Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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hoc eſt celeritatem K F, quia K F æquatur ipſis H G, B D,
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ſunt enim partes ſingulæ H K, F G, æquales ipſi A B,
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ac proinde utraque ſimul ipſi B D, quam eſſe duplam
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A B oſtendimus propoſitione 2. </
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<
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xml:space
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">Itaque celeritatem in fine
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deſcenſus K acquiſitam ſurſum convertendo, ſi grave æqua-
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bili motu ferretur, conficeret una temporis parte ſpatium
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K F. </
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<
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xml:space
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">Atqui, gravitatis actione accedente, diminuetur
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aſcenſus K F ſpatio F G ipſi A B æquali, ut patet ex di-
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ctis ad hypotheſin initio ſumptam. </
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<
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">Ergo parte prima tempo-
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ris aſcendet grave tantum per K G, quo eodem ſpatio parte
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temporis noviſſima deſcenderat. </
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<
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xml:space
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">Simul vero & </
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<
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">celeritati tan-
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tum deceſſiſſe neceſſe eſt, quantum acquiritur temporis parte
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una deorſum cadendo, hoc eſt celeritatem B D. </
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<
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xml:space
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">Itaque gra-
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ve, ubi ad G aſcenderit, habet celeritatem reliquam H G,
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cum initio aſcenſus habuerit celeritatem H G una cum cele-
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ritate B D. </
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<
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xml:space
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">Eſt autem ipſi H G æqualis G D; </
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<
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">quum æque-
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tur ipſi F E una cum D B, hoc eſt una cum dupla A B,
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hoc eſt una cum duabus F G & </
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<
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">E D; </
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<
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xml:space
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">Ergo ſi ex G, cum
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celeritate æquabili, quantam illic habet, ſurſum pergeret,
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conficeret una parte temporis ſpatium G D. </
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<
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xml:space
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">Accedente au-
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tem gravitatis actione, diminuetur aſcenſus iſte ſpatio D E,
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ipſi A B æquali. </
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<
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xml:space
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">Ergo, hac ſecunda parte temporis, aſcendet
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per ſpatium G E, quod ſimili temporis parte etiam cadendo
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tranſierat. </
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<
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">Simul autem celeritati tantum deceſſiſſe denuo de-
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bet quantum temporis parte una ex caſu acquiritur, nempe
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celeritas B D. </
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<
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xml:space
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">Itaque ubi uſque ad E aſcenderit, habet dun-
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taxat celeritatem F E, quæ nimirum relinquitur quum à
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celeritate G D aufertur celeritas B D. </
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<
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xml:space
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">Nam B D, ut jam
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diximus, æqualis eſt duabus D E, F G.</
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<
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">Eſt autem ipſi F E æqualis E A, quum F E æquetur ipſi
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B D bis ſumptæ, hoc eſt ipſi B D una cum dupla A B,
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hoc eſt una cum duabus A B, D E. </
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<
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xml:space
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">Ergo ſi ex E cum ce-
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leritate æquabili, quantam illic habet, ſurſum pergeret, con-
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fecturum eſſet una temporis parte ſpatium E A. </
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<
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dente actione gravitatis, diminuetur aſcenſus iſte ipſo ſpatio
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A B. </
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