Ceva, Giovanni, Geometria motus, 1692

Table of figures

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              ratione logarithmica A ad B poteſtatum hyperbolæ)
                <expan abbr="quã">quam</expan>
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              poteſtas ex A, cuius exponens eſt differentia
                <expan abbr="exponentiũ">exponentium</expan>
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              poteſtatum hyperbolæ ad ſimilem poteſtatem ex B. </s>
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              DEMONSTRATIO.
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              <s id="s.000301">QVam rationem habet rectangulum BAE ad ſpatium
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              & BAE &, eandem habet rectangulum CDE ad </s>
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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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              <s id="s.000303">Quod &c. </s>
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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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              <s id="s.000306">SI ab exponente poteſtatis applicatarum hyperbolę de­
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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. </s>
              <s id="s.000307">Itaque
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              cum in ſuperiori hyperbola reſidui exponentis poteſtas </s>
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