Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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GH, MN. </
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<
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>Dico ſolidi ABC ſectionum, minorem eſſe
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proportionem, ipſius IK ad GH, quàm GH ad MN.
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<
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>Iunctis enim MRS, KSN; quoniam tres rectæ IK,
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RS, MN, ſeſe æqualiter excedunt in trapezio KM; mi
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nor erit proportio IK ad RS, quàm RS ad MN: ſed cir
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culi, & ſimiles ellipſes duplicatam habent inter ſe propor
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tionem diametrorum eiuſdem rationis; trium igitur præ
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dictarum ſolidi ABC ſectionum minor erit proportio IK
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ad RS quàm RS ad MN: ſed maior eſt proportio circu
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li, vel ellipſis GH ad circulum, vel ellipſim MN, quàm
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circuli, vel ellipſis RS, ad circulum, vel ellipſim MN;
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multo ergo minor proportio erit circuli, vel ellipſis IK ad
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circulum, vel ellipſim RS, quàm circuli, vel ellipſis GH ad
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circulum, vel ellipſim MN: ſed minor eſt proportio cir
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culi vel ellipſis I
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K
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ad circulum, vel ellipſim GH, quàm
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eiuſdem circuli, vel ellipſis IK ad circulum, vel ellipſim
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RS; multo ergo minor proportio erit circuli, vel ellipſis
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IK ad circulum, vel ellipſim GH quàm circuli, vel ellip
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ſis GH ad circulum, vel ellipſim MN. </
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<
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>Quod demon
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ſtrandum erat. </
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PROPOSITIO VI.
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<
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>Si ſphæroides ſecetur plano vtcumque præter
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quàm ad axem, circa quem ſphæroides deſcribi
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tur erecto nam tunc circulus fit. </
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<
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>ſectio ellipſis erit:
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ſimilis autem ipſi alia quæcumque ſectio ſphæ
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roidis eidem parallela: earumque omnes diame
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tri quæ eiuſdem ſunt rationis erunt in eodem pla
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no per axem. </
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<
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>Extant hæc demonſtrata ab Archimede in ſuo de ſphæ
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roidibus, & conoidibus. </
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