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 |< < (96) 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-div271" type="math:theorem" level="3" n="142">
              <pb o="96" rhead="IO. BAPT. BENED." n="108" file="0108" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0108"/>
              <p>
                <s xml:id="echoid-s1246" xml:space="preserve">Vnde cum aliquis diceret priori modo, dolium habeo vrnarum .400. vini, & per
                  <lb/>
                vices .25. extraxi & impleui ipſum, vt dictum eſt. </s>
                <s xml:id="echoid-s1247" xml:space="preserve">Nunc verò velim ſcire proportio-
                  <lb/>
                nem vini ad a quam hac vltima vice. </s>
                <s xml:id="echoid-s1248" xml:space="preserve">Nunc igitur ſi procedemus iuxta doctrinam
                  <lb/>
                primi exempli huius theorematis, obtinebimus quod quærebamus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1249" xml:space="preserve">Sed ſi diceret iuxta Tartaleæ quæſitum, hoc eſt dolium habeo, quod ignoro quot
                  <lb/>
                  <reg norm="nam" type="context">nã</reg>
                urnas contineat, volo tamen per .25. vices extrahere, & implere vt
                  <reg norm="ſupradictum" type="context">ſupradictũ</reg>
                  <lb/>
                eſt, ita vt vltima vice proportio vini ad aquam ſit ſeſquialtera. </s>
                <s xml:id="echoid-s1250" xml:space="preserve">Tunc ſi iuxta mo-
                  <lb/>
                dum ſecundi exempli huius theorematis procedemus habebimus quod cupimus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1251" xml:space="preserve">Alio etiam modo aliquis quærere poſſet, hoc eſt, habeo
                  <reg norm="dolium" type="context">doliũ</reg>
                quod capit .400.
                  <lb/>
                vrnas. </s>
                <s xml:id="echoid-s1252" xml:space="preserve">Habeo etiam vas trium vrnarum, quo mediante me oportet extrahere, &
                  <lb/>
                implere. </s>
                <s xml:id="echoid-s1253" xml:space="preserve">Velim tamen ſcire quoties me hoc facere oporteat, ita vt poſtrema vi-
                  <lb/>
                ce vinum ſe habeat ad aquam in proportione ſeſquialtera, vnde multoties accidet
                  <lb/>
                vltimam extractionem, & impletionem mutilatam, ſeu imperfectam, euadere.</s>
              </p>
              <p>
                <s xml:id="echoid-s1254" xml:space="preserve">Exempli gratia, ſi proportio vini ad aquam in vltima miſtione deberet eſſe vt
                  <var>.n.
                    <lb/>
                  u.</var>
                ad
                  <var>.n.a.</var>
                ita vt extrema vice fuiſſet
                  <var>.t.m.</var>
                quæ quidem
                  <var>.t.m.</var>
                excederet terminum per
                  <var>.
                    <lb/>
                  n.m.</var>
                quæ
                  <var>.n.m.</var>
                reuera eſſet nobis cognita, eò quòd ex priori modo hic ſupra dicto
                  <lb/>
                proportio
                  <var>.a.m.</var>
                ad
                  <var>.m.u.</var>
                nobis in-
                  <lb/>
                noteſceret, & proportio
                  <var>.n.a.</var>
                ad
                  <var>.
