Ceva, Giovanni
,
Geometria motus
,
1692
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29
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ratione logarithmica A ad B poteſtatum hyperbolæ)
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poteſtas ex A, cuius exponens eſt differentia
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poteſtatum hyperbolæ ad ſimilem poteſtatem ex B. </
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DEMONSTRATIO.
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& BAE &, eandem habet rectangulum CDE ad </
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ſpatium & CDE, & permutando erit rectangu
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lum BAE ad CDE, ſicut ſpatium & BAE & ad ſpatium̨
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& CDE &; ſi igitur in eadem propoſita hyperbola ſit po
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teſtas applicatarum DC, AB quintuplicata ipſius A ad B,
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& AE ad ED ſeptuplicata ſit eiuſdem; erit ſeptuplicatą
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applicatarum in eadem ratione, ac quintuplicata abſciſſa
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rum; ſcilicet quadratoquadratocubus ex DC ad ſimilem
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poteſtatem ex AB erit vt quadratocubus ex AE ad qua
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dratocubum ex DE, eritque ſic maior poteſtas applicata
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rum, atque adeo componetur rectangulum EAB ad EDC
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ex ſeptuplicata ipſius A ad B, qualis eſt AE ad ED, & ſub
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quintuplicata eiuſdem A ad B, quæ eſt AB ad DC; nimi
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rùm erit rectangulum EAB ad EDC in duplicata tantum
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ratione ipſius A ad B: quare ſpatium & BAE & ad id
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& CDE &, quæ ſunt inter ſe, vt ipſa rectangula, erit vt po
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teſtas ex A, cuius exponens eſt differentia exponentium &
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S poteſtatum hyperbolæ ad ſimilem poteſtatem ex B.
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Pr.
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12.
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huius.
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PROP. XV. THEOR. XV.
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trahatur exponens minoris poteſtatis abſciſſarum, po
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teſtas reliqui exponetis erit applicatarum auuerſæ figuræ,
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in abſciſſis verò adeſt vtrobique eadem poteſtas. </
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cum in ſuperiori hyperbola reſidui exponentis poteſtas </
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