Bošković, Ruđer Josip
,
Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium
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diſtantiarum ſupra omnes ulteriores æquari progreſſui plani to-
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ties ſumpto, quot puncta habentur, & </
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<
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contrario, quidquid in ejuſmodi progreſſu eſt factum, atque id-
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circo ad æqualitatem reditur. </
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<
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accuratiſſima evadat, exprimat in fig. </
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<
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diſtantiarum æqualium, & </
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<
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mnia puncta diſtribui poterunt in claſſes tres, in quorum prima
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ſint omnia puncta jacentia citra utrumque planum, ut punctum
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E; </
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<
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in tertia omnia puncta adhuc jacentia ultra utrumque, ut G.
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</
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currant rectæ AB in M, H, K, & </
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L; </
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<
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currens in O, P. </
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HI, KL. </
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claſſis E, & </
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<
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F ſecundæ claſſis F, & </
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<
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claſſis ſumma G, & </
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<
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OP dicatur O. </
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ſummam omnium HI fore, FxO; </
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fore GxO; </
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<
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<
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vis FI = HI-FH; </
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<
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re ſumma omnium EN erit e + ExO; </
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<
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= FxO-f, & </
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<
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adeoque ſumma omnium diſtantiarum punctorum jacentium ci-
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tra planum CD, primæ nimirum, ac ſecundæ claſſis, erit e
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+ ExO + FxO-f, & </
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<
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tra, nimirum claſſis tertiæ, erit g-GxO. </
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<
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prioris ſummæ ſupra ſecundam erit e + ExO + FxO-f
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-g + GxO; </
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<
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fuerit e=f + g; </
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<
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e-f-g, totus exceſſus erit ExO + FxO + GxO, ſive (E
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+ F + G)xO, ſumma omnium punctorum ducta in diſtan-
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tiam planorum; </
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<
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ni BC fuerit æqualis huic ſummæ ductæ in diſtantiam O, o-
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portebit, e-f-g æquetur nihilo, adeoque ſit e= f + g, ni-
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mirum reſpectu primi plani AB ſummas diſtantiarum hinc,
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& </
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<
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<
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tum demon-
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ſtrationis, ut
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extendatur ad
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omnes caſus.</
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rioribus formulis contineri poſſunt, concepta zero ſingulorum
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diſtantia a plano, in quo jacent; </
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<
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poſſent, concipiendo alias binas punctorum claſſes; </
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<
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priora ſint in priore plano A B, poſteriora in poſteriore CB,
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quæ quidem nihil rem turbant: </
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<
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">nam prioris claſſis diſtantiæ a
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priore plano erunt omnes ſimul zero, & </
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<
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tur diſtantiæ O ductæ in eorum numerum, quæ ſumma acce-
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dit priori ſummæ punctorum jacentium citra; </
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<
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tem claſſis diſtantiæ a priore erant prius ſimul æquales ſummæ
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ipſorum ductæ itidem in O, & </
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