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="117" rhead="THEOR. ARITH." n="129" file="0129" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0129"/>
                do ſe inuicem habentes, vt .24. et .16. quæ ſunt .21. cum tribus quintis, et .14.
                  <reg norm="cum" type="context">cũ</reg>
                dua
                  <lb/>
                bus quintis, ex quo ſequitur, vt quod fit ex .21. cum tribus quintis, in 16. ęquale ſit ei
                  <lb/>
                quod fit ex .14 cum duabus quintis, in .24. & ita reperiuntur duo producta æqualia,
                  <lb/>
                vnum lucri, reliquum vero perditionis, vt in figura
                  <var>.M.</var>
                clarè videtur.</s>
              </p>
              <p>
                <s xml:id="echoid-s1472" xml:space="preserve">A Liud verò exemplum eſt .39. quod quidem à ſuperiori non differt, niſi quod
                  <lb/>
                in fine operationis, operarius dictus lucratus eſt ſolidos .60: </s>
                <s xml:id="echoid-s1473" xml:space="preserve">quęritur
                  <reg norm="nunc" type="context">nũc</reg>
                vt ſu-
                  <lb/>
                pra, quot fuerunt dies lucri, & quot perditionis.</s>
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              <p>
                <s xml:id="echoid-s1474" xml:space="preserve">Hoc etiam abſque vlla falſa poſitione dicto citius poteſt ſolui, hoc modo,
                  <reg norm="diuidem" type="context">diuidẽ</reg>
                  <lb/>
                do ſcilicet illos .60 ſolidos per .40. ideſt per aggregatum .24. cum .16. proueniens
                  <lb/>
                autem, quod erit .1. cum dimidio, adde ad latus ſuperius inuentum, hoc eſt .21. cum
                  <lb/>
                tribus quintis, & ſunima erit .23. cum decima parte pro numero dierum lucri, dein-
                  <lb/>
                de idem prouentum deme ex alio latere ſuperius reperto .14. cum duabus quintis, &
                  <lb/>
                refiduum erit .12. cum nouem decimis, vnde habebis numerum dierum perdi-
                  <lb/>
                tionis.</s>
              </p>
              <p>
                <s xml:id="echoid-s1475" xml:space="preserve">Pro cuius rei ſpeculatione cogitemus in figura
                  <var>.N.</var>
                duo dicta producta inuicem
                  <lb/>
                æqualia
                  <var>.o.b.</var>
                et
                  <var>.n.c.</var>
                exiſtente latere
                  <var>.u.c.</var>
                vt .24.
                  <var>u.o.</var>
                ut .16: </s>
                <s xml:id="echoid-s1476" xml:space="preserve">b.u. vt .21. cum tribus quin
                  <lb/>
                tis, et
                  <var>.u.n.</var>
                vt .14. cum duabus quintis. </s>
                <s xml:id="echoid-s1477" xml:space="preserve">Nunc verò ſi mente concepta fuerit recta
                  <var>.e.
                    <lb/>
                  a.t.</var>
                æquidiſtans
                  <var>.o.c.</var>
                ita vt rectangulum
                  <var>.o.e.</var>
                ſit .60. </s>
                <s xml:id="echoid-s1478" xml:space="preserve">tunc rectangulum, ſeu productum
                  <lb/>
                  <var>b.t.</var>
                ſuperabit rectangulum ſeu productum
                  <var>.n.e.</var>
                per idem .60. ex communi conceptu,
                  <lb/>
                eo quòd ex producto
                  <var>.n.c.</var>
                ſublatum eſt productum
                  <var>.a.c.</var>
                24. & producto
                  <var>.o.b.</var>
                additum
                  <lb/>
                eſt productum
                  <var>e.a.</var>
                16. rectè igitur feci cum diuiſerim .60 per .40. vnde prouenit mi
                  <lb/>
                hi
                  <var>.u.a.</var>
                ideſt .1. cum dimidio, quod additum ipſi
                  <var>.b.u.</var>
                compoſuit
                  <var>.b.a.</var>
                & dempto ex
                  <var>.u.
                    <lb/>
                  n.</var>
                relinquit
                  <var>.a.n.</var>
                pro lateribus duorum productorum
                  <var>.b.t.</var>
                et
                  <var>.n.e</var>
                .</s>
              </p>
              <p>
                <s xml:id="echoid-s1479" xml:space="preserve">Sed ſi idem operator perdidiſſet .60. tunc cogitaremus parallelam dictam
                  <var>.e.a.</var>
                t
                  <lb/>
                ſuperius ductam eſſe ita vt ſecaret
                  <var>.b.u.</var>
                & non
                  <var>.u.n.</var>
                vnde adderet .24. ipſi producto
                  <var>.n.
                    <lb/>
                  c.</var>
                & d@meret .16. à producto
                  <var>.b.o</var>
                .</s>
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              <figure position="here" number="177">
                <image file="0129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0129-01"/>
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                <s xml:id="echoid-s1480" xml:space="preserve">CIRCA verò talia quæſita videtur mihi non inutile fore ſi aliquid notatu di-
                  <lb/>
                gnum aduerterim, hoc eſt quod ſæpe accidere poterit ut caſus impoſſibiles
                  <lb/>
                proponantur. </s>
                <s xml:id="echoid-s1481" xml:space="preserve">Quemadmodum ſi aliquis diceret, cupio mihi ueſtimentum con-
                  <lb/>
                ficere ex duobus pannis colore & pretio differentibus, quorum unus exempli gra- </s>
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