Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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lineis, vel lateribus homologis deſcriptarum figurarum; </
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bus deſcriptæ figuræ ex traiectis planis producentur (quæ in ſequenti li-
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bro dicuntur, ſolida ad inuicem ſimilaria genita ex dictis ſectionum por-
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tionibus) erunt ſimilia, & </
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<
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">figurarum homologarum eorundem regulæ
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_lib. 2._</
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oppoſita tangentia plana dictis iam deſcriptis figuris æquidiſtantia, quo-
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rum & </
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<
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tiones, vel in earum planis iacebunt. </
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<
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eſſe ſimiles, nam ſi ſecentur planis per axem, conceptæ figuræ fiunt ſimi-
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les, ideſt circuli, quod ſi ſecentur adhuc planis ad horum circulorum pla-
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_huius pr._</
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na erectis, productæ figuræ fiunt pariter circuli deſcripti tanquam dia-
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metris eiſdem rectis lineis, in quibus coincidunt circulis per axem du-
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ctis, quæ diametri ſunt etiam incidentes eorundem deſcriptorum circu-
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lorum, & </
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_huius._</
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tangentes omnes inter ſe æquidiſtant, vt facilè patet, & </
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dentes, ſiue diametri deſcriptorum circulorum, quæ axem diuidunt fi-
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militer ad eandem partem, vt ipſi axes, igitur ſpbæræ omnes ſunt ſimi-
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les, & </
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_huius._</
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qui iungit puncta contactuum ductis planis, hinc effecti circuli erunt
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figuræ incidentes dictorum tangentium, & </
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tangentia erunt regulæ homologarum figurarum earundem, vnde tan-
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dem patet quoſuis circulos in ſphæris per centrum tranſeuntes poſſe eſſe
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figuras incidentes earundem ſphærarum, & </
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gentium ſphæras in extremis punctis diametrorum quorumuis dictorum
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circulorum per centrum tr anſeuntium.</
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quitur & </
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iuxta definitionem particu-
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larem de ipſis allatam, AB
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CD, FEHG. </
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eſſe ſimiles iuxta definitio.
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ſolidorum; </
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<
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nis per axes, AC, FH,
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producantur in eiſdem el-
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lipſes, ABCD, FEHG,
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quæ erunt eædem illis, ex quarum reuolutione circa axes, AC, FH,
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