DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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ad parabolen DBE eam habet proportionem, quam linea
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AF ad lineam L. Quoniam autem ita eſt KG ad GB, vt
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HG ad L, & vt eadem KG ad GB, ita eſt DG ad GH. vt
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verò DG ad GH, ita eſt AF ad DG; crunt quatuor lineæ AF
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DG HG L in continua proportione. </
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">& quoniam cubi in tri
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pla ſunt proportione laterum, erit cubus ex AF ad cubum ex
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DG, vt AF ad L. cubus ergo ex AF ad cubum ex DG eam
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habet proportionem, quam parabole ABC ad parabolen
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DBE. quod demonſtrare oportebat. </
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17.34. A
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r
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ch.de qua.
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par.
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16.
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quinti.
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ex prima
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ſextt.
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ex
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4.
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ſexti.
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20.
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primi
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conicorum
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Apoll. </
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ex
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3. A
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rch.
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de quad.
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parab.
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ex cor.
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20.
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ſexti.
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1.
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ſexti.
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11.
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quintl.
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<
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<
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id
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">Oportet autem banc quoquè
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propoſitionẽ
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nobis eſſe cogni
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tam, nem pè quòd ſolida parallelepipeda in eadem baſi conſti
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tuta eam inter ſe proportionem habent, quam ipſarum alti
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tudines. </
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<
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">Hoc quidem à Federico Commandino in eius libro de cen
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tro grauitatis ſolidorum propoſitione decimanona demon
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ſtratum fuit. </
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<
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<
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">Omnis fruſti à rectanguli coni portione abſciſſi
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centrum grauitatis eſt in recta linea, quæ fruſti dia
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meter exiſtit, ita poſitum, vt diuiſa linea in quin
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〈que〉 partes æquales, ſit in quinta parte media; ita
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vt ipſius portio propinquior minoribaſi fruſti ad
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reliquam portionem eandem habeat proportio
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nem, quam habet ſolidum baſim habens quadra
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tumex dimidia maioris baſis fruſti, altitudinem au
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tem lineam æqualem vtri〈que〉 ſimul duplæ mino
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ris baſis, & maiori ad ſolidum baſim habens qua
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dratum ex dimidia minoris baſis fruſti,
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altitudinẽ
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autem lineam æqualem vtri〈que〉 duplæ maioris, &
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minori. </
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</
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