Ceva, Giovanni
,
Geometria motus
,
1692
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eiuſdem ſubduodecuplæ, erit figura GFK illius naturæ, vt
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ſit ſemper cubus ex FK ad cubum ex KI ſicut GF ad IH, &
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hoc modo eadem illa figura erit trilineum tertium, ſeu cu
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bicum, ex quo ergo ſequitur, GFK ad HIK ſit in eadem ra
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tione, in qua quadroquadratum ex FK ad quadroqua
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dratum ex KI, hoc eſt ſit vt AE ad ED; ſequiturque etiam
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ob hoc figuram GFK ſubquadruplam eſle circumſcripti
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rectanguli GF in FK; eſt autem vt trilineum GFK ad
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rectã-
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gulum GF in FK circumſcriptum, ſic rectangulum ABME
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ad auuerſam eidem trilineo figuram AB & EA, ergo re
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ctangulum ABME ſubquadruplum erit eiuſdem figuræ
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AB & EA longitudinis infinitæ, quare ipſum rectangulum
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erit ſubtriplum portionis & BM & longitudinis pariter im
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menſæ. </
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">Cum ita ſit, conſtat exemplo hoc quoque,
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eandẽ
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illam rationem eſſe exceſſum maioris exponentis ſuprą
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minorem exponentem ad hoc ipſum, dictarum
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poteſtatũ
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hyperbolæ. </
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Def.
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8.
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huius.
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Pr.
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10.
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huius.
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Pr.
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10.
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huius.
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Pr.
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9.
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huius
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PROP. XIII. THEOR. XIII.
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<
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">SVperior demonſtratio effecta fuiſſet ampliſſima, ſi prę
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ponere voluiſſemus
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quadraturã
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vt datam omnis ge
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neris parabolarum, & trilineorum, verùm cum iſta pars
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ſit plenè tradita, vt videre eſt quinto libro infinitarum pa
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rabolarum eiuſdem de Angelis, ſatius ideo duximus qua
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draturam hyperbolarum à VValiſio, & Fermatio acutiſſi
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mis illis viris propoſitam omnino veram admittere, vt indè
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eam parabolarum & trilineorum vniuerſalem, quam adhuc
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ab alijs non habemus, facillimè, compendiosèque depro
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meremus. </
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<
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">Hanc igitur ita proponimus vt ſubinde oſten
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damus. </
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<
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tione, ac ſunt interſe poteſtates quædam aliæ, & eiuſdem
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gradus diametrorum ab ipſis applicatis abſciſſarum vſque </
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