Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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lineam GE per theorem. 5.
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impulſus ſubcontrarij; erit
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motus E per prop. 31. de proportione motûs, parallelus lineæ
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GK mediæ inter GB & GE. </
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LEMMA III.
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Si figura maior in motu percutiat minorem; habeat verò ſegmentum
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ſemidiametri figuræ motûs, quod eſt inter lineam hypomochlij, & ex
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tremum motûs, maiorem rationem ad reliquum ſegmentum, quod eſt
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inter eandem lineam hypomochlij & figuræ centrum, quàm habeat mi
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nor figura ad maiorem; motus maioris erit parallelus lineæ mediæ inter
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tangentem circuli & eiuſdem perpendicularem ad contactum.
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>Habeat AF ad EF maiorem rationem, quàm circulus H ad
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quadratum ABCD: Dico, huius motum ab illâ plagâ eſſe pa
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rallelum lineæ mediæ inter GB & GH. </
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plagæ AF ad reſiduum impulſum in FE maiorem rationem
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habet, quàm circulus H ad quadratum ABCD: & permu
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tando AF ad H, quàm FE ad ABCD, erit velocior motus
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circuli H, quàm quadrati ABCD. nullam ergo à circulo per
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cuſſo recipit plagam. </
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>Et quia præpondium in E, neceſſe libra
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tionem fieri in G: ac proinde motum in E eſſe parallelum lineæ
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mediæ inter GB & GH. </
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PROBLEMA V.
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Circulo æquale quadratum ex motu invenire.
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>Percutiat quadratum ABCD circulum H, & ex illâ plagà
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moveatur centrum E per lineam parallelam lateri GB: duca
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tur autem linea hypomochlij FG ſecans ſemidiametrum figu
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ræ motûs AE in F. </
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per 1. Lemma AF ad FE, ut circulus </
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