Ceva, Giovanni
,
Geometria motus
,
1692
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eius HIK eße in octuplicata ratione eiuſdem A ad B; quod
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idem omnino diceretur ſi figura GFK trilineum eſſet. </
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">Ratio
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autem A ad B dicetur impoſterum logarithmica poteſtatum
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parabolæ, ſeu trilinei, aut hyperbolæ.
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ASSVMPTVM.
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">REliquum eſt vt oſtendamus, parabolam GFK ad
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portionem HIK eſſe vt rectangulum GF ad rectan
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gulum HI in IK, ſcilicet eſſe in ratione compoſita baſium,
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& altitudinum parabolarum, quod nempe ſic oſtendetur,
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Sit vt ſupra FGK parabola, eiuſque portio IHK; exiſtenti
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bus verò applicatis FG, IH, fiat EG ad IE vt FK ad KI, ſit
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que IE baſis, et K vertex parabolę IEK ſimilis ipſi GFK pa
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tet propter ſimilitudinem figurarum, eſſe parabolam GFK
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ad parabolam IEK in eadem duplicata ratione FG ad IE,
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in qua nempe eſt rectangulum GF in FK ad ſibi ſimile re
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ctangulum EI in IK, ob idque rectangulum GF in FK ad
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rectangulum EI in IK, cum ſint interſe vt parabola GFK ad
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parabolam EIK, hæc verò parabola ad ipſam IHK habeat
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eandem rationem, ac IE ad IH; ſeu ob eandem altitudinem
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IK vt rectangulum EI in IK ad rectangulum HI in IK, erit
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ex æquali parabola GFK ad parabolam HIK vt rectangu
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lum GF in FK ad rectangulum HI in IK. </
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Tab.
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3.
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Fig.
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2.</
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PROP. XIV. THEOR. XIV.
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Tab.
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2.
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fig.
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3.</
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<
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">IN quacunque hyperbola (excepta ſemper conica) cu
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ius aſſymptoti EA, EM, ſi ſit poteſtas applicatarum DC
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AB altior poteſtate abſciſſarum AE, ED (ſic enim finitą
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erit magnitudine ſecundum eam aſſymptoton, quæ appli
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catis parallela eſt) ſpatium ipſum hyperbolæ & BAE &
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ad ſui portionem & CDE & habebit eandem rationem, ac
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rectangulum BAE ad rectangulum CDE, ſeu (aſſumpta </
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