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="110" rhead="IO. BAPT. BENED." n="122" file="0122" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0122"/>
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                <s xml:id="echoid-s1400" xml:space="preserve">DEmpto poſteà quo volueris horum altero productorum ex maximo,
                  <reg norm="diuiſoque" type="simple">diuiſoq́;</reg>
                  <lb/>
                reliquo per differentiam conſequentium, ipſi diametraliter oppoſitam, pro
                  <lb/>
                ueniet tibi numerus antecedens
                  <reg norm="correſpondensque" type="simple">correſpondensq́;</reg>
                illi.</s>
              </p>
              <p>
                <s xml:id="echoid-s1401" xml:space="preserve">Animaduertendum tamen eſt, quòd ſi in figura à me ita ordinata, ſumma ſim-
                  <lb/>
                plex propoſita medium locum occuparet, vt in figura
                  <var>.D.</var>
                arithmetica videri poteſt;
                  <lb/>
                </s>
                <s xml:id="echoid-s1402" xml:space="preserve">tunc vt habeatur eius productum, addenda ſimul erunt circunſtantia producta .eo
                  <lb/>
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                eius ſecundum latus eſſet antecedens medio loco conſtitutum, & prima pars
                  <reg norm="quae- ſita" type="simple">quę-
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                  ſita</reg>
                numeri propoſiti: </s>
                <s xml:id="echoid-s1403" xml:space="preserve">in qua figura
                  <var>.D.</var>
                manifeſtè patet ratio, quare colligendi ſint
                  <lb/>
                tam errores, quam producta, dum eorum alterum eſt plus, reliquum verò minus.</s>
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              <p>
                <s xml:id="echoid-s1404" xml:space="preserve">Speculatio figurę
                  <var>.D.</var>
                arithmeticę videbitur in figura
                  <var>.D.</var>
                geometrica, eodem fe
                  <lb/>
                rè modo quo fecimus in figuris
                  <var>.C.</var>
                mutatis mutandis, reſpectu ipſius plus, & minus.</s>
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              <p>
                <s xml:id="echoid-s1405" xml:space="preserve">Collectio namque
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                ſimiliter accidentalis eſt, eo quod eſſentialis numerus
                  <lb/>
                diuiſor per ſe, eſt maxima differentia ſummarum ſimplicium, vt in dicta figura
                  <var>.D.</var>
                  <lb/>
                cerni poteſt.</s>
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              <p>
                <s xml:id="echoid-s1406" xml:space="preserve">Sed vt ſuperius dixi, nunc etiam repeto, quòd rectè hoc loco multiplicabatur
                  <lb/>
                ſumma ſimplex propoſita, cum prima par
                  <lb/>
                te primę poſitionis, vt productum diuide
                  <lb/>
                retur per primam ſimplicem ſummam,
                  <lb/>
                  <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a" number="167">
                    <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0122-01"/>
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                vnde proueniret nobis pars prima
                  <reg norm="quaeſi- ta" type="simple">quęſi-
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                  ta</reg>
                noſtri numeri propoſiti, ex regula de
                  <lb/>
                tribus, vnica poſitione.</s>
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              <p>
                <s xml:id="echoid-s1407" xml:space="preserve">Vt exempli gratia, datus numerus diui
                  <lb/>
                dendus ſit .100. in quinque partes, tales
                  <lb/>
                verò,
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                ſecunda duplo maior ſit prima
                  <lb/>
                cum .2. ſimul, tertia autem æqualