Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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qualis radio AW, & ſinus CD eiuſdem arcus DW æqualis ſi
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nui WR. </
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<
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>Verùm licet in principio illorum arcuum ita res
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habeat, in lapſu tamen ob nouas inclinationes, continuò mu
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tatur illa proportio. </
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<
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>Vnde incrementa velocitatis, cùm ex a
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liâ
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aliâ radice naſcantur, non eadem ratione fiunt. </
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>Nam ſinus AB ad ſinum proximum minorem rationem ha
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bet, quàm CD ad ſinum æquè proximum: plus igitur hic
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quàm ibi decedit virtuti motrici. </
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<
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>Quòd ſi
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fiat BD ad
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DF, ut AB ad CD; hoc eſt, vis movens in B ad uim mouentem
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in D, non eodem tempore agitabitur ex D in F, quo ex B in D;
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verùm per ſpatium minus, quàm ſit DF. </
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<
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>Nihil tamen officit
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hoc noſtræ demonſtrationi: quin imò uim affert maiorem. </
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<
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>Sit enim arcus ille minor, per quem ex D fit motus D b: &
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ducatur ſinus ab. </
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ſinus ab eſt maior ſinu EF, mi
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nor verò arcu reſiduo b W; habebit maiorem rationem ad ar
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cum minorem D b, quam recta EF minor ad arcum maiorem
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DF. </
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<
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>Igitur per 4. lemma, arcus D b eſt multò minor ſinu ab, ac
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proinde arcu reliquo b W. </
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<
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>Ex quo cùm pars proportionalis
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abſcindi debeat continuò minor, concludam pendulum non
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priùs ex D quàm ex B attingere W. </
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ratione F non an
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te D, & H non ante F, ac proinde
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H ante D vel B præcur
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currere in W. </
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<
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>Quod ſi dicas, pendulum ex maiori interuallo præcurrere:
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ſequitur plura pendula eiuſdem longitudinis,
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in eodem
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Circulo, ex inæqualibus ſpatijs ſimul recurrendo ſe percutere
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in motu: quod nemo experitur. </
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<
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>Ne tamen ullus dubitationi
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locus ſuperſit, placet aliâ viâ magis planâ idem demonſtrare. </
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THEOREMA I.
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Lapſus gravium in plano inclinato, eſt æqualis duratione
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