
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jus punctum extremum, ut A, cum ſuperiori puncto coincidit & </
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alterum tranſit.</
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Corpus projiciatur per AB, in tempore, in quo poteſt
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fig. I.</
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percurrere AB, vi gravitatis, fertur terræ centrum verſus
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per BF, & </
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per AF ; </
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<
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FC, ipſi AF æqualem, niſi ſecundo momento eadem vi
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gravitatis translatum foret per CG, ita ut motus in ſecun-
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do momento ſit per FG; </
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menti eſt per GH, & </
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vis gravitatis continuò agat, illa temporis momenta mini-
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ma ſunt, & </
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<
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directionis inflexio; </
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<
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nea curva.</
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<
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ſiderari poteſt in omnibus projectionibus, quæ a nobis fie-
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ri poſſunt; </
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dunt, pro parallelis haberi poſſunt; </
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ex gravitate ſemper eſt eadem; </
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ex duobus tantum motibus conſtat, primo æquabili per li-
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neam projectionis, ſecundo terram verſus accelerato .</
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fig. 25</
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temporibus æqualibus, hoc motu, percurret partes æquales
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AB, BC, CD, DE: </
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<
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perpendiculari, directione BF, CG, DH, aut EI, quæ hìc
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parallelæ ponuntur; </
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