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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              <pb o="116" rhead="IO. BAPT. BENED." n="128" file="0128" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0128"/>
              <figure position="here" number="174">
                <image file="0128-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0128-01"/>
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              <figure position="here" number="175">
                <image file="0128-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0128-02"/>
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              <p>
                <s xml:id="echoid-s1462" xml:space="preserve">I Dem etiam poteſt dici de .15. problemate (ſicut de alijs multis) vbi ponit tres
                  <lb/>
                homines habentes .40. aureos quorum primus habet duas quintas partes ſecun-
                  <lb/>
                di,
                  <reg norm="ſecundus" type="context">ſecũdus</reg>
                verò
                  <reg norm="quinque" type="simple">quinq;</reg>
                octauas tertij,
                  <reg norm="quæritur" type="simple">quærit̃</reg>
                  <reg norm="nunc" type="context">nũc</reg>
                quot ducatos habeat vnuſquiſque.</s>
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                <s xml:id="echoid-s1463" xml:space="preserve">Quis non videt quæſo,
                  <reg norm="quod" type="simple">ꝙ</reg>
                omnes partes erunt .15. quare cum dixerimus ſi .15. dat
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                nobis .2. (pro prima portione primi hominis) quid dabit .40? </s>
                <s xml:id="echoid-s1464" xml:space="preserve">vnde nobis proueniet
                  <lb/>
                5. cum tertia parte.</s>
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              <p>
                <s xml:id="echoid-s1465" xml:space="preserve">Et de .29. ſimiliter aſſero, vbi ponit
                  <reg norm="alium" type="context">aliũ</reg>
                emiſſe tria fruſta panni pro ducatis .48.
                  <lb/>
                quarum ſecundam habuit pro dimidio precio primæ, tertiam autem pro quarta
                  <lb/>
                parte ipſius ſecundæ, </s>
                <s xml:id="echoid-s1466" xml:space="preserve">quare omnes partes erunt .13. quapropter precium tertiæ pe-
                  <lb/>
                tiæ erit tertiadecima pars ipſius .48. hoc eſt .3. cum .9. tertijs decimis.</s>
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                <s xml:id="echoid-s1467" xml:space="preserve">Adhuc duo exempla videtur mihi proponere, quorum primum eſt .38. eiuſdem
                  <lb/>
                lib. vbi ſupponitur operarium quendam velle perficere opus quoddam ſpacio die-
                  <lb/>
                rum .36. tali pacto, quod qualibet die, in qua ipſe operaturus ſit lucretur ſolidos
                  <num value="16">.
                    <lb/>
                  16.</num>
                qualibet verò die, in qua nihil agat perdat ſolidos .24. </s>
                <s xml:id="echoid-s1468" xml:space="preserve">Tunc accidit, vt exacto
                  <lb/>
                termino
                  <reg norm="perfectoque" type="simple">perfectoq́;</reg>
                opere, tantum lucratus ſit, quantum perdiderit. </s>
                <s xml:id="echoid-s1469" xml:space="preserve">Quæritur
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                  <lb/>
                quot fuerint dies lucri, quotúe perditionis.</s>
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              <p>
                <s xml:id="echoid-s1470" xml:space="preserve">Huiuſmodi problematis operatio breuiſſima abſque vlla falſa poſitione ita erit,
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                hoc eſt diuidendo productum .36. in .24. per .40. ideſt per aggregatum ipſius .24.
                  <reg norm="cum" type="context">cũ</reg>
                  <lb/>
                16. & prouentus erit .21. cum tribus quintis pro diebus lucri, vnde reliquum ex .36.
                  <lb/>
                erit .14. cum duabus quintis pro diebus perditionis.</s>
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              <p>
                <s xml:id="echoid-s1471" xml:space="preserve">Cuius operationis ratio ex ſe ſatis patet, cum duo producta, vnum lucri, alterum
                  <lb/>
                vero perditio-
                  <lb/>
                nis æqualia eſſe
                  <lb/>
                  <figure xlink:label="fig-0128-03" xlink:href="fig-0128-03a" number="176">
                    <image file="0128-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0128-03"/>
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                debeant, vnde
                  <lb/>
                ex duodecima,
                  <lb/>
                & vigeſimaſepti
                  <lb/>
                mi ex regula de
                  <lb/>
                tribus reperiun
                  <lb/>
                tur partes ipſius
                  <lb/>
                36. eodem mo- </s>
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