Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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              <p>
                <s xml:id="echoid-s1418" xml:space="preserve">
                  <pb o="112" rhead="IO. BAPT. BENED." n="124" file="0124" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0124"/>
                ſecundo itinere iterum duplicauit ſuos aureos, ex quibus etiam poſtea conſumpſit
                  <num value="8">.
                    <lb/>
                  8.</num>
                numeratis poſteà pecunijs reperit tantummodo .24. aureos in eius marſupio,
                  <reg norm="quae­ ritur" type="simple">quę­
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                  ritur</reg>
                nunc quot habebat aureos in principio primi itineris.</s>
              </p>
              <p>
                <s xml:id="echoid-s1419" xml:space="preserve">Intali caſu, cum ipſe quolibet itinere duplicabat eius pecuniam, nulli dubium
                  <lb/>
                eſt quòd in fine ſecundi itineris ipſe habuiſſet pecuniam ſuam quadruplicatam, ſi
                  <lb/>
                ex ipſa nihil detractum fuiſſet, ſed quia in fine primi itineris conſumpſit .4. aureos,
                  <lb/>
                quibus alios .4. lucratus eſſet in ſecundo itinere, poſteà conſumpſit iterum
                  <num value="8">.
                    <lb/>
                  8.</num>
                aureos, ita
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                ex quadruplo ſuæ primæ pecuniæ, rectè dici poteſt, quod conſum-
                  <lb/>
                pſerit .16. aureos; </s>
                <s xml:id="echoid-s1420" xml:space="preserve">qui quidem numerus ex communi conceptu erit differentia in-
                  <lb/>
                ter .24. & quadruplum prioris pecuniæ, cum qua profectus fuit in principio eius iti-
                  <lb/>
                neris; </s>
                <s xml:id="echoid-s1421" xml:space="preserve">quapropter ſi addiderimus .16. ipſi .24. habebimus .40. pro quadruplo eius
                  <lb/>
                prioris pecuniæ. </s>
                <s xml:id="echoid-s1422" xml:space="preserve">Rectè igitur dici poteſt, ſi .4. prouenit ab vno, à quo numero pro
                  <lb/>
                ueniet .40.</s>
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              <p>
                <s xml:id="echoid-s1423" xml:space="preserve">Videamus igitur nunc quo pacto hoc reſpondeat cum methodo antiquorum.
                  <lb/>
                </s>
                <s xml:id="echoid-s1424" xml:space="preserve">Ego enim inueni duas poſitiones ſcriptas à Tartalea pro prima pecunia hoc eſt .12.
                  <lb/>
                et .14. ſed à .12. pro primo errore reperi .8. more antiquo à .14. verò pro ſecundo er-
                  <lb/>
                rore proueniebat .16. producta autem horum numerorum diametraliter, ſunt .112.
                  <lb/>
                et .192. quorum differentia eſt .80. pro tertio producto, quo diuiſo per differen-
                  <lb/>
                tiam
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                .8. ſcilicet, præbetnobis .10. pro pecunia quæſita, vt etiam ego inueni.</s>
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              <p>
                <s xml:id="echoid-s1425" xml:space="preserve">Sed hoc mihi viſum eſt ſubtilius examinare mea methodo mediante, vtin figu-
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                ra
                  <var>.G.</var>
                videre eſt, prius enim ſuo loco poſuitria producta dicta, deinde duas poſitio
                  <lb/>
                nes .12. et .14. & quia ſciebam productum .112. oriri à multiplicatione .14. cum .8.
                  <lb/>
                ideo poſui talem numerum .8. ſuo loco diametraliter oppoſito ei producto .112.
                  <lb/>
                & quia ſciebam etiam productum .192. naſci ex .12. et .16. ideo ſuo loco poſui hunc
                  <lb/>
                numerum .16. qui eſt maxima differentia inter duos conſequentes ( ita à me ſupra
                  <lb/>
                nominatos) à qua differentia dempta priori .8. iam inuenta, reliqua .8. mihi daba-
                  <lb/>
                tur,
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                ſuo loco notaui, ſuo
                  <reg norm="etiam" type="context">etiã</reg>
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                loco ſcripſi .2. differentiam inter
                  <lb/>
                12. et .14. antecedentium. </s>
                <s xml:id="echoid-s1426" xml:space="preserve">ſed
                  <lb/>
                  <figure xlink:label="fig-0124-01" xlink:href="fig-0124-01a" number="169">
                    <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0124-01"/>
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                quia ſciebam eandem proportio
                  <lb/>
                nem eſſe inter hanc differentiam
                  <lb/>
                &
                  <reg norm="differentiam" type="context">differentiã</reg>
                .8. huic
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                ,
                  <lb/>
                quæ reperitur inter .12.
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                  <lb/>
                tem, &
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                conſequentem; </s>
                <s xml:id="echoid-s1427" xml:space="preserve">ideo
                  <lb/>
                poſui .48. pro dicto conſequenti,
                  <lb/>
                diuiſi poſtea productum .80. per
                  <num value="8">.
                    <lb/>
                  8.</num>
                differentiam ei diametraliter
                  <lb/>
                oppoſitam, vnde prouenit mihi
                  <lb/>
                10. cui ita proportionatus eſt
                  <reg norm="ſuus" type="simple">ſuꝰ</reg>
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                numerus conſequens .40. vt .48.
                  <lb/>
                ad .12. et .56. ad .14. exijſdem ra-
                  <lb/>
                tionibus à meſupra dictis.
                  <lb/>
                </s>
                <s xml:id="echoid-s1428" xml:space="preserve">In tali igitur figura videntur nu-
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                merinaturaliter
                  <reg norm="correſpondentes" type="context">correſpondẽtes</reg>
                  <lb/>
                ipſis poſitionibus, & hac metho-
                  <lb/>
                do poſſumus inuenire tales numeros conſequentes in omnibus alijs exemplis à no-
                  <lb/>
                ſtris maioribus ſcriptis.</s>
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