Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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Lapſus grauium in eodem ſegmento Circuli per plures
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chordas eſt velocior.
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>Moueatur graue ex Q in F: Dico velociùs labi per chordas Q
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B. BC. CF, quàm per chordas QB. BF. </
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>Quia enim velociùs de
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ſcendit per duas chordas BC. CF, quàm| per chordam BF per
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Theorema tertium: addito motu communi QB, erit velocior
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lapſus per QB. BC. CF, quàm per QB. BF. </
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THEOREMA V.
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Pendulum æquali tempore mouetur per arcum Circuli &
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chordam eidem ſubtenſam.
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>Moveatur pendulum TC ex C in B: Dico æquali tempore la
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bi per arcum CEB, & chordam CB. </
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>Concipiantur enim per ſin
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gula puncta CGHIK eiuſdem arcus CEB duci tangentes, &
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chordæ his parallelæ BL. BM.BN. BO & c. </
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itaq;
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ex C la
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bendo in ſingula momenta mutat inclinationem, quam indu
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cunt lineæ tangentes; erit ratio motûs in his homologa motui
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per chordas parallelas. </
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>Vt ſi labi incipiat per tangentem CD,
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interuallum motûs in hac erit æquale motui per chordam pa
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rallelam AB. </
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>Nullus autem fit motus in CD, verùm immedi
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atè transfertur in alias tangentes. </
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<
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>Simili modo in GHIK ex
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illâ obliquatione contrahetur motus, inſpatia æqualia chordis
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parallelis BL. BM. BN, BO: in EPQRS verò æquatur chor
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dis BC. BG. BH &c. quæ quidem chordæ ſubten dunt duplum
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illius arcûs, cuiús tangens eſt parallela. </
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<
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>Eſt enim CEB duplum
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arcùs ESB. </
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Atq;
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hæc ratio arcûs dupli, continuatur
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uſq;
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ad
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tangentem BV. quam ubi attigit pendulum ex C, attingit
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