                    <lb/>
                  n.u.</var>
                nobis data eſt ſimul cum
                  <reg norm="quan­ titate" type="context">quã­
                    <lb/>
                    <figure xlink:label="fig-0108-01" xlink:href="fig-0108-01a" number="149">
                      <image file="0108-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0108-01"/>
                    </figure>
                  titate</reg>
                  <var>.a.u.</var>
                </s>
                <s xml:id="echoid-s1255" xml:space="preserve">quare quantitas
                  <var>.n.u.</var>
                &
                  <lb/>
                  <var>m.u.</var>
                nobis cognita, remanebit, et
                  <lb/>
                  <var>n.m.</var>
                eorum differentia ſimiliter, etiam, et
                  <var>.t.n.</var>
                reſiduum vaſis, quo metimur, vnde
                  <lb/>
                neceſſe erit, quo
                  <unsure/>
                d vltima vice vas contineret ſolum
                  <var>.t.n.</var>
                reliqua uerò per ſe patent.</s>
              </p>
            </div>
            <div xml:id="echoid-div274" type="math:theorem" level="3" n="143">
              <head xml:id="echoid-head162" xml:space="preserve">THEOREMA
                <num value="143">CXLIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s1256" xml:space="preserve">HIeronymus Cardanus in
                  <ref id="ref-0015">lib. ſuæ arithmeticæ cap .66. quæſtione .56.</ref>
                quam Car­
                  <lb/>
                danicam vocat, ita inquit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1257" xml:space="preserve">Quidam perambulauit prima die certam quantitatem ſpatij, & ſecunda die,
                  <reg norm="tan­ tò" type="context">tã­
                    <lb/>
                  tò</reg>
                plus proportionaliter, quantò diameter eſt maior coſta, & tertia die tantò plus
                  <lb/>
                ſecunda, quantò proportionaliter portio lineæ diuiſæ ſecundum proportionem ha
                  <lb/>
                bentem medium, & duo extrema excedit minorem portionem, & quarta die in
                  <lb/>
                proportione ad tertiam vt ſecunda ad primam, & quinta die proportionaliter tan-
                  <lb/>
                tò plus quarta, quantò in tertia plus ſecunda, & ita alternatis vicibus in diebus no-
                  <lb/>
                uem peregit nouem milliaria. </s>
                <s xml:id="echoid-s1258" xml:space="preserve">Quæritur igitur quantum ambulauit die prima.</s>
              </p>
              <p>
                <s xml:id="echoid-s1259" xml:space="preserve">Hoc autem nihil aliud eſt, quàm ſi aliquis diceret, propono tibi, exempli gratia,
                  <lb/>
                lineam
                  <var>.a.l.</var>
                nouem partibus inuicem non æqualibus ita diuiſam
                  <var>.a.c</var>
                :
                  <var>c.d</var>
                :
                  <var>d.e</var>
                : & cæte-
                  <lb/>
                ris, quarum partium proportiones tibi etiam do, vt putà.
                  <var>a.c.</var>
                ad
                  <var>.c.d.</var>
                et
                  <var>.c.d.</var>
                ad
                  <var>.d.e.</var>
                et
                  <var>.
                    <lb/>
                  d.e.</var>
                ad
                  <var>.e.f.</var>
                & ſic de cæteris vſque ad poſtremam
                  <var>.k.l.</var>
                quæ quidem proportiones ſint
                  <lb/>
                etiam inuicem diſſimiles, ſeu inæquales, do tibi etiam
                  <reg norm="proportionem" type="context">proportionẽ</reg>
                totius lineæ
                  <var>.a.l.</var>
                  <lb/>
                ad
                  <var>.a.b.</var>
                ſuam partem, quæ vt in propoſito exemplo nonupla eſt.</s>
              </p>
              <p>
                <s xml:id="echoid-s1260" xml:space="preserve">Quæro nunc quam proportionem habebit
                  <var>.a.c.</var>
                ad
                  <var>.a.b.</var>
                & ſic de cæteris partibus
                  <lb/>
                eiuſdem ad eandem
                  <var>.a.b</var>
                .</s>
              </p>
              <p>
                <s xml:id="echoid-s1261" xml:space="preserve">Quod quidem facillimum erit ſpeculari, nec non operari vnicuique, qui omnino
                  <lb/>
                practicæ numerorum ignarus non fuerit, dum ab ordine ſcientifico non diſcedat.</s>
              </p>
              <p>
                <s xml:id="echoid-s1262" xml:space="preserve">Cum enim cognoſcimus proportionem
                  <var>.a.c.</var>
                ad
                  <var>.c.d.</var>
                conſequenter cognoſcemus
                  <lb/>
                ctiam proportion em aggregati
                  <var>.a.c.d.</var>
                ad
                  <var>.c.d.</var>
                cum autem cognouerimus proportio- </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum