DelMonte, Guidubaldo - In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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Ex hac nona propoſitione duo corolloria elicere poſſum^{9};
quæ quidem tanquam valde nota fortafſe videtur omiſiſſe Ar
chimedes. quamuis primum in ſe〈que〉nti demonſtratione inſeruit.

COROLLARIVM. I.

Ex hoc perſpicuum eſt cuiuſlibet parallelogrammi centrum
grauitatis eſſe punctum, in quo coincidunt rectæ lineæ, quæ
oppoſita latera bifariam ſecant.

Nam (vt Archimedes etiam ſe

〈que〉nti demonſtratione inquit)
ſi parallelogrammi ABCD lineę
EF GH bifariam diuident late
ra oppoſita AB DC, & AD BC.
patet in EF centrum eſſe graui
tatis parallelogrammi AC. ſimi
liter conſtat idem centrum eſſe
in linea GH, quæ oppoſita latera AD BC bifariam ſecat. e
ritigitur in K, vbi EF GH ſeinuicem ſecant.

50[Figure 50]

COROLLARIVM. II.

Ex hoc patet etiam, cuiuſlibet parallelogrammi centrum gra
uitatis eſſe in medio rectæ lineę, quæ bifariam oppoſita latera
diſpeſcit.

Cùm enim oſtenſum ſit centrum grauitatis parallelogram
mi AC eſſe punctum K. & ob parallelogrammum EH eſt
EK æqualis BH. propter parallelogrammum verò
linea KF eſt æqualis HC. ſuntquè BH HC æqua
les. erit EK ipſi KF æqualis. punctum ergo K eſt in medio
rectæ lineę EF, quæ oppoſita latera AB DC bifariam diui
dit. Eoden〈que〉; prorſus modo oſtendetur, K medium eſſe rectę lineę
GH, quæ bifariam ſecat oppoſita latera AD BC.

34. primi.

In ſe〈que〉nti Archimedes adhuc perſiſtit in inuentione cen
tri grauitatis parallelogrammorum, alia tamen methodo.
nam hoc peripſorum parallelogrammorum diametros duo
bus modis aſſequitur.

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