Bošković, Ruđer Josip
,
Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium
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THEORIÆ
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<
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<
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cationis ad o-
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ſcillationes in
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latus ponderum
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jacentium in
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eodem plano.</
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ſinuum q, & </
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<
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">g variatos, niſi QP tranſeat per G, quo caſu
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ſit q = g; </
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<
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<
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">quidem ubi G accedit in infinitum ad P R, de-
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creſcente g in infinitum, ſi PQ non tranſeat per G, manen-
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te finito q, valor {q/g} excreſcit in infinitum; </
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<
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">contra vero appel-
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lente QP ad P R, evadit q = o, & </
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<
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">g remanet aliquid, adeo-
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que {q/g} evaneſcit. </
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<
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">Id vero accidit, quia in appulſu G ad verti-
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calem totum ſyſtema vim acceleratricem in infinitum immi-
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nuit, & </
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<
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<
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">adeoque ut radius PQ adhuc
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obliquus ſit ipſi in ea particula oſcillationis infiniteſima iſo-
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chronus, nimirum æque parum acceleratus, debet in infini-
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tum produci. </
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<
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">Contra vero appellente PQ ad PR ipſius ac-
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celeratio minima eſſe debet, dum adhuc acceleratio radii P G
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obliqui eſt in immenſum major, quam ipſa; </
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<
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te ſua ipſe radius compenſare debet accelerationis imminutio-
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nem.</
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<
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">Quare ut habeatur pendulum ſimplex conſtantis longi-
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cum formula
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generali.</
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tudinis, & </
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<
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">in quacunque inclinatione iſochronum compoſito,
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debet radius PQ ita aſſumi, ut tranſeat per centrum gravita-
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tis G, quo unico caſu fit conſtanter q = g, & </
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<
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conſtans QP = {AxAP
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+ BxBP
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/MxGP} &</
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<
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">c, quæ eſt formula ge-
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neralis pro oſcillationibus in latus maſſarum quotcumque, & </
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quomodocunque collocatarum in eodem plano perpendiculari
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ad axem rotationis, qui caſus generaliter continet caſum maſ-
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ſarum jacentium in eadem recta tranſeunte per punctum ſuſ-
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penſionis, quem prius eruimus.</
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<
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<
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">Inde autem pro hujuſmodi caſibus plura corollaria de-
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">Corollarium
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pro poſitione
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centri oſcilla-
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tionis, & gra-
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vitatis ex ea-
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dem parte a
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puncto ſuſpen.
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ſionis.</
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ducuntur. </
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<
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<
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">gravitatis centrum debere jacere in
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recta, quæ a centro ſuſpenſionis ducitur per centrum oſcillationis,
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uti demonſtratum eſt num. </
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<
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<
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<
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partem cum ipſo centro oſcillationis. </
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<
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">Nam utcumque mutetur ſi-
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tus maſſarum per illud planum, manentibus puncto ſuſpenſio-
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nis P, & </
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<
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">centro gravitatis G, ſignum valoris quadrati cujuſ-
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vis A P, BP manebit ſemper idem. </
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<
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">Quare formula valoris
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ſui ſignum mutare non poterit; </
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<
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">adeoque ſi in uno aliquo ca-
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ſu jaceat Q reſpectu P ad eandem plagam, ad quam jacet G;
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</
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<
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">debebit jacere ſemper. </
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<
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">Jacet autem ad eandem plagam in ca-
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ſu, in quo concipiatur, omnes maſſas abire in ipſum centrum
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gravitatis, quo caſu pendulum evadit ſimplex, & </
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<
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ſcillationis cadit in ipſum centrum gravitatis, in quo ſunt
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maſſæ. </
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<
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