Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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huius ſeſquialtera BEF: & ſumpta axis BD quarta par
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te DF, & tertia DG: qua ratione erit FG duodecima
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pars axis BD quarta ab ea, cuius terminus D; fiat vt
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IB ad BD, ita FH ad HG. </
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>Dico conoidis, vel portio
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nis ABC centrum grauitatis eſſe H. </
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>Nam vt eſt EB
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ad BD ita fiat DK ad KA: & ponatur KDY ſeſqui
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altera ipſius DK, & ex AK abſcindatur KM ſubſeſ
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quialtera ipſius AK: & ipſis DK DM, DA, æquales
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eodem ordine abſcindantur DL, DN, DC: & deſcri
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bantur triangula, KBL, MBN: & per puncta ABC
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vertice communi B, tranſeant duæ ſectiones parabolæ
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AOB, & BPC, ita vt contingat recta BK parabolam
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AOB, recta autem BL parabolam BPC; ſit autem
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AKLC, parabolarum diametris parallela,. Deinde
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ſecto axe BD bifariam, & ſingulis eius partibus rurſus bi
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fariam in quotlibet partes æquales, ſint ex illis duæ
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partes DQ, QF: & per puncta QF planis quibuſdam
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baſi parallelis ſecentur vnà ſolidum & hyperbole ABC:
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ſintque hyperboles ſectiones, quæ continent ſectiones trian
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gulorum ABC mixti, & rectilinei KBL, rectæ RTX
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ZVS:
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>ſolidi autem ABC ſectiones erunt cir
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culi, vel ellipſes ſimiles baſi circa diametros RS,
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.
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<
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>Quoniam igitur eſt vt
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K ad KD, ita AK ad KM;
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vtrobique enim eſt proportio ſeſquialtera: erit permutan
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do vt YK ad A
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K
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, hoc eſt vt IB ad BD, vel FH, ad
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HG, ita D
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K
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ad
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K
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M, hoc eſt triangulum BDK ad
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triangulum BKM, hoc eſt ad æquale huic ex demon
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ſtratis triangulum A
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K
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B mixtum: hoc eſt in duplis ita,
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triangulum BKL ad duo mixta rriangula AKB, BLC
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ſimul. </
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<
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>ſed duorum triangulorum AKB, BLC ſimul eſt
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centrum grauitatis F, vt in hoc tertio libro demonſtra
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uimus: trianguli autem BKL, vt in primo, centrum gra
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uitatis G; totius igitur trianguli ABC centrum graui
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tatis erit H. </
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