Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648

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1
THEOREMA IX.
Impulſus quieſcens eſt æqualis reliquo ſegmento, quod abſcindit hy­
pomochlium à ſemidiametro figuræ motûs.
12[Figure 12]
Quia impulfus mouens & quieſcens ſimul ſumpti, toti impul­
ſui, hic autem ſemidiametro figuræ motus AC ponitur æqua­
lis per Axioma 2: Eſt veró impulſus movens æqualis uni ſe­
gmento AD per theorema 8. erit quoque impulſus quieſcens
æqualis alteri ſegmento DC.
LEMMA.
Centrum grauitatis cuius〈que〉 figuræ rectilineæ invenire.
Sit primùm in triangulo iſopleuro ABC inquirendum cen­
trum grauitatis. in quo ex duobus angulis B & C demittantur
lineæ ad baſim rectæ BD CE. Dico in communi illarum ſecti­
one F eſſe centrum grauitatis. Quia enim recta BD ſecat ba­
ſim mediam; eritineâ centrum grauitatis, per prop. 13 lib. 1
Archimedis de æquipond. Eſt verò idem in recta CE: igitur in
communi ſectione F.

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