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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IO. BAPT. BENED.
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              <pb o="96" rhead="IO. BAPT. BENED." n="98" file="0098" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0098"/>
              <p>
                <s xml:id="echoid-s1125" xml:space="preserve">Sint exempli gratia, tria corpora æquè ponderantia, & vnumquodque illorum
                  <lb/>
                ſitquinque librarum, quorum vnum ſit aureum, aliud argenteum, reliquum verò
                  <lb/>
                mixtum ex ijs duobus metallis, vnde corpus aureum ſimplex minus erit, & argen
                  <lb/>
                teum maius corpore mixto, quod nulli dubium eſt, ſit nunc pondus corporis aquei
                  <lb/>
                ęqualis corpori aureo,
                  <reg norm="librarum" type="context">librarũ</reg>
                .3. aquei verò ęqualis miſto, ſit
                  <reg norm="librarum" type="context">librarũ</reg>
                3.
                  <reg norm="cum" type="context">cũ</reg>
                quarta par
                  <lb/>
                te, aquei demum æqualisargenteo, librarum .4. cum dimidia, vnde exijs, quæ in præ
                  <lb/>
                cedenti theoremate, & in .126. theoremate diximus, ſi imaginatione concipiemus
                  <lb/>
                alia duo corpora ſimplicia, auri, & argenti, ſed æqualium magnitudinum mixto,
                  <lb/>
                habebimus proportionem ponderis aurei ad pondus corporis mixti vt
                  <reg norm="trium" type="context">triũ</reg>
                librarum
                  <lb/>
                cum quarta vnius ad .3. libras, & proportio ponderis mixti ad pondus argentei erit,
                  <lb/>
                vt proportio librarum .4. cum dimidia ad tres libras cum quarta parte vnius libræ,
                  <lb/>
                & proportio ponderis aurei ad pondus argentei vt librarum .4. cum dimidia ad li-
                  <lb/>
                bras .3: hoc eſt aurei ad mixtum, vt .13. ad .12. & mixti ad argenteum, vt .18. ad .13.
                  <lb/>
                & aurei ad argenteum, vt .3. ad .2. ideſt, vt .18. ad .12.</s>
              </p>
              <p>
                <s xml:id="echoid-s1126" xml:space="preserve">Nunc inueniantur duo numeri ita inter ſe proportionati, vt .3. ad .2. habentes ta-
                  <lb/>
                men inter ipſos numerum ita proportionatum ad maximum, vt .12. ſe habet ad
                  <num value="13">.
                    <lb/>
                  13.</num>
                & ita proportionatum ad minimum, vt ſe habet .18. ad .13. quod hoc modo in-
                  <lb/>
                ueniemus, multiplicabimus .18. per .12. & proueniet nobis .216. pro numero me-
                  <lb/>
                dio, poſteà multiplicabimus .18. per .13. & proueniet .234. pro maximo,
                  <reg norm="demum" type="context">demũ</reg>
                multi
                  <lb/>
                plicando .12. per .13. proueniet .156. pro minimo, ita quod .234. correſpondebit
                  <lb/>
                ponderi corporis aurei: </s>
                <s xml:id="echoid-s1127" xml:space="preserve">216. verò ponderi mixti, et .156. ponderi argentei æqua-
                  <lb/>
                lium magnitudinum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1128" xml:space="preserve">Cum autem proportiones horum trium corporum inuenerimus, ſi ordinem theo
                  <lb/>
                rematis .122. ſequemur, habebimus quod quærebamus, & inueniemus in præſenti
                  <lb/>
                exemplo proportionem ponderis auri ad pondus argenti in corpore mixto eſſe, vt
                  <num value="180">.
                    <lb/>
                  180.</num>
                ad .36. ſed quia ſuppoſitum fuit corpus mixtum eſſe quinque librarum, propte-
                  <lb/>
                reà dicemus. </s>
                <s xml:id="echoid-s1129" xml:space="preserve">Si .216. hoc eſt toti corpori mixto correſpondent quinque libræ tunc
                  <lb/>
                parti .180. hoc eſt auro in ipſo corpore mixto, correſpondent libræ .4. cum duabus
                  <lb/>
                vncijs, ex regula detribus, reſiduum verò quinque librarum, ideſt vnciæ decem,
                  <lb/>
                correſpondent parti .36. hoc eſt argento in dicto corpore mixto.</s>
              </p>
              <p>
                <s xml:id="echoid-s1130" xml:space="preserve">Sed ſi tria corpora dicta fuiſſent inuicem ita proportionata, vt .40. 47. 60. </s>
                <s xml:id="echoid-s1131" xml:space="preserve">tunc
                  <lb/>
                proportio auri ad argentum in corpore mixto eſſet vt .13. ad .7. quapropter
                  <reg norm="cum" type="context">cũ</reg>
                pon
                  <lb/>
                dus mixti fuiſſet .120. librarum, </s>
                <s xml:id="echoid-s1132" xml:space="preserve">tunc aurum ipſius eſſet librarum .78. argentum ve-
                  <lb/>
                rò librarum .42. ex eadem regula.</s>
              </p>
              <p>
                <s xml:id="echoid-s1133" xml:space="preserve">Pro quarum rerum ſpeculatione nil aliud oportet nunc dicere cum ſatis dictum à no
                  <lb/>
                bis ſuperius fuerit, vno excepto, hoc eſt rationem reddere, qua motus fui ad inue
                  <lb/>
                niendos illos .3. numeros ita inter ſe diſpoſitos, vt dictum eſt, quæ quidem ratio fuit,
                  <lb/>
                vt haberemus .3. numeros ita inter ipſos ordinatè diſpoſitos, vt ſunt pondera trium
                  <lb/>
                illorum corporum æqualium magnitudinum. </s>
                <s xml:id="echoid-s1134" xml:space="preserve">Proptereà quòd quamuis inter pri-
                  <lb/>
                mos .3. numeros ponderum corporum aqueorum eædem fuerint proportiones pon
                  <lb/>
                derum corporum metallicorum, nihilominus medius numerus extra proprium lo-
                  <lb/>
                cum, & inordinatè inueniebatur, reſpectu extremorum, vnde medius numerus in
                  <lb/>
                ſuo vero ſitu inter .18. et .12. fuiſſent .16.
                  <reg norm="cum" type="context">cũ</reg>
                .8. tertijs decimis, ſed vt
                  <reg norm="fractorum" type="context">fractorũ</reg>
                incom
                  <lb/>
                moditatem euitemus, præcepi, vt multiplicarentur extrema per .13. vnde produ-
                  <lb/>
                cti fuerunt numeri .234. et .156. in
                  <reg norm="eadem" type="context">eadẽ</reg>
                proportione, quæ eſt .18. ad .12. ex .18. ſepti
                  <lb/>
                mi, iuſſi etiam multiplicari .18. per .12. vt nobis prodiret .216. ad quem numerum,
                  <lb/>
                numerus .234. ita ſe haberet, ut .13. ad .12. ex .19. ſeptimi, quod autem ita ſit propor­ </s>
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