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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            <div xml:id="echoid-div262" type="math:theorem" level="3" n="137">
              <p>
                <s xml:id="echoid-s1199" xml:space="preserve">
                  <pb o="92" rhead="IO. BAPT. BENED." n="104" file="0104" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0104"/>
                ipſorum prochictorum per ſummam lucri hoc eſt per .60. vnde multiplicatio primi
                  <lb/>
                producti erit .2190000. multiplicatio verò ſecundi producti erit .795000. tertij po
                  <lb/>
                ſtca erit .247500. quarum multiplicationum vnaquæque diuidatur per ſummam
                  <lb/>
                53875. productori
                  <unsure/>
                t, & proueniet ex prima diuiſione .40.
                  <reg norm="cum" type="context">cũ</reg>
                fractis .35000. vnius in-
                  <lb/>
                tegri diuiſi in partes .53875. quod erit lucrum primi, prouentus autem ſecundæ di-
                  <lb/>
                uiſionis erit .14. cum fractis .41050. vnius integri diuiſi in partes .53875. lucrum
                  <reg norm="ſecu­ di." type="context">ſecũ­
                    <lb/>
                  di</reg>
                </s>
                <s xml:id="echoid-s1200" xml:space="preserve">prouentus verò quartæ diuiſionis erit .4. cum fractis .32000. vnius integri, vt ſu
                  <lb/>
                pra diuiſi in partes .53875. hoc eſt lucrum tertij.</s>
              </p>
              <p>
                <s xml:id="echoid-s1201" xml:space="preserve">Cuius rei ſpeculatio ex ſe in ſub ſcripta figura patet, vbi
                  <var>.a.q.</var>
                ſignificat numerum
                  <lb/>
                dierum totius anni pro primo mercatore
                  <var>.q.n.</var>
                autem ſignificat numerum dierum ſe
                  <lb/>
                cundi mercatoris
                  <var>.e.q.</var>
                poſteà ſignificat numerum dierum tertij ſit etiam
                  <var>.s.a.</var>
                pro nu-
                  <lb/>
                mero denariorum primi, et
                  <var>.o.n.</var>
                pro numero ſecundi, et
                  <var>.e.t.</var>
                pro numero
                  <lb/>
                tertij, productum autem
                  <var>.q.s.</var>
                ſignificet valorem primi lucri, et
                  <var>.q.o.</var>
                ſecundi,
                  <lb/>
                et
                  <var>.q.t.</var>
                tertij
                  <var>.x.y.</var>
                autem ſignificet ſummam lucri omnium, et
                  <var>.x.i.</var>
                ſignificet
                  <lb/>
                partem primi, et
                  <var>.i.p.</var>
                ſecundi, et
                  <var>.p.y.</var>
                tertij. </s>
                <s xml:id="echoid-s1202" xml:space="preserve">vnde clarè patebit ex communi
                  <lb/>
                ſcientia quòd eadem proportio erit
                  <var>.x.y.</var>
                ad
                  <var>.x.i.</var>
                quæ aggregati omnium producto-
                  <lb/>
                rum
                  <var>.q.s</var>
                :
                  <var>q.o.</var>
                et
                  <var>.q.t.</var>
                ad
                  <var>.q.s.</var>
                & ita
                  <var>.x.y.</var>
                ad
                  <var>.i.p.</var>
                vt aggregati dictiad
                  <var>.q.o.</var>
                et
                  <var>.x.y.</var>
                ad
                  <var>.p.y.</var>
                  <lb/>
                vt dicti aggregati ad
                  <var>.q.t</var>
                . </s>
                <s xml:id="echoid-s1203" xml:space="preserve">Rectè igitur ex regula de tribus multiplicatio
                  <var>.q.s.</var>
                in
                  <var>.x.y.</var>
                  <lb/>
                diuiditur per aggregatum omnium
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0104-01a" xlink:href="fig-0104-01"/>
                productorum, ita vt ſi aliquis dice-
                  <lb/>
                ret, ſi ex dicto aggregato, prouenit
                  <lb/>
                  <var>x.y.</var>
                quid proueniet vnicuique
                  <reg norm="illo- rum" type="context">illo-
                    <lb/>
                  rũ</reg>
                  <reg norm="productorum" type="context">productorũ</reg>
                . </s>
                <s xml:id="echoid-s1204" xml:space="preserve">
                  <reg norm="Nam" type="context">Nã</reg>
                ſi numerus dena-
                  <lb/>
                riorum
                  <reg norm="ſecundi" type="context">ſecũdi</reg>
                æqualis eſſet numero
                  <lb/>
                  <var>a.s.</var>
                primi vt putà.
