Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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<
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>Sit recta linea AB ſecta in puncto C biſariam, & non
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bifariam in puncto D. </
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<
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>Dico rectangulum ADB æqua
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le eſſe rectangulo BDC bis vnà cum quadrato BD.
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>Quoniam enim rectangulum ADB, æquale eſt duobus
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rectangulis, & ex BD, DC, & ex AC, BD, hoc eſt ex
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CB, BD: ſed rectangulum ex CB, BD, eſt rectangu
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lum ex BD, DC, vnà cum quadrato BD; rectangulum
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igitur ex AD, DB, æquale eſt duobus rectangulis ex
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BD, DC, vnà cum quadiato BD. </
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<
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>Si igitur recta linea
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ſecta fuerit bifariam, & non bifariam, &c. </
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<
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>Quod demon
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ſtrandum erat. </
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PROPOSITIO II.
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<
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>Si circulum, vel ellipſim duæ rectæ lineæ tan
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gentes in terminis coniugatarum diametrorum,
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conueniant: & punctum in quo conueniunt, &
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centrum figuræ iungantur recta linea; quæcun
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que hanc vnà cum prædictæ figuræ termino al
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terutri diametrorum parallela ſecuerit recta li
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nea, ita ipſa ſecabitur in duobus punctis, vt re
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ctangulum bis contentum ſegmentis, quorum al
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terum inter diametrum, & terminum figuræ, al
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terum inter figuræ terminum & contingentem
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interijcitur, vnà cum huius quadrato, ſit æquale
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quadrato reliqui ſegmenti inter diametrum, & </
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