Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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culus AC: centrum autem F propinquius eſſe puncto B,
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quàm centrum S, conſtat ex præcedenti: quare centrum
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G, totius cylindri LM inter puncta F, S cadet. </
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GF ad FS eſſe vt exceſſus, quo recta DE ſuperat tertiam
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partem minoris extremæ maiori poſita ipſa DE in propor
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tione continua ipſius DH ad DE vnà cum ſubſeſquial
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tera ipſius BD, ad axim BE, ita GF ad FS. </
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>Quoniam
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enim portio ABC ad cylindrum LM eſt vt prædictus ex
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ceſſus vnà cum ſubſeſquialtera ipſius BD ad axim BE:
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& vt portio ABC ad LM cylindrum, ita eſt GF ad FS,
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ob centra grauitatis F, G; erit vt prædictus exceſſus vna
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cum ſubſeſquialtera ipſius BD ad axim BE, ita GF ad
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FS. </
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PROPOSITIO XXXIX.
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>Omnis portionis ſphæræ abſciſſæ duobus pla
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nis parallelis centrum intercipientibus, & à cen
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tro æqualiter diſtantibus, centrum grauitatis eſt
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in medio axis, vel idem, quod centrum ſphæræ. </
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<
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>Sit portio ABCD, ſphæræ, cuius centrum G, abſciſsa
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duobus planis parallelis
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centrum G intercipien
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tibus, & æquè ab eo di
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ſtantibus: ſectiones
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circuli minores, quorum
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diametri ſint AD, BC
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centra autem F,E, qui
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bus axis portionis termi
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nabitur, eritque ad pla
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na vtriuſque circuli per
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pendicularis tranſiens per centrum G: & quia illa plana </
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