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

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1tra grauitatis habere; ac centra grauitatis MNOP intra pa
rallelogramma exiſtere, quoniam parallelogramma fi
guræ ad eaſdem partes concauæ. quod quidem eodem modo
ab Archimede in ſe〈que〉nti ſupponitur.

9. poſt hu
ius.

PROPOSITIO. IX.

Omnis parallelogrammi centrum grauitatis
eſt in recta linea, quæ oppoſita latera parallelo
grammi bifariam diuiſa coniungit.

49[Figure 49]

Sit parallelogrammum ABCD, linea verò EF bifariam diuidat la
tera AB CD. Dico parallelogrammi ABCD centrum grauitatis eſſe
in linea EF. Non ſit quidem, ſed, ſi fieri poteſt, ſit H. & ab ipſo vſ〈que〉
ad lineam EF ducatur H æquidistansipſi AB. Diuiſa verò EB
ſemper bifariam in G. rurſuſquè EG brfariam in K; idèquè
ſemper fiat, tandem quædam relin〈que〉tur linea, putà EK, minor
ipſa HI. Diuidaturquè vtra〈que〉 AE EB in partes AN NM
LE GO OB ipſi EK æquales. quod quidem fieri poteſt, quia
diuiſa eſt EB in partes ſemper ęquales. & ex his diuiſionum pun
ctis ducantur NP MQ LR kS GT OV ipſi EF æquidistantes.
diuiſum enim erit totum parallelogrammum in parallelogramma æqualia
& ſimiliaipſi kF. cùm enim ſint parallelogrammorum baſes
EL LM MN NA KG GO OB ipſi KE parallelo
grammaquè in ijſdem ſint parallelis AB CD conſtituta;
erunt parallelogramma æqualia. ſimilia verò, quoniam
ſunt ęquiangula. Parallelogrammis igitur æqualibus, at〈que〉

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