Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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<
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>Aliter breuiùs. ex D centro figuræ ducta DA ſecetur in da
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tâ ratione in O: per quod agatur linea CE,
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eidem peralle
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la AH: é centro verò D ſemidiameter figuræ motûs DH. </
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<
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>Di
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co hanc ſecari à lineâ hypomochlij in eadem ratione. </
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>Cùm
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enim ſimilia ſint triangula ADH. ODG: erit DH ad DG, ut
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DA ad DO, hoc eſt in datâ ratione. </
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LEMMA II
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Si duabus inæqualibus lineis addantur æquales; maiorem rationem ha
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bet maior ad minorem, quàm eadem maior aucta ad auctam
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minorem.
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>Duabus inæqualibus AB. CD addantur æquales BF. DL. </
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>Dico AB ad CD maiorem rationem habere, quàm AF ad CL. </
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<
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>Fiat enim ut AB ad CD minorem: ita BF ad aliam minorem
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DG. erit ergo
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antecedens AF ad
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conſequen
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tem CG, ut AB ad CD. </
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<
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>Sed AF ad CG maiorem habetra
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tionem, quàm ad CL: igitur & AB ad CD maiorem habet ra
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tionem, quà AF ad CL. </
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LEMMA III
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Si ex eadem baſi deſcribantur plures figuræ rectilineæ æqualium late
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rum; & ex illâ baſi per illarum centra agatur linea recta; ea quæ
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plura habet latera, centrum magis abducit à baſi.
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<
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>Deſcribantur ex eadem communi baſi AC triangulum A
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BC, quadratum ADEC, & pentagonum AFGHC æquali
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um laterum: & per illarum centra agatur linea recta
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ſe
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cans baſim AC æqualiter per problema theorem. 1. </
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<
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>Quia
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altitudo trianguli BQ eſt minor latere BA, hoc eſt QR; </
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