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
31 19
32 20
33 21
34 22
35 23
36 24
37 25
38 26
39 27
40 28
41 29
42 30
43 31
44 32
45 33
46 34
47 35
48 36
49 37
50 38
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
60 48
< >
page |< < (34) 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-div109" type="math:theorem" level="3" n="52">
              <p>
                <pb o="34" rhead="IO. BAPT. BENED." n="46" file="0046" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0046"/>
                <s xml:id="echoid-s455" xml:space="preserve">11. dabuntur .110. quo producto multiplicato cum .12. dabuntur .1320. hoc pro
                  <lb/>
                ueniens per primum nempe .10. diuiſum dabit .132. numerum æqualem producto
                  <lb/>
                ſecundi in tertium numerorum propoſitorum, ſcilicet .132.</s>
              </p>
              <p>
                <s xml:id="echoid-s456" xml:space="preserve">Hoc vt ſpeculemur, primus numerus ſignificetur line
                  <var>a.o.u.</var>
                ſecundus
                  <var>.e.o.</var>
                tertius
                  <var>.
                    <lb/>
                  e.a.</var>
                productum verò
                  <var>.o.u.</var>
                in
                  <var>.o.e.</var>
                ſit
                  <var>.o.i.</var>
                ipſius ve
                  <lb/>
                  <var>.o.i.</var>
                per
                  <var>.e.a.</var>
                  <reg norm="productum" type="context">productũ</reg>
                  <reg norm="corporeum" type="context">corporeũ</reg>
                ſit
                  <var>.i.c.</var>
                tum
                  <lb/>
                  <figure xlink:label="fig-0046-01" xlink:href="fig-0046-01a" number="63">
                    <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0046-01"/>
                  </figure>
                  <reg norm="productum" type="context">productũ</reg>
                  <var>.e.o.</var>
                in
                  <var>.e.a.</var>
                ſit
                  <var>.e.c</var>
                . </s>
                <s xml:id="echoid-s457" xml:space="preserve">Dico
                  <reg norm="nunc" type="context">nũc</reg>
                quod di-
                  <lb/>
                uiſo numero corporeo
                  <var>.i.c.</var>
                per
                  <reg norm="primum" type="context">primũ</reg>
                  <var>.o.u.</var>
                  <reg norm="proue" type="simple">ꝓue</reg>
                  <lb/>
                niens æquale erit numero producti
                  <var>.e.c</var>
                . </s>
                <s xml:id="echoid-s458" xml:space="preserve">Qua-
                  <lb/>
                re in primis cogitandum eſt, quod cum produ-
                  <lb/>
                ctum
                  <var>.i.c.</var>
                ortum fuerit ex multiplicatione
                  <var>.o.i.</var>
                  <lb/>
                in
                  <var>.e.a</var>
                : dictum
                  <var>.o.i.</var>
                toties ingredietur
                  <var>.i.c.</var>
                quo-
                  <lb/>
                ties vnitas reperitur in
                  <var>.e.a.</var>
                eadem ratione, to-
                  <lb/>
                ties
                  <var>.e.c.</var>
                in
                  <var>.i.c.</var>
                quot vnitates erunt in
                  <var>.o.u</var>
                . </s>
                <s xml:id="echoid-s459" xml:space="preserve">
                  <reg norm="Itaque" type="simple">Itaq;</reg>
                  <lb/>
                ſequitur quòd diuiſo
                  <var>.i.c.</var>
                per
                  <var>o.u.</var>
                proueniens ſit
                  <lb/>
                  <var>e.c.</var>
                corporeum, æquale nihilominus producto
                  <var>.e.c.</var>
                ſuperficiali.</s>
              </p>
            </div>
            <div xml:id="echoid-div111" type="math:theorem" level="3" n="53">
              <head xml:id="echoid-head69" xml:space="preserve">THEOREMA
                <num value="53">LIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s460" xml:space="preserve">CVR diuidens propoſitum numerum in tres partes ſic ſe habentes vt produ-
                  <lb/>
                ctum primi in ſecundam, in tertia
                  <reg norm="multiplicatum" type="context">multiplicatũ</reg>
                , præbeat numerum alteri nu-
                  <lb/>
                mero propoſito æqualem. </s>
                <s xml:id="echoid-s461" xml:space="preserve">Rectè ſecundum numerum per quemcunque alium mino
                  <lb/>
                rem primo diuidit, qui diuidens vna erit ex tribus partibus quæſitis, proueniens
                  <lb/>
                autem erit productum vnius in alteram reliquarum duarum, quarum ſumma cogni
                  <lb/>
                ta erit, detracto numero diuidente ex primo dato, quam quidem ſi diſtinguere
                  <lb/>
                quis voluerit, vtetur theoremate .45.</s>
              </p>
              <p>
                <s xml:id="echoid-s462" xml:space="preserve">Exempli gratia, proponitur numerus .20. in tres partes diuidendus, quæ ſic ſe
                  <lb/>
                habeant, ut productum primæ in ſecundam in tertia multiplicatum det .90. itaque
                  <lb/>
                ſumenda erit pro prima vna pars ipſius .20. quæcunque illa ſit, verbi gratia .2. qua
                  <lb/>
                ſecundus numerus, nempe .90. diuidatur, dabitur igitur .45. quod erit productum
                  <lb/>
                cæterarum partium inter ſe, quarum ſumma eſt .18. quam ſummam ſi diſtinguere
                  <lb/>
                volueris in cęteris duabus partibus ſeparatis, vteris .45. theoremate, vt quàm citiſ-
                  <lb/>
                ſimè quod cupis exequaris, erunt autem partes .3. et .15.</s>
              </p>
              <p>
                <s xml:id="echoid-s463" xml:space="preserve">In cuius ſpeculationis gratiam nihil aliud occurrit, quàm quod præcedenti theo-
                  <lb/>
                remate, & ſuperiore .45. allatum eſt.</s>
              </p>
            </div>
            <div xml:id="echoid-div112" type="math:theorem" level="3" n="54">
              <head xml:id="echoid-head70" xml:space="preserve">THEOREMA
                <num value="54">LIIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s464" xml:space="preserve">
                  <emph style="sc">DIvidere</emph>
                numerum in .3. eiuſmodi partes, vt quadratum vnius ſit æquale
                  <lb/>
                producto reliquarum duarum inter ſe, idem omnino eſt cum 51. theoremate.
                  <lb/>
                </s>
                <s xml:id="echoid-s465" xml:space="preserve">Nam qui ſumet quamlibet partem propoſiti numeri, quæ tertia parte maior tamen
                  <lb/>
                non ſit,
                  <reg norm="reſiduumque" type="simple">reſiduumq́</reg>
                in duas tales partes diuiſerit, vt prima ſumpta, media proportio
                  <lb/>
                nalis ſit ex probatione .51. theoremate allata, propoſitum conſequetur.</s>
              </p>
            </div>
            <div xml:id="echoid-div113" type="math:theorem" level="3" n="55">
              <head xml:id="echoid-head71" xml:space="preserve">THEOREMA
                <num value="55">LV</num>
              .</head>
              <p>
                <s xml:id="echoid-s466" xml:space="preserve">ID ipſum alia ratione ab ea diuerſa
                  <reg norm="quam" type="context">quã</reg>
                .51. theoremate adduximus,
                  <reg norm="profici" type="simple">ꝓfici</reg>
                poteſt.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>