Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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ALIA QVADRATVRA CIRCVLI
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per motum.
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>DVcatur à contactu G per centrum figuræ E linea GL æ
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qualis GB: & ex L ad eam perpendicularis LM ſecans B
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C in M:
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LM æqualis BM. </
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>Si enim iungatur recta BL,
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duo anguli GBL. GLB, ac proinde reſidui MBL. MLB ſunt
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æquales. </
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M, interuallo ML deſcribatur arcus LB
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ſecans
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motûs reflexi GK in O: ex O verò demittantur per
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pendiculares ON. OP. </
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punctum G à plagâ re
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ciprocâ ex H per lineam agitur GL per 5 theorema: impulſus
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verò reſiduus in FE per lineam GB per lemma 2. </
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motus
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medius GK, erit per problem. propoſitionis 35 de propor. mo
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tûs, vt OP ad ON, ita impulſus in GB ad impulſum in GL, æ
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qualem impulſui in H. </
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>Et ſi quidem ON eſt ſemiſſis OP, erit
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impulſus in OP ad impulſum in ON ut 4 ad 2. ſupponamus ve
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rò ſpatium decurſum ab E, ad ſpatium decurſum ab H eſſe in
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ſeſquialterâ ratione, hoc eſt ut 3 ad 2. </
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>Igitur ſi circulus H acci
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piat impulſum ut 3, movebitur ad idem interuallum cum qua
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drato ABCD per corollarium 2 Axiomatis 1 & poſitionem 4. </
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>Etſi fiat ut 4 ad 3 ita ABCD ad aliud; inventum erit quadra
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tum dato circulo H æquale. </
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COROLL ARIVM
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Eadem ratione inveniemus quadratum æquale ſectionibus
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conicis,
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atq;
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adeo illarum fruſtis; ſi loco circuli hu
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iuſmodi figuras ſubſtituamus.
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