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
161 149
162 150
163 151
164 152
165 153
166 154
167 155
168 156
169 157
170 158
171 159
172 160
173 161
174 162
175 163
176 164
177 165
178 166
179 167
180 168
181 169
182 170
183 171
184 172
185 173
186 174
187 175
188 176
189 177
190 178
< >
page |< < (112) 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-div293" type="appendix" level="3" n="1">
              <p>
                <s xml:id="echoid-s1418" xml:space="preserve">
                  <pb o="112" rhead="IO. BAPT. BENED." n="124" file="0124" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0124"/>
                ſecundo itinere iterum duplicauit ſuos aureos, ex quibus etiam poſtea conſumpſit
                  <num value="8">.
                    <lb/>
                  8.</num>
                numeratis poſteà pecunijs reperit tantummodo .24. aureos in eius marſupio,
                  <reg norm="quae­ ritur" type="simple">quę­
                    <lb/>
                  ritur</reg>
                nunc quot habebat aureos in principio primi itineris.</s>
              </p>
              <p>
                <s xml:id="echoid-s1419" xml:space="preserve">Intali caſu, cum ipſe quolibet itinere duplicabat eius pecuniam, nulli dubium
                  <lb/>
                eſt quòd in fine ſecundi itineris ipſe habuiſſet pecuniam ſuam quadruplicatam, ſi
                  <lb/>
                ex ipſa nihil detractum fuiſſet, ſed quia in fine primi itineris conſumpſit .4. aureos,
                  <lb/>
                quibus alios .4. lucratus eſſet in ſecundo itinere, poſteà conſumpſit iterum
                  <num value="8">.
                    <lb/>
                  8.</num>
                aureos, ita
                  <reg norm="quod" type="simple">ꝙ</reg>
                ex quadruplo ſuæ primæ pecuniæ, rectè dici poteſt, quod conſum-
                  <lb/>
                pſerit .16. aureos; </s>
                <s xml:id="echoid-s1420" xml:space="preserve">qui quidem numerus ex communi conceptu erit differentia in-
                  <lb/>
                ter .24. & quadruplum prioris pecuniæ, cum qua profectus fuit in principio eius iti-
                  <lb/>
                neris; </s>
                <s xml:id="echoid-s1421" xml:space="preserve">quapropter ſi addiderimus .16. ipſi .24. habebimus .40. pro quadruplo eius
                  <lb/>
                prioris pecuniæ. </s>
                <s xml:id="echoid-s1422" xml:space="preserve">Rectè igitur dici poteſt, ſi .4. prouenit ab vno, à quo numero pro
                  <lb/>
                ueniet .40.</s>
              </p>
              <p>
                <s xml:id="echoid-s1423" xml:space="preserve">Videamus igitur nunc quo pacto hoc reſpondeat cum methodo antiquorum.
                  <lb/>
                </s>
                <s xml:id="echoid-s1424" xml:space="preserve">Ego enim inueni duas poſitiones ſcriptas à Tartalea pro prima pecunia hoc eſt .12.
                  <lb/>
                et .14. ſed à .12. pro primo errore reperi .8. more antiquo à .14. verò pro ſecundo er-
                  <lb/>
                rore proueniebat .16. producta autem horum numerorum diametraliter, ſunt .112.
                  <lb/>
                et .192. quorum differentia eſt .80. pro tertio producto, quo diuiſo per differen-
                  <lb/>
                tiam
                  <reg norm="errorum" type="context">errorũ</reg>
                .8. ſcilicet, præbetnobis .10. pro pecunia quæſita, vt etiam ego inueni.</s>
              </p>
              <p>
                <s xml:id="echoid-s1425" xml:space="preserve">Sed hoc mihi viſum eſt ſubtilius examinare mea methodo mediante, vtin figu-
                  <lb/>
                ra
                  <var>.G.</var>
                videre eſt, prius enim ſuo loco poſuitria producta dicta, deinde duas poſitio
                  <lb/>
                nes .12. et .14. & quia ſciebam productum .112. oriri à multiplicatione .14. cum .8.
                  <lb/>
                ideo poſui talem numerum .8. ſuo loco diametraliter oppoſito ei producto .112.
                  <lb/>
                & quia ſciebam etiam productum .192. naſci ex .12. et .16. ideo ſuo loco poſui hunc
                  <lb/>
                numerum .16. qui eſt maxima differentia inter duos conſequentes ( ita à me ſupra
                  <lb/>
                nominatos) à qua differentia dempta priori .8. iam inuenta, reliqua .8. mihi daba-
                  <lb/>
                tur,
                  <reg norm="quam" type="context">quã</reg>
                ſuo loco notaui, ſuo
                  <reg norm="etiam" type="context">etiã</reg>
                  <lb/>
                loco ſcripſi .2. differentiam inter
                  <lb/>
                12. et .14. antecedentium. </s>
                <s xml:id="echoid-s1426" xml:space="preserve">ſed
                  <lb/>
                  <figure xlink:label="fig-0124-01" xlink:href="fig-0124-01a" number="169">
                    <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0124-01"/>
                  </figure>
                quia ſciebam eandem proportio
                  <lb/>
                nem eſſe inter hanc differentiam
                  <lb/>
                &
                  <reg norm="differentiam" type="context">differentiã</reg>
                .8. huic
                  <reg norm="ſuppoſitam" type="context">ſuppoſitã</reg>
                ,
                  <lb/>
                quæ reperitur inter .12.
                  <reg norm="antecedem" type="context">antecedẽ</reg>
                  <lb/>
                tem, &
                  <reg norm="ſuum" type="context">ſuũ</reg>
                conſequentem; </s>
                <s xml:id="echoid-s1427" xml:space="preserve">ideo
                  <lb/>
                poſui .48. pro dicto conſequenti,
                  <lb/>
                diuiſi poſtea productum .80. per
                  <num value="8">.
                    <lb/>
                  8.</num>
                differentiam ei diametraliter
                  <lb/>
                oppoſitam, vnde prouenit mihi
                  <lb/>
                10. cui ita proportionatus eſt
                  <reg norm="ſuus" type="simple">ſuꝰ</reg>
                  <lb/>
                numerus conſequens .40. vt .48.
                  <lb/>
                ad .12. et .56. ad .14. exijſdem ra-
                  <lb/>
                tionibus à meſupra dictis.
                  <lb/>
                </s>
                <s xml:id="echoid-s1428" xml:space="preserve">In tali igitur figura videntur nu-
                  <lb/>
                merinaturaliter
                  <reg norm="correſpondentes" type="context">correſpondẽtes</reg>
                  <lb/>
                ipſis poſitionibus, & hac metho-
                  <lb/>
                do poſſumus inuenire tales numeros conſequentes in omnibus alijs exemplis à no-
                  <lb/>
                ſtris maioribus ſcriptis.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum