Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER VII.
"/>
AP, in æqualia parallelogramma, A &</
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xml:space
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<
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xml:space
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">rurſus autem per
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xml:space
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">Elicit. ex
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ant. Lem.</
note
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alias ipſi, QY, parallelas diuidantur dictæ altitudinis portiones bi-
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fariam, & </
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<
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">ſic ſemper ſiat (ſectis inſimul conſtitutis parallelogram-
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mi@, quæ idcircò etiam bifariam diuidentur) donec ad parallelo-
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grammum, vt ad, ℟Q, deueniatur minus ſpatio, +, ſit igitur ſe-
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xml:space
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">1. Deoim@
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Elem.</
note
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ctum, AP, in parallelogramma, æquè alta, AZ, β&</
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<
s
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xml:space
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">, γ℟, Δ Ρ, per
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ęquidiſtantes lineas, βκ, γV, ΔΧ, quæ ſecent lineas, AQ, in pun-
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ctis, β, Γ, Δ, CQ, in, E, I, N, DP, in, Z, &</
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<
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xml:space
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">, ℟, FT, in, ΛΠΣ, HT,
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in, O, R, S, & </
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<
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xml:space
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">tandem, LY, in, K, V, X, compleanturq; </
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<
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xml:space
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">paralle-
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logramma, BZ, 2&</
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<
s
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xml:space
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">, 3℟, ΔΡ, iuxta deſcriptionem ſuperius tradi-
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tam, erunt enim lineæ, BE.</
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<
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xml:space
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">, 2I, 3N, ΔQ, extra figuram, CQPD,
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quod patebit, veluti, AQ, extra, CQPD, fimiliter cadere oſten-
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ſa eſt, & </
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<
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xml:space
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">conſequeuter figura ex parallelogrammis, BZ, 2&</
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<
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xml:space
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">, 3℟, Δ
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P, compoſita comprehendet ſpatium, CQPD, ſint autem etiam
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completa parallelogramma, E&</
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<
s
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xml:space
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">, Ι℟, NP, quorum deſcriptæ li-
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neæ, ΕΦ, ΙΩ, NM, intra figuram, CQPD, quidem cadere oſtende-
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mus ex eadem ratione, quod dictæ parallelæ ipſi, PQ, propinquio-
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res remotioribus ſint ſemper maiores, & </
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<
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xml:space
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">ſubinde patebit figuram
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ex parallelogrammis, E&</
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<
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xml:space
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">, Ι℟, NP, compoſitam comprehendi à
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figura, CQPD. </
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<
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xml:space
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">Tandem compleantur parallelogramma quoque,
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Gκ, 6V, 9X, ΣΥ, ex quibus compoſitam figuram ſpatium, HTYL,
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eadem methodo comprehendere demonſtrabimus. </
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<
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xml:space
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">Cum ergo fi-
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gura comprehendens ſpatium, CQPD, ſuperet ab eo compreh en-
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ſam parallelogrammis, BZ, 2Φ, 3Ω, ΔΜ, hoc eſt parallelogram-
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mo, ΔΡ, quod eſt minus ſpatio, +, dicta comprehendens figura
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ſuperabit, CQPD, muitò minori ſpatio, quam ſit, +, ſed, HTY
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L, ſuperat, CQPD, ex hypoteſi ſpatio, +, ergo figura compre-
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hendens, CQPD, minor eſt, HTYL, & </
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<
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">multò minor figura ipſum,
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HTYL, comprehendente, quæ iam deſcripta fuit, hoc autem eſt
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xml:space
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">Ex antec.
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Lem.</
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abſurdum, cum enim paralſelogràmmum, BZ, æquetur ipſi, GK, 2
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&</
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<
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xml:space
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">, 6V, 3℟, 9X, &</
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<
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xml:space
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">, ΔΡ, ΣΥ, tota toti adæquatur contra præde-
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monſtrata, non ergo figura, HTYL, maior eſt, CQPD.</
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<
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">Sit nunc eadem minor, ſi poſſibile eſt, eodem ſpatio, +, igitur
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deſcriptis circa, CQPD, eiſdem figuris, ita vt comprehendens, CQ
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PD, ſuperet ab eo comprehenſam minori ſpatio, quam ſit, +, cõ-
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pleantur parallelogramma, OV, RX, SY, ex quibus compoſitam
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figuram, vt ſupra à ſpatio, HTYL, comprehendi oſtendemus. </
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<
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tur ſi comprehendens, CQPD, ſuperat figuram comprehenſam
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minori ſpatio, quam ſit, +, ipſum ſpatium, CQPD, ſuperabit ab
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eo comprehenſam figuram multò minori ſpatio, quam ſit, +, idẽ
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autem ſuperat, HTYL, ſpatio, +, ergo figura comprehenſa </
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