Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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ac voluntas, pulchras demonſtrationes etſi difficiles, ac longas infracto
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quodam animi vigore ſuperandi, potius quam ab ipſis ſuperari velint.
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<
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">Poterat quidem in plures Propoſitiones commodius diſtribui, ſed cum-
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illæ omnes in hanc ſimpliciſſimam eſſent conſpiraturæ, eas omnes ſub
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hac vna Propoſit. </
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<
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bra distinguere placuit, ne Lectoris mens nimium defatigaretur. </
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<
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quanti hæc Propoſitio ſit momenti, ſicut & </
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<
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<
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ta præcipuè earum vniuerſalitate, neminem, qui eaſdem intellex erit,
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fore puto, qui itidem non agnoſcat; </
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<
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">quid enim fuit, quo ad figuras pla-
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nas, Euclidem lib. </
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<
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triangula, & </
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<
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te um homologorum, necnon lib. </
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">Circulos eſſe, vt diame-
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trorum quadrata, hoc eſt in dupla ratione diametrorum? </
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<
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quod ſpectat ad ſolida, quid fuit ipſum nobis in lib. </
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diſſe ſimiles Pyramides eſſe in tripla ratione laterum homologorum, & </
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in Prop. </
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rum quæ ſunt in baſibus, & </
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pla proportione diametrorum? </
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ſe, quædam alia ſimilia ſolida, vt portiones Sphærarum, necnon Sphæ-
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roidearum, & </
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vel laterum homologorum? </
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">Præ huius comparatione, quod in his duabus
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tantum Propoſitionibus edocemur; </
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Prop. </
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">& </
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quod mebercle conſideratione dignum videtur.</
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<
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laterum homologorum, quę ſunt in eorundem homo-
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logis figuris.</
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<
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pla ratione linearum, ſiue laterum homologorum, quæ ſunt in
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eorundem homologis figuris. </
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<
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">Quia ergo dicta ſolida ſunt ſimilia, po-
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terunt duci duo plana oppoſita tangentia in vnoquoque propoſito-
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rum ſolidorum (quæ in ſolido, AP, repræſententur peripſas, AH,
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lib. 1.</
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P {00/ }, & </
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figuris æquidiſtantia, inter quæ etiam ducibilia erunt alia duo plana
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lib. 1.</
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æqualiter ad ipſa, & </
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