Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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149129LIBER II. veluti, BE, ID, iunctæ ſunt in linea, QL, & , Σ 2, 3 Λ, in linea,
Τ Γ,) ergo quę tangentibus dictis æquidiſtant in ſigur s, KQM, Π
Τ Ω, & diuidunt incidentes, KM, ΠΩ, ſimiliter ad eandem par-
tem, & iacent inter ipſas incidentes, & circuitum figurarum ad ean-
dem partem eodem ordine ſumptæ, ſunt vt ipſæ incidentes, ergo fi-
gurę, KQM, ΠΤΩ, ſunt ſimiles, & earundem homologarum re-
11Defin. 10.
lib. 1. gulæ eædem tangentes, & earum incidentes ipſæ, KM, Π Ω.

B. SECTIO SECVNDA.

PRoducantur nunc ipſę, KM, ΠΩ, indefinitè verſus puncta, M,
Ω, & ab ipſis productis ſumantur partes æquales, MP, ipſi, K
M, & , ω & , ipſi, ΠΩ, & per puncta, P, & , ducantur dictis tangen-
tibus parallelę, ZP, ℟ & , quoniam ergo, KM, ΠΩ, ſunt inciden-
22Corollar.
23. lib. 1. tes ſimilium figurarum, KQM, ΠΤΩ, ideò habebimus etiam ho-
mòlogas earundem regulis ipſis incidentibus, KM, ΠΩ, ductis er-
go ex oppoſito tangentibus eaſdem figuras, KQM, ΠΤΩ, paral-
lelis ipſis, KP, Π & , quæ ſint, XZ, β ℟, poterimus transferre om-
nes lineas figura@um, KQM, ΠΤΩ, in figuras ipſis, ZP, ℟ & , ad-
iacentes, translatione facta regulis, KP, Π & , fiant ergo dictę tran-
33Iux. Sect.
A. huius
Propoſ. ſlationes, vnde reſultent figu@æ, MZP, Ω℟ & , quæ erunt æqua-
les ipſis, KQM, ΠΤΩ, & ſubinde ipſis, ABD, ΦΣΛ, probab-
mus autem etiam eaſdem eſſe ſimiles (veluti in figuris, KQM, Π
443. huius. Τ Ω, factum eſt) & , ZP, ℟ & , eſſe dictarum figurarum incidentes,
& homologarum regulas ipſas, MP, Ω & , patet autem ex conſtru-
ctione integras eſſe in figuris, MZP Π℟ & , tum quæ æquidiſtant
ipſis, ZP, ℟ & , tum ipſis, MP, Π ℟, nam ex prima translatione
integras habuimus, quę in figuris, KQM, ΠΤΩ, ipſis, FM, ΔΩ,
erant æquidiſtantes, & ſubinde etiam integras, quæ in figuris, MZ
P, Ω ℟ & , ipſis, ZP, ℟ & , æquidiſtant, ex ſecunda translatione ve-
rò integras habuimus eas, quę ipſis, MP, Ω & , æquidiſtant, & hęc
per conſtructionem, quæ omnia ſeruare opus eſt.

C. SECTIO III.

NVncin figuris, MZP, Ω ℟ & , à maiori homologarum, MP,
Ω & , quæ ſit, MP, aicindatur, OP, æqualis ipſi, Ω & , &
vt, MP, ad, PO, ita ſit quælibet in figura, MZP, parallela ipſi,
MP, adeius portionem, & portionum termini ſint ex vna parte in
recta, ZP, ex alia verò inlinea, ZO, erit ergo, vt vna ad vnam . i.
vt, MP, ad, PO, ita omnia ad omnia, . ſ. ita omnes lineæ

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