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. </s>
              <s>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. </s>
              <s>Vnde incrementa velocitatis, cùm ex a­
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              liâ
                <expan abbr="atq;">atque</expan>
              aliâ radice naſcantur, non eadem ratione fiunt. </s>
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              <s>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. </s>
              <s>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. </s>
              <s>Nihil tamen officit
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              hoc noſtræ demonſtrationi: quin imò uim affert maiorem. </s>
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              <s>Sit enim arcus ille minor, per quem ex D fit motus D b: &
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              ducatur ſinus ab. </s>
              <s>Quia
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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. </s>
              <s>Igitur per 4. lemma, arcus D b eſt multò minor ſinu ab, ac
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              proinde arcu reliquo b W. </s>
              <s>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. </s>
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                <expan abbr="Eadémq;">Eadémque</expan>
              ratione F non an­
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              te D, & H non ante F, ac proinde
                <expan abbr="neq;">neque</expan>
              H ante D vel B præcur­
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              currere in W. </s>
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              <s>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. </s>
              <s>Ne tamen ullus dubitationi
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              locus ſuperſit, placet aliâ viâ magis planâ idem demonſtrare. </s>
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              THEOREMA I.
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              Lapſus gravium in plano inclinato, eſt æqualis duratione
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