Ceva, Giovanni
,
Geometria motus
,
1692
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ponetur ex ijſdem rationibus; & quoniam ductis inuicem
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exponentibus poſſunt conſiderari quindecim rationes in
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ter ſe ſimiles, ex quibus conſtet tam ratio dictorum cubo
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rum, quàm huic ſimilis altera quadratocuborum, & tunc
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GF ad IH erit triplicata, et FK ad KI quintuplicata
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eiuſdẽ
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ſubquindecuplæ rationis, quæ ſit A ad B; ergo ſimul ad
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ditis ijſdem rationibus, quintuplicata ſcilicet, & triplicata
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exiliet ratio octuplicata ipſius A ad B; proptereaque pa
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rabola GFK ad HIK, ſeu ſi conſideremus figuram & BAEL
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auuerſam parabolæ GFK, ita vt AE ad ED ſit vt para
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bola GFK ad
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parabolã
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HIK; AE ad ED erit pariter octu
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plicata eiuſdem A ad B; & cum ſit ob naturam
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auuerſarũ
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FG ad HI vt DC ad AB; erit DC ad AB triplicata
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eiuſdẽ
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rationis A ad B, qnare vt cubus AE ad cubum DE, itą
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quadratocubocubus DC ad quadratocubocubum ex
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AB: rectangulum igitur ABME ad ſpatium hyperbolicum
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infin
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è longum & BM & erit vt quinque ad tria, & ad vni
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uerſum ſpatium & BAE & vt 5 ad 8, in qua nempe ratio
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ne debet eſſe parabola GF
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K
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ad rectangulum GF in FK.
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Quod &c. </
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Def.
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8.
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huius.
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Pr.
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12
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huius.
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Pr.
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9.
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huius.
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Corollarium.
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Conſtat ſi fuerit ratio A ad B eò ſubmultiplicata rationis
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applicatarum, quoties eſt numerus exponentis poteſtatis ab
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ſciſſarum eiuſdem parabolæ, eſſe ipſam parabolam ad ſui por
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tionem in tam multiplicata ratione A ad B, ac eſt numerus
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aggregati exponentium ambarum poteſtatum parabola. </
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cum eſſet quadratocubus ex FG ad quadratocubum ex IH, ſi
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cut cubus ex FK ad cubum ex IK, propoſita inſuper eſſet A ad
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B. ſubquindecupla alterius dictarum ſimilium rationum ex
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poteſt atibus parabola, oſtenſum fuit rationem A ad B ſubtri
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plicatam ipſius GF ad IH, & ſubquintuplicatam alterius FK
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ad KI, & tandem oſtendimus parabolam GFK ad portionem
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