                  <var>n.b</var>
                . </s>
                <s xml:id="echoid-s1205" xml:space="preserve">tunc eius
                  <reg norm="lucrum" type="context">lucrũ</reg>
                  <lb/>
                ſignificaretur à rectangulo
                  <var>.q.b.</var>
                & ita
                  <lb/>
                de tertio dico
                  <reg norm="quod" type="simple">ꝙ</reg>
                ſignificaretur à
                  <reg norm="re- ctangulo" type="context">re-
                    <lb/>
                  ctãgulo</reg>
                  <var>.q.c.</var>
                vel ſi ſi
                  <unsure/>
                antibus
                  <reg norm="ijſdem" type="context">ijſdẽ</reg>
                  <reg norm="denariorum" type="context">denariorũ</reg>
                quantitatibus
                  <var>.n.o.</var>
                et
                  <var>.e.t.</var>
                omnes ſuas pe-
                  <lb/>
                cunias eodem tempore poſuiſſent, </s>
                <s xml:id="echoid-s1206" xml:space="preserve">tunc rectangula ſignificantia eorum lucra eſlent
                  <lb/>
                  <var>q.s.q.d.</var>
                et
                  <var>.q.f.</var>
                ſed cum nec eodem tempore, nec eandem quantitatem poſueruntr
                  <unsure/>
                e
                  <lb/>
                ctè eorum lucra ſignificantur à rectangulis
                  <var>.q.s.q.o.</var>
                et
                  <var>.q.t.</var>
                  <reg norm="quod" type="simple">ꝙ</reg>
                ex prima .6. vel .18. aut
                  <num value="19">.
                    <lb/>
                  19.</num>
                ſeptimi ratiocinando clarè patebit.</s>
              </p>
              <div xml:id="echoid-div262" type="float" level="4" n="1">
                <figure xlink:label="fig-0104-01" xlink:href="fig-0104-01a">
                  <image file="0104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0104-01"/>
                </figure>
              </div>
            </div>
            <div xml:id="echoid-div264" type="math:theorem" level="3" n="138">
              <head xml:id="echoid-head156" xml:space="preserve">THEOREMA
                <num value="138">CXXXVIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s1207" xml:space="preserve">NIcolaus Tartalea in primo libro vltimæ partis numerorum ad .35. quæſitum
                  <lb/>
                docet inuenire quantitatem laterum vnius propoſiti trianguli, cuius la-
                  <lb/>
                r
                  <unsure/>
                erum proportio nobis data ſit ſimul cum area ſuperſiciali ipſius trianguli, ſed quia
                  <lb/>
                ipſe Tartalea vtiturregula algebræ, mihi viſum eſt breuiori methodo hoc idein fa
                  <lb/>
                cere, & etiam vniuerſaliori via.</s>
              </p>
              <p>
                <s xml:id="echoid-s1208" xml:space="preserve">Supp onamus igitur duo triangula, quorum vnum
                  <var>.u.n.i.</var>
                ſit nobis
                  <reg norm="propoſitum" type="context">propoſitũ</reg>
                , &
                  <lb/>
                cognitæ ſuperficiei, proportiones ſimiliter laterum
                  <var>.i.n.</var>
                ad
                  <var>.n.u</var>
                : et
                  <var>.u.n.</var>
                ad
                  <var>.u.i.</var>
                ſint no
                  <lb/>
                bis datæ,
                  <reg norm="alterum" type="context">alterũ</reg>
                verò
                  <reg norm="triangulum" type="context">triangulũ</reg>
                ſit
                  <var>.a.o.u.</var>
                à nobis tamen ita
                  <reg norm="confectum" type="context">confectũ</reg>
                , v
                  <unsure/>
                latera ſint in­
                  <lb/>
                er ſe proportionata eodem modo, quo latera prioris trianguli, ſed hæc nobis
                  <reg norm="etiam" type="context">etiã</reg>
                  <lb/>
                cognita ſint,
                  <reg norm="quod" type="simple">ꝙ</reg>
                facillimum eſt. </s>
                <s xml:id="echoid-s1209" xml:space="preserve">Nunc vero ſi
                  <reg norm="demptum" type="context">demptũ</reg>
                fuerit
                  <reg norm="quadratum" type="context">quadratũ</reg>
                  <var>.a.o.</var>
                minimi
                  <lb/>
                lateris, ex quadrato
                  <var>.o.u.</var>
                maximi, relinquet nobis duplum producti
                  <var>.o.u.</var>
                in
                  <var>.u.e.</var>
                per
                  <lb/>
                  <reg norm="penultimam" type="context">penultimã</reg>
                .2. Eucli.
                  <reg norm="ſupponendo" type="context">ſupponẽdo</reg>
                  <var>.a.e.</var>
                perpendicularem ad
                  <var>.o.u.</var>
                vnde tale productum
                  <lb/>
                quòd fit ex
                  <var>.o.u.</var>
                in
                  <var>.u.e.</var>
                conſequenter nobis cognitum erit, & quia
                  <var>.o.u.</var>
                nobis cogni- </s>
              </p>
            </div>
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