Ceva, Giovanni, Geometria motus, 1692

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              quadratum eſſet, porrò in eius auuerſa eſſet poteſtas appli­
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              catarum quadratica, & abſciſſarum quadratocubica. </s>
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              DEMONSTRATIO.
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              Tab.
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              3.
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              Fig.
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              3.</s>
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              <s id="s.000310">ESto rurſus hyperbola & BAE &, et ſicut dictum eſt
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              AE ad ED ſit in ſeptuplicata ratione logarithmicæ
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              rationis A ad B, at DC ad AB in quintuplicata, videlicet
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              quadratocubus ex AE ad quadratocubum ex DE eandem
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              habeat rationem, ac quadratoquadratocubus ex DC ad
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              ſimilem poteſtatem ex AB; Dico in auuerſa figura poteſta­
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              tem aplicatarum eſſe quadratum, cuius
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              2 eſt dif­
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              ferentia exponentium poteſtatum hyperbolæ; poteſtatem
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              verò abſciſſarum eandem eſſe, abſciſſarum eiuſdem hyper­
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              bolæ. </s>
              <s id="s.000311">Sit vt ſupra FK ad KI vt hyperbola & BAE & ad
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              & CDE &, hoc eſt, ſit vt poteſtas ex A, cuius exponens </s>
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              eſt differentia exponentium poteſtatum hyperbolæ ad ſi­
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              milem poteſtatem ex B, & ideo FK ad KI erit duplicata ip­
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              ſius A ad B, ſed DC ad AB eiuſdem illius logarithmicæ
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              quintuplicata; eſtque in hac eadem ratione etiam GF ad
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              IH; ergo cum duplicata huius ſit ſimilis quintuplicatæ KF
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              ad KI (nam vtraque ratio continet decies A ad B) pater,
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              quadratum ex FG ad quadratum ex IH eſſe eam poteſta­
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              tem, quam propoſuimus euenire in applicatis auuerſæ, cum
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              aliàs in abſciſſis ſit vtrobique poteſtas eadem, nempe qua­
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              dratocubi. </s>
              <s id="s.000313">Quod &c. </s>
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              Pr.
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              14.
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              huius.
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              Corollarium.
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              Patet ex noto trilineo, vel parabola FGK eſſe in auuerſa,
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              ſcilicet in hyperbola & BAE & (quæ tunc eſt ſemper magnitu­
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              dine finita iuxta aſsymptoton EM &) poteſtatem
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              ,
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              qua pro exponente habet ſummam exponentium poteſtatum
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              parabolæ, aut trilinei; nam cum eßet in trilineo pracedenti
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              </s>
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