Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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oriuntur dictæ ſphæroides, & </
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nit. </
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<
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<
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<
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xml:space
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planis ad axem rectis in dictis ſphæroidibus gignuntur circuli, vt ex.
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</
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<
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">BNDO, EXGV, (qui ſecent axes, AC, FH, ſimiliter ad ean-
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">34. huius.</
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dem partem in punctis, M, I,) quorum diametri ſunt communes ſe-
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ctiones cum figuris per axem tranſeuntibus, vt ipſę, BD, BG, ideò
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iſtæ erunt incidentes ipſorum circulorum, BNDO, EXGV, & </
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huius.</
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oppoſitarum tangentium in punctis, B, D; </
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<
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cæteris intelligemus. </
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<
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">Ergo ſi per axium, AC, FH, extrema ducta
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ſint duo oppoſita tangentia plana, quæ erunt circulis, BNDO, E
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XGV, parallela, habebimus plana ellipſium, ABCD, FEHG,
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illis incidentia ad eundem angulum ex eadem parte; </
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<
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erecta, in quibus reperientur ſimiles figuræ, ellipſes nempè iam di-
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ctæ, & </
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">homologarum earundem regulæ erunt communes ſectiones
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earundem productorum planorum cum oppoſitis tangentibus pla-
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nis, quæ homologę erunt incidentes homologarum figurarum (qua-
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rum regulæ ſunt dicta tangentia plana) & </
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<
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per earundem extrema ductarum, quæ ſemper duabus quibuſdam re-
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gulis æquidiſtabunt. </
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<
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fin. </
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<
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">earum, ac dictorum oppoſitorum tangentium pla-
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norum figuræ incidentes erunt eædem ellipſes, ABCD, FEHG,
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per axes tranſeuntes, quod &</
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">P Oſita definitione ſimilium portionum ſphæràrum, vel
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ſphæroidum, aut conoidum, ſiue earundem portionum,
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ſequitur etiam definitio generalis ſimilium 4olidorum.</
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<
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">Sint ſolida, FMH, BAC, ſimiles
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0115-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0115-01
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portiones ſphęrarum, vel ſphæroidum,
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vel ſimiles conoides, ſeu conoidum por-
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tiones iuxta particularem definitionem
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de illis allatam. </
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lia iuxta definitionem generalem ſimi-
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lium ſolidorum. </
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<
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circuli, vel ſimiles ellipſes, nempè, F
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GHN, BDCE, ductis autem planis
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per axes ad rectos angulos baſibus fiant
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in ipſis figuræ, FMH, BAC, quæ e-
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runt ſimiles ſectionum coni portiones, & </
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