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]

Page concordance

< >
Scan Original
61 49
62 50
63 51
64 52
65 53
66 54
67 55
68 56
69 57
70 58
71 59
72 60
73 61
74 62
75 63
76 64
77 65
78 66
79 67
80 70
81 71
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
< >
page |< < (92) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div7" type="chapter" level="2" n="1">
            <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/>
                  <figure xlink:label="fig-0104-01" xlink:href="fig-0104-01a" number="143">
                    <image file="0104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0104-01"/>
                  </figure>
                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>
            <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>
          </div>
        </div>
      </text>
    </echo>
Impressum