Bošković, Ruđer Josip
,
Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium
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poſſe eſſe utcunque parvam, facile patet. </
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<
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<
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">que magnam
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vel parvam:
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partis ſecundæ
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demonſtratio.</
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ſegmentum axis utcunque parvum, vel magnum; </
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<
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utcunque magna, vel parva. </
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<
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">Ea applicata ad MQ exhibebit
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quandam altitudinem MN ita, ut, ducta NR parallela MQ,
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ſit MNRQ æqualis areæ datæ, adeoque aſſumpta QS dupla
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QR, area trianguli MSQ erit itidem æqualis areæ datæ.
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</
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<
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">Jam vero pro ſecundo caſu ſatis pater, poſſe curvam tranſi-
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re infra rectam NR, uti tranſit XZ, cujus area idcirco eſſet
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minor, quam area MNRQ; </
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<
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">nam eſſet ejus pars. </
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<
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mo licet ordinata QV ſit utcunque magna; </
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<
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ſe arcum M a V ita accedere ad rectas MQ, QV; </
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<
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incluſa iis rectis, & </
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<
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">ipſa curva, minuatur infra quoſcunque
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determinatos limites. </
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<
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">Poteſt enim jacere totus arcus intra duo
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triangula Q a M, Q a V, quorum altitudines cum minui poſ-
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ſint, quantum libuerit, ſtantibus baſibus MQ, QV, poteſt u-
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tique area ultra quoſcunque limites imminui. </
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<
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ea area eſſe minor quacunque data; </
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ptotus, qua de re paullo inferius.</
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<
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primæ.</
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MQ, ut in T, vel in altero extremo, ut in M; </
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<
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rit, ut ejus arcus TV, vel MV tranſeat per aliquod pun-
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ctum V jacens ultra S, vel etiam per ipſum S ita, ut cur-
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vatura illum ferat, quemadmodum figura exhibet, extra trian-
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gulum MSQ, quo caſu patet, aream curvæ reſpondentem in-
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tervallo MQ fore majorem, quam ſit area trianguli MSQ,
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adeoque quam ſit area data; </
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<
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areæ pertinentis ad curvam. </
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<
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cubi axem, ut in H inter M, & </
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">Q, tum vero fieri poſſet, ut
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area reſpondens alteri e ſegmentis MH, QH eſſet major,
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quam area data ſimul, & </
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<
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">area alia aſſumpta, qua area aſſumpta
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eſſet minor area reſpondens ſegmento alteri, adeoque exceſſus
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prioris ſupra poſteriorem remaneret major, quam area data.</
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<
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ptoticam poſſe
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eſſe infinitam,
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vel finitam ma-
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gnitudinis cu-
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juſcunque.</
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tam quamvis, ut in fig. </
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<
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nita, vel finita magnitudinis cujuſvis ingentis, vel exiguæ.
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</
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<
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">Id quidem etiam geometrice demonſtrari poteſt, ſed multo
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facilius demonſtratur calculo integrali admodum elementari; </
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& </
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<
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">in Geometriæ ſublimioris elementis habentur theoremata,
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ex quibus id admodum facile deducitur . </
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<
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y
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= I; erit y = x
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,
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v d x elementum areæ = x
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d x, cujus integrale {n/n-m} x
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+ A,</
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