Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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<
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xml:space
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">Hæc Propoſitio manifeſta eſt, inuoluit. </
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<
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<
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xml:space
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">requiſita omnia defini-
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xml:space
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">Defin. 21.
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huius.</
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tionis ſimilium ſolidorum; </
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<
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">nam hic habemus duo ſolida, ea nempè,
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quæ ſecantur planis dictarum figurarum, quorum duo extrema ſiue
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primo ducta æquidiſtantia plana talia ſunt, vt illis incidant duo pla-
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na (in quibus nempè reperiuntur propoſitæ figuræ ſimiles, quarum
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homologarum regulę ſunt communes ſectiones earum, & </
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<
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">dictorum
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oppoſitorum planorum tangentium) ad eundem angulum ex eadem
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parte, ſunt autem figuræ planę deſcriptæ lineis, vel lateribus homo-
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logis propoſitarum figurarum inter ſe ſimiles, illæ. </
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<
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<
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">quæ ſecant in-
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cidentes propoſitarum figurarum, & </
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<
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xml:space
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">ſubinde altitudines dictorum ſc-
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">17. Vnd.
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Elem.</
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lidorum ſimiliter ad eandem partem, & </
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<
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">æquidiſtant dictis tangenti-
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bus planis, reſpectu quorum altitudines dictas aſſumptas intelligo;
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</
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<
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">& </
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<
s
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xml:space
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">quia ſupponimus omnium deſcriptarum ſimilium figurarum late-
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ra homologa deſcribentia eſſe lineas, vel latera homologa ſimilium
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figurarum, quæ omnia ſunt inter ſe æquidiſtantia, ideò omnes ea-
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<
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xlink:label
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xml:space
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">Corol. 23.
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huius.</
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rum lineæ homologæ duabus quibuſdam regulis æquidiſtabunt, & </
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ipſa latera deſcribentia erunt etiam lineæ incidentes, vel in eiſdem
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productis ſaltem reperiri poterunt incidentes deſcriptarum ſimilium
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figurarum, & </
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<
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">oppoſitarum tangentium duabus quibuſdam ſemper
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ęquidiſtantium, ſcilicet eis, quę cum dictis incidentibus angulos con-
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tinent ęquales (erunt autem dicta latera homologa incidentes, ſi di-
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ctæ tangentes tranſeant per extrema laterum deſcribentium, ſi au-
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tem non, poterunt tamen in ipſis lateribus productis aſſumi earun-
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<
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">Ex Lem.
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antec.</
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dem incidentes, quæ erunt, vtipſa latera homologa) & </
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<
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propoſitæ figuræ ſint ſimiles, ſubinde etiam erunt ſimiles illæ, quæ
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capient omnes dictas incidentes, ſi fortè accidat ipſa latera homolo-
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ga deſcribentia non eſſe incidentes, vt dictum eſt, igitur adſunt hic
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omnes conditiones definitionis meæ ſimilium ſolidorum, ergo ſoli-
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da, in quibus dictæ ſimiles deſcriptæ figuræ ex traiectione dictorum
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planorum producuntur, erunt ſimilia, & </
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<
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">regulæ figurarum homo-
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logarum erunt dicta plana tangentia, & </
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<
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">eorum, ac dictorum ſolido-
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rum figuræ incidentes, propoſitæ primò figuræ, vel aliæ in eiſdem
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planis inuentæ, illæ ſcilicet, in quibus iacent omnium ſimilium de-
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ſcriptarum figurarum lineæ incidentes, quod oſtendere opus erat.</
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<
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">_H_Inc apparet ſi deſcriptæ figuræ omnes ſint inter ſe ſimiles, dicta,
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ſolida pariter eſſe ſimilia. </
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<
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">Vnde ſi intelligamus ſimiles coni ſe-
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ctionum portiones, ſiue eaſdem integras, circa axes, vel diametros, & </
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ab ordinatim applicatis ad axim, vel diametrum, earundem deſcribi ſi-
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mil. </
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<
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">s figuras planas eiſdem ſectionum portionibus erectas, tanquam </
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