Bošković, Ruđer Josip
,
Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium
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THEORIÆ
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centrum illud, quod fuerat punctuna ſuſpenſionis; </
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<
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ſtantia a centro gravitatis mutata, mutetur & </
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in eadem ratione reciproca. </
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<
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ctangulum debeat eſſe conſtans; </
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<
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quem habuerat prima; </
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<
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habuerat ſecunda, & </
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<
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diviſæ per alteram.</
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<
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">Altera ex iis
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diſtantiis eva-
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neſcente, abire
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alteram in in-
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ſ
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nitum.</
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evaneſcente, abibit altera in infinitum, niſi omnes maſſæ in uni-
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co puncto ſint ſimul compenetratæ. </
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<
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">Nam ſine ejuſmodi compe-
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netratione ſumma omnium productorum ex maſſis, & </
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<
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tis diſtantiarum a centro gravitatis, remanet ſemper finita
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quantitas: </
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<
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">adeoque remanet finita etiam, ſi dividatur per ſum-
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mam maſſarum, & </
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<
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">quotus, manente diviſo finito, creſcit in
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infinitum; </
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<
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">ſi diviſor in infinitum decreſcat.</
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<
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">Hinc vero iterum deducitur: </
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xml:space
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">Suſpenſione fa-
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cta per centrum
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gravitatis, nul-
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lum haberi mo-
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tum.</
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pſum centrum gravitatis nullum motum conſequi. </
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<
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">Evaneſcit enim
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in eo caſu diſtantia centri gravitatis a puncto ſuſpenſionis, a-
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deoque diſtantia centri oſcillationis creſcit in infinitum, & </
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celeritas oſcillationis evadit nulla.</
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<
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<
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">Quæ diſtantia
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centri oſcilla-
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tionis omnium
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minima pro da-
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ta poſitione mu-
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tua maſſarum
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datarum; ma-
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<
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imam haberi
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nullam.</
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poteſt autem centrum oſcillationis abire in infinitum; </
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<
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erit maxima e longitudinibus penduli ſimplicis iſochroni pen-
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dulo facto per ſuſpenſionem dati ſyſtematis; </
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>
<
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">ſed aliqua debet
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eſſe minima, ſuſpenſrone quadam inducente omnium celerri-
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mam dati ſyſtematis oſcillationem. </
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>
<
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">Ea vero minima debet eſ-
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ſe, ubi illæ binæ diſtantiæ æquantur inter ſe: </
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>
<
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">ibi enim evadit
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minima earum ſumma, ubi altera creſcente, & </
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<
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">altera decre-
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ſcente, incrementa prius minora decrementis, incipiunt eſſe
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majora, adeoque ubi ea æquantur inter ſe. </
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<
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">Quoniam autem il-
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læ binæ diſtantiæ mutantur in eadem ratione, utut reciproca;
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</
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<
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">incrementum alterius infiniteſimum erit ad alterius decremen-
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tum in ratione ipſarum, nec ea æquari poterunt inter ſe, niſi
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ubi ipſæ diſtantiæ inter ſe æquales fiant. </
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<
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">Tum vero illarum
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productum evadit utriusl ibet quadratum, & </
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<
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">longitudo penduli
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ſimplicis iſochroni æquat ur eorum ſummæ; </
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<
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">ac proinde habe-
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tur hujuſmodi theorema: </
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<
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">Singulæ maſſæ ducantur in quadrata
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ſuarum diſtantiarum a centro gravitatis, ac productorum ſumma
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dividatur per ſummam maſſarum: </
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<
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">dupla radix quadrata quo-
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ti exhibebit minimam penduli ſimplicis iſocbroni longitudinem. </
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Vel Geometrice ſic: </
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<
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">Pro quavis maſſa capiatur recta, quæ ad
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diſtantiam cujuſvis maſſæ a centro gravitatis ſit in ratione ſub-
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duplicata ejuſdem maſſæ ad maſſarum ſummam: </
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<
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">inveniatur re-
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cta, cujus quadratum æquetur quadratis omnium ejuſmodi recta-
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rum ſimul: </
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<
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<
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">ipſius duplum dabit quæſitam longitudinem me-
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diam, quæ breviſſimam præſtet oſcillationem.</
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<
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<
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">Hæc quidem omnia locum habent, ubi omnes maſſæ
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<
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bere locum tan-
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tummodo, ubi</
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ſint in unico plano perpendiculari ad axem rotationis, ut </
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