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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              <p>
                <s xml:id="echoid-s1443" xml:space="preserve">
                  <pb o="114" rhead="IO. BAPT. BENED." n="126" file="0126" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0126"/>
                ret, mediante ipſa regula de tribus, vt
                  <reg norm="iam" type="context">iã</reg>
                ſępius
                  <reg norm="dictum" type="context">dictũ</reg>
                eſt, quod
                  <reg norm="etiam" type="context">etiã</reg>
                clarè patet ex di-
                  <lb/>
                uerſis problematibus .17. lib. ipſius Tartaleæ, vt ex primo, quod aſſumpſimus pro
                  <lb/>
                noſtro etiam primo exemplo, ex .9. 15. 16. 17. 18. 19. 20. 27. 28. 29. 30. 33. & ex
                  <lb/>
                alijs multis, vbi facillimè inue nitur conſequens ipſius poſitionis, qui quidem nume-
                  <lb/>
                rus eſt diuiſor producti ipſius numeri propoſiti in numerum poſitionis, vnde poſteà
                  <lb/>
                prouenit
                  <reg norm="ſecundum" type="context">ſecundũ</reg>
                latus huiuſmodi producti, hoc eſt numerus quæſitus, per
                  <reg norm="regulam" type="context">regulã</reg>
                  <lb/>
                de tribus, vt dixi.</s>
              </p>
              <p>
                <s xml:id="echoid-s1444" xml:space="preserve">Alia verò multa problemata inueniuntur, pro quorum re@olutione poſſumus ali
                  <lb/>
                qua methodo vti, in qua manifeſtè pateant
                  <reg norm="eorum" type="context">eorũ</reg>
                rationes abſque regula falſi, cuius
                  <lb/>
                regulæ rationes non ita promptè ipſi intellectui ſe offerunt, vt ſupra vidimus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1445" xml:space="preserve">Accipiamus pro exemplo .21. problema ipſius Tartalæ in dicto .17. libr. vbi ſup-
                  <lb/>
                ponit vnum hædum diuiſum in .4. partes, quarum quælibet vendebatur eodem pre
                  <lb/>
                cio, interiora vero .6. denarijs minus quam quælibet dictarum partium, ſumma
                  <lb/>
                autem omnium iſtorum denariorum fuit .127. quæritur nunc precium cuiuſque
                  <lb/>
                partis.</s>
              </p>
              <p>
                <s xml:id="echoid-s1446" xml:space="preserve">Tale enim problema hoc etiam alio breuiori modo poteſt ſolui, vt rationes ma-
                  <lb/>
                gis pateant, quam ex regula falſi.</s>
              </p>
              <p>
                <s xml:id="echoid-s1447" xml:space="preserve">Nam ſi illi numero .127. denariorum, additus fuerit numerus .6. ſumma erit .133.
                  <lb/>
                qua diuiſa per quinque, illico proueniet .26. cum tribusquintis pro precio vniuſcu-
                  <lb/>
                iuſque quatuor partium, à quo .26. cum tribusquintis dempto .6. remanebit .20. cum
                  <lb/>
                tribusquintis pro precio interiorum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1448" xml:space="preserve">Simili modo in .24. problemate inquit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1449" xml:space="preserve">Duodecim pyra cum .28. pomis venduntur .36. denarijs, et .20. pyra. cum .200 po
                  <lb/>
                mis
                  <reg norm="venduntur" type="context">vẽduntur</reg>
                .44. denarijs,
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                nunc, quod
                  <reg norm="nam" type="context">nã</reg>
                fuerit
                  <reg norm="precium" type="context">preciũ</reg>
                  <reg norm="vniuſcuiuſque" type="simple">vniuſcuiuſq;</reg>
                illorum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1450" xml:space="preserve">Hoc etiam problema, hac alia methodo ſolui poteſt, dicendo exregula de tribus,
                  <lb/>
                ſi ex .20. vtrorunque qui ea vendit, vult .44. quid volet ex .12? </s>
                <s xml:id="echoid-s1451" xml:space="preserve">
                  <reg norm="manifeſtum" type="context">manifeſtũ</reg>
                erit quod
                  <lb/>
                volet .26. cum duobus quintis, </s>
                <s xml:id="echoid-s1452" xml:space="preserve">quare .12. pyra cum .12. pomis valebunt .26. cum duo
                  <lb/>
                bus quintis, ſed 12. cum .28. pomis valebant .36. ergo .16. poma ſola valebunt .9.
                  <lb/>
                cum tribus quintis, hoc enim clarè ex ſe patet; </s>
                <s xml:id="echoid-s1453" xml:space="preserve">quare cum dixerimus, ſi .16. poma ſo
                  <lb/>
                la valent .9. cum tribusquintis, vnum valebit
                  <var>.o.</var>
                cum tribusquintis, ſed quemadmo-
                  <lb/>
                dum .20. pyra cum .20. pomis valent .44. vnum pyrum, cum vno pomo valebunt .2.
                  <lb/>
                cum quinta parte, à quo numero detractus cum fuerit
                  <var>.o.</var>
                cum tribus quintis, precio
                  <lb/>
                ſcilicet vnius pomi, reliquum .1. cum tribusquintis, erit precium vnius pyri.</s>
              </p>
              <p>
                <s xml:id="echoid-s1454" xml:space="preserve">Idem etiam dico de .28. problemate, vbi ſupponit quod quidam comparaſſet
                  <lb/>
                quatuor petias, vt vulgo dicitur, panni pro ducatis .96. quarum primæ precium ob-
                  <lb/>
                litus ſit, ſed memoria tenet pro ſecunda ſoluiſſe .6. plusquam pro prima, & pro ter-
                  <lb/>
                tia ſoluiſſe .8. plus quam pro ſecunda, & pro quarta ſoluiſſe .10. plus quam pro ter-
                  <lb/>
                tia, quæritur nunc quantum fuerit precium vniuſcuiuſque illarum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1455" xml:space="preserve">Quod
                  <reg norm="quidem" type="context">quidẽ</reg>
                problema
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0126-01a" xlink:href="fig-0126-01"/>
                breuius eſſetita ſolui, vt in
                  <lb/>
                ſubſcripta figura
                  <var>.I.</var>
                videri
                  <lb/>
                poteſt,
                  <reg norm="addendo" type="context">addẽdo</reg>
                ſimul omnes
                  <lb/>
                exceſſus. </s>
                <s xml:id="echoid-s1456" xml:space="preserve">Nam exceſſus
                  <reg norm="ſecum" type="context">ſecũ</reg>
                  <lb/>
                dæ ſupra primam eſt .6. ſed
                  <lb/>
                cum exceſſus tertiæ ſupra ſe
                  <lb/>
                cundam ſit .8. ergo exceſſus
                  <lb/>
                tertiæ ſupra primam erit .14 </s>
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