Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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THEOREMA IX.
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Impulſus quieſcens eſt æqualis reliquo ſegmento, quod abſcindit hy
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pomochlium à ſemidiametro figuræ motûs.
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>Quia impulfus mouens & quieſcens ſimul ſumpti, toti impul
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ſui, hic autem ſemidiametro figuræ motus AC ponitur æqua
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lis per Axioma 2: Eſt veró impulſus movens æqualis uni ſe
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gmento AD per theorema 8. erit
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impulſus quieſcens
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æqualis alteri ſegmento DC. </
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LEMMA.
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Centrum grauitatis cuius〈que〉 figuræ rectilineæ invenire.
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>Sit primùm in triangulo iſopleuro ABC inquirendum cen
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trum grauitatis. in quo ex duobus angulis B & C demittantur
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lineæ ad baſim rectæ BD CE. </
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>Dico in communi illarum ſecti
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one F eſſe centrum grauitatis. </
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>Quia enim recta BD ſecat ba
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ſim mediam; eritineâ centrum grauitatis, per prop. 13 lib. 1
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Archimedis de æquipond. </
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<
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>Eſt verò idem in recta CE: igitur in
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communi ſectione F. </
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