Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CONTROVERSIA.
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Rogantur hac occaſione eruditi, ut examinent, qualem le-
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gem communicationis celeritatum obſervent corpora mota,
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quæ ex una parte innituntur firmo fulcimento, ex altera alii
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corpori itidem, ſed tardius moto: </
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<
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">ſi namque celeritatis ex-
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ceſſus, qui hinc inde communicandus eſt, in eadem ratione
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diſtribueretur, in qua diſtribuitur onus aliquod, quod vecti
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duobus ſuſtento fulcris impoſitum eſt, nimirum in ratione
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reciproca diſtantiarum mobilis a fulcris, tum imitando ra-
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tiocinium Dn. </
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">Catelani, deprehenderemus, ſummam altitu-
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dinum, ad quas aſcendunt ſeparata penduli pondera, viciſ-
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ſim nunc minorem eſſe ſumma altitudinum, e quibus antea
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conjunctim deſcenderant, quod iterum Hugenianam Propo-
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ſitionem everteret.</
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">En calculum: </
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xml:space
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">Altitudo B N = 4 ped.</
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Celeritas ponderis A acquiſita in puncto L, ubi deſcendit
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ſeparatim # = 1
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Celeritas ponderis B acquiſita in puncto N, quando cadit
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ſeparatim # = 2
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Celeritas ponderis A acquiſita in puncto L, quando deſcen-
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dit conjunctim # = x
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Igitur Exceſſus celeritatis ponderis A, qui tam in axem,
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quam in pondus B redundat # = 1 - x
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Et pars hujus exceſſus, quæ ſoli ponderi B communicatur
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# = {1/4} - {1/2} x
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Tota ergo celeritas ponderis B in puncto N cum conjun-
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ctim cadit # = 2 {1/4} - {1/4} x
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xml:space
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">4 x = {36/17} eorum-
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que quadrata {81/289} & </
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">{1296/289} quorum ſumma 4 {13/17} minor eſt 1 + 4 = 5.
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">Catelani hoc monebo,
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quod etiamſi commune gravitatis centrum juxta illum altius
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aſcendere deberet, quam deſcendit, nondum tamen ſequa-
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tur, repertum fore motum perpetuum, ut ſibi perſuadet Ill. </
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Hugenius; </
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">quoniam in iſtis abſtrahi ſolet ab aëris reſiſtentia,
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a diminutione celeritatis, quæ neceſſario ſequitur disruptio-
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nem vinculi, quo connectebantur partes penduli, </
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