Ceva, Giovanni
,
Geometria motus
,
1692
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bit minorem rationem, quàm omnes illæ ſimul imagines,
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ſeu quam circumſcripta figura AE, HF, IG, KC ad ean
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dem imaginem HPGN; quare Y, quæ priùs oſtenſa fuit
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maior, nunc reperitur minor eadem circumſcripta, quod
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cum fieri nequeat, impoſſibile etiam eſt magnitudinem Y
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maiorem eſſe magnitudine imaginis ABCD. </
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<
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nor, ſi etiam fieri poteſt, & defectus ipſius Y ſupra ABCD
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ſit Z. </
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">Inſcribatur imagini figura ex rectangulis æquealtis, vt
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nempe deficiat ab imagine defectu minori Z; ſic enim ipſa
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inſcripta, quæ ſit AB, IE, KF, DG erit magnitudine pro
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pinquior imagini ABCD, quàm Y, ideoque Y minor erit
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dicta inſcripta figura. </
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">Deinde, quoniam, ſi ponantur mo
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tus æquabiles, quorum imagines rect angula inſcripta HB,
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IE, KF, DG, quæque inter ſe, & propoſitis imaginibus ſint
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homogeneæ; velocitates, quibus efficerentur dicti motus,
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eſſent AB, IE, KF, DG, minimæ ſcilicet imaginum ABEH
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HEFI, IFGK. KGCD, & ideo ſpatia, quæ percurrerentur
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temporibus HA, HI, IK, KD imaginibus illis, maiora eſ
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ſent, quàm quæ ijſdem temporibus tranſigerentur iuxtą
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imagines prædictas rectangula circumſcripta, hinc fit vt
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ſpatium AB ad DE, ſeu magnitudo Y ad imagine HPGN
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habeat maiorem rationem, quàm inſcripta figura ad ean
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dem imaginem HPGN; quare Y, quæ minor erat inſcripta
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figura, modò reſultat maior, non ergo Y minor eſſe poteſt
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imagine ABCD, ſed neque maior vt oſtendimus, ergo ſpa
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tium AB ad DE erit, vt imago ABCD ad imaginem
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PHNG. </
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Ax.
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2.
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huius.
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Cor. </
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1.
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hu
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ius.
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Ex.
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2
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huius.
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<
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">3. & 4. Si verò imagines acuminatæ ſint, aut demum
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quæ cumque, eodem prorsùs modo, quo prima propoſitio
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ne, oſtendemus hoc etiam propoſitum, ergo patet omne
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intentum. </
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