Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
"/>
veluti, BE, ID, iunctæ ſunt in linea, QL, &</
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xml:space
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">, Σ 2, 3 Λ, in linea,
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Τ Γ,) ergo quę tangentibus dictis æquidiſtant in ſigur s, KQM, Π
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Τ Ω, & </
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<
s
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xml:space
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">diuidunt incidentes, KM, ΠΩ, ſimiliter ad eandem par-
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tem, & </
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<
s
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xml:space
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">iacent inter ipſas incidentes, & </
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<
s
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xml:space
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">circuitum figurarum ad ean-
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dem partem eodem ordine ſumptæ, ſunt vt ipſæ incidentes, ergo fi-
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gurę, KQM, ΠΤΩ, ſunt ſimiles, & </
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<
s
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xml:space
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">earundem homologarum re-
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lib. 1.</
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gulæ eædem tangentes, & </
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<
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xml:space
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<
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xml:space
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head
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xml:space
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">PRoducantur nunc ipſę, KM, ΠΩ, indefinitè verſus puncta, M,
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Ω, & </
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<
s
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xml:space
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">ab ipſis productis ſumantur partes æquales, MP, ipſi, K
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M, &</
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<
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<
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">per puncta, P, &</
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tibus parallelę, ZP, ℟ &</
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<
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">, quoniam ergo, KM, ΠΩ, ſunt inciden-
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23. lib. 1.</
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tes ſimilium figurarum, KQM, ΠΤΩ, ideò habebimus etiam ho-
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mòlogas earundem regulis ipſis incidentibus, KM, ΠΩ, ductis er-
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go ex oppoſito tangentibus eaſdem figuras, KQM, ΠΤΩ, paral-
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lelis ipſis, KP, Π &</
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<
s
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">, quæ ſint, XZ, β ℟, poterimus transferre om-
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nes lineas figura@um, KQM, ΠΤΩ, in figuras ipſis, ZP, ℟ &</
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<
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iacentes, translatione facta regulis, KP, Π &</
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<
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A. huius
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Propoſ.</
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ſlationes, vnde reſultent figu@æ, MZP, Ω℟ &</
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<
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les ipſis, KQM, ΠΤΩ, & </
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<
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">ſubinde ipſis, ABD, ΦΣΛ, probab-
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mus autem etiam eaſdem eſſe ſimiles (veluti in figuris, KQM, Π
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<
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Τ Ω, factum eſt) &</
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<
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<
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& </
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<
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">homologarum regulas ipſas, MP, Ω &</
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<
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ctione integras eſſe in figuris, MZP Π℟ &</
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<
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ipſis, ZP, ℟ &</
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<
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">, tum ipſis, MP, Π ℟, nam ex prima translatione
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integras habuimus, quę in figuris, KQM, ΠΤΩ, ipſis, FM, ΔΩ,
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erant æquidiſtantes, & </
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<
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P, Ω ℟ &</
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rò integras habuimus eas, quę ipſis, MP, Ω &</
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per conſtructionem, quæ omnia ſeruare opus eſt.</
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<
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<
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Ω &</
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<
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vt, MP, ad, PO, ita ſit quælibet in figura, MZP, parallela ipſi,
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MP, adeius portionem, & </
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recta, ZP, ex alia verò inlinea, ZO, erit ergo, vt vna ad vnam .</
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</
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