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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              <pb o="108" rhead="IO. BAPT. BENED." n="120" file="0120" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0120"/>
              <p>
                <s xml:id="echoid-s1389" xml:space="preserve">Diſponantur igitur huiuſmo-
                  <lb/>
                  <figure xlink:label="fig-0120-01" xlink:href="fig-0120-01a" number="163">
                    <image file="0120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0120-01"/>
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                di numeri tali ordine, vt fim-
                  <lb/>
                plex ſumma, quæ ab vna reli-
                  <lb/>
                quarum ſuperatur, & aliam ſupe-
                  <lb/>
                rat, medium locum teneat; </s>
                <s xml:id="echoid-s1390" xml:space="preserve">@t
                  <lb/>
                in propoſito exemplo ſumma
                  <lb/>
                mediocris eft .48. quę à ſumma
                  <num value="60">.
                    <lb/>
                  60.</num>
                ſuperatur, & ſuperat ſum-
                  <lb/>
                mam .39. locata igitur fit hęc .48.
                  <lb/>
                inter illas, ſuæ verò primæ partes
                  <lb/>
                fimiliter conftitutæ ſint ſupra di-
                  <lb/>
                ctas ſummas, cum ſuis
                  <reg norm="differentijs" type="context">differẽtijs</reg>
                ,
                  <lb/>
                & tria producta iam dicta, vt in fi
                  <lb/>
                guris
                  <var>.C.</var>
                et
                  <var>.D.</var>
                arithmeticis
                  <lb/>
                clarè patet: </s>
                <s xml:id="echoid-s1391" xml:space="preserve">figura enim
                  <var>.C.</var>
                eft
                  <lb/>
                pro exemplo ipſius plus ſimpli-
                  <lb/>
                citer: </s>
                <s xml:id="echoid-s1392" xml:space="preserve">figura verò
                  <var>.D.</var>
                pro exem-
                  <lb/>
                plo ipſius plus, & minus. </s>
                <s xml:id="echoid-s1393" xml:space="preserve">Et fic
                  <lb/>
                  <figure xlink:label="fig-0120-02" xlink:href="fig-0120-02a" number="164">
                    <image file="0120-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0120-02"/>
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                in figura
                  <var>.C.</var>
                habebimus tres
                  <lb/>
                numeros confequentes .60. 48.
                  <lb/>
                39. & tres antecedentes .10. 8.
                  <lb/>
                6. cum dimidio, vnam, & ean-
                  <lb/>
                dem proportionem terminantes,
                  <lb/>
                ex .24. quinti, vt diximus; </s>
                <s xml:id="echoid-s1394" xml:space="preserve">qua-
                  <lb/>
                re eorum differentiæ fimiliter
                  <lb/>
                proportionales erunt, quod etiam
                  <lb/>
                vidimus. </s>
                <s xml:id="echoid-s1395" xml:space="preserve">Supponamus nunc nos
                  <lb/>
                ignorare æqualitatem maximi
                  <lb/>
                producti cum reliquis duobus,
                  <lb/>
                accipiendo ſolum pro hypoteſi,
                  <lb/>
                quòd dicta producta oriantur
                  <lb/>
                ex lateribus iam dictis.</s>
              </p>
              <p>
                <s xml:id="echoid-s1396" xml:space="preserve">Demonſtrandum nobis nunc relinquetur, maximum productum æquale effere-
                  <lb/>
                liquis duobus; </s>
                <s xml:id="echoid-s1397" xml:space="preserve">hoc eſt productum .168. æquale effe productis .90. et .78. quorum
                  <lb/>
                duorum productorum alterum .90. ſcilicet, generatur à differentia .9. quæ eft ſe-
                  <lb/>
                cundę, & tertię ſummæ, in primum numerum antecedentem, qui eſt .10. alterum vc-
                  <lb/>
                ro productum .78. ſcilicet, generatur à differentia .12. quę eſt primę, & ſecundę, ſum
                  <lb/>
                mę in tertium numerum antecedentem, qui eſt .6. cum dimidio, maximum vero
                  <lb/>
                productum .168. ſcilicet generatur à differentia maxima .21. quę eft primę, & tertię
                  <lb/>
                ſummę (& ſemper ęqualis prioribus duabus differentijs .12. et .9.) in ſecundum nu-
                  <lb/>
                merum antecedentem, qui eſt .8.</s>
              </p>
              <p>
                <s xml:id="echoid-s1398" xml:space="preserve">Conſtituantur igitur duo producta fimul iuncta ęqualia duobus .90. et .78.
                  <lb/>
                lateralibus ſupra vnam aliquam rectam lineam
                  <var>.q.p.</var>
                  <reg norm="fitque" type="simple">fitq́;</reg>
                productum
                  <var>.f.g.</var>
                ęquale
                  <num value="90">.
                    <lb/>
                  90.</num>
                productum verò
                  <var>.g.n.</var>
                ęquale .78. fit etiam baſis
                  <var>.g.p.</var>
                vt .9. et
                  <var>.g.q.</var>
                vt .12. vnde
                  <var>.g.i.</var>
                  <lb/>
                vel
                  <var>.q.n.</var>
                erit vt .6. cum dimidio .et
                  <var>.g.d.</var>
                vel
                  <var>.p.f.</var>
                vt .10. & ideo
                  <var>.i.d.</var>
                differentia erit .3. </s>
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