Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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ſdem Fimiles alteri deſcriptarum .</
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<
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">i. </
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<
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xml:space
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">ita omnia plana ſolidi ſimilaris ge-
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niti ex, ABC, iuxta regulam, BC, (ſimilibus exiſtentibus eiuſdem fi-
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guris vni deſcriptarum) ad omnia plana ſolidi ſimilaris geniti ex eadem
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figura iuxta eandem regulam (huius ſimilibus exiſtentibus figuris alteri
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deſcriptarum) ideſt ita erunt ſolida ſimilaria genita ex eadem figura, A
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BC, iuxta communem regulam, BC, non tamen ſimilaria ad inuicem.
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</
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<
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xml:space
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">ſed, quarum omnia plana ſunt omnes figuræ ſimiles eiuſdem, ABC, ſi-
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miles inquam, quæ ſunt vnius dictorum ſolidorum vni deſcriptar um à,
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BC, figurarum, & </
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<
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xml:space
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">quæ ſunt alterius, ſimiles alteri deſcriptarum fi-
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gurarum.</
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">_V_Nde ſolida ſimilaria, ſed non ad inuicem, genita ex. </
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<
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<
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">à figuris,
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ABC, DEF, iuxta regulas, BC, EF, quæ duas figuras planas
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diſſimiles deſcripſerint, quibus ſint ſimiles figuræ, quæ dicuntur omnia
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plana dictorum ſimilarium ſolidorum, erunt ad inuicem, vt ipſæ figuræ
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diſſimiles deſcriptæ ab ipſis, BC, EF, nam ſolidum ſimilare genitum ex,
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DEF, iuxta regulam, EF, ad ſibi ſimilare genitum ex figura, ABC,
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iuxta regulam, BC, erit vt figura deſcripta ab, EF, ad ſibi ſimilem fi-
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guram deſcriptam à, BC, item ſolidum boc ſimilare genitum ex figu-
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ra, ABC, iuxta regulam, BC, ad ſolidum ſimilare, ſed non fibi,
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genitum ex eadem figura iuxta eandem regulam, BC, erit vt figura de-
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ſcripta à, BC, ſimilis deſcriptæ ab, EF, ad figuram ſibi diſſimilem de-
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ſcriptam ab eadem, BC, (quibus figuris diſſimilibus ſint ſimiles figuræ,
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quæ dicuntur omnia plana ſolidorum ſimilarium genitorum ex eadem fi-
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gura, ABC, iuxta communem regulam, BC,) ergo, ex æquali ſolidum
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ſimilare genitum ex figura, DEF, ad ſolidum ſimilare, ſed non ſibi, ge-
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nitum ex figura, ABC, (genita intellige iuxta regulas, EF, BC,) erit
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vt figura deſcripta ab, EF, cui ſunt ſimiles figuræ huius ſolidi, ad figu-
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ram deſcriptam à, BC, prædictæ diſſimilem, cui ſunt ſimiles figuræ ſoli-
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di ex, BAC, geniti iuxta regulam, BC.</
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lam vnum eorundem laterum, ſunt cylindrici; </
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da ſimilaria genita ex triangulis iuxta regulam vnum eorun-
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dem laterum, ſunt conici, quorum baſes erunt figuræ à re-
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gulis deſcriptæ, & </
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vel triangulorum latera regulis inſiſtentia.</
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