Ceva, Giovanni - Geometria motus

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1eius HIK eße in octuplicata ratione eiuſdem A ad B; quod
idem omnino diceretur ſi figura GFK trilineum eſſet. Ratio
autem A ad B dicetur impoſterum logarithmica poteſtatum
parabolæ, ſeu trilinei, aut hyperbolæ.

ASSVMPTVM.

REliquum eſt vt oſtendamus, parabolam GFK ad
portionem HIK eſſe vt rectangulum GF ad rectan
gulum HI in IK, ſcilicet eſſe in ratione compoſita baſium,
& altitudinum parabolarum, quod nempe ſic oſtendetur,
Sit vt ſupra FGK parabola, eiuſque portio IHK; exiſtenti
bus verò applicatis FG, IH, fiat EG ad IE vt FK ad KI, ſit

que IE baſis, et K vertex parabolę IEK ſimilis ipſi GFK pa
tet propter ſimilitudinem figurarum, eſſe parabolam GFK
ad parabolam IEK in eadem duplicata ratione FG ad IE,
in qua nempe eſt rectangulum GF in FK ad ſibi ſimile re
ctangulum EI in IK, ob idque rectangulum GF in FK ad
rectangulum EI in IK, cum ſint interſe vt parabola GFK ad
parabolam EIK, hæc verò parabola ad ipſam IHK habeat
eandem rationem, ac IE ad IH; ſeu ob eandem altitudinem
IK vt rectangulum EI in IK ad rectangulum HI in IK, erit
ex æquali parabola GFK ad parabolam HIK vt rectangu
lum GF in FK ad rectangulum HI in IK. Quod &c.

Tab. 3. Fig. 2.

PROP. XIV. THEOR. XIV.

Tab. 2. fig. 3.

IN quacunque hyperbola (excepta ſemper conica) cu
ius aſſymptoti EA, EM, ſi ſit poteſtas applicatarum DC
AB altior poteſtate abſciſſarum AE, ED (ſic enim finitą
erit magnitudine ſecundum eam aſſymptoton, quæ appli
catis parallela eſt) ſpatium ipſum hyperbolæ & BAE &
ad ſui portionem & CDE & habebit eandem rationem, ac
rectangulum BAE ad rectangulum CDE, ſeu (aſſumpta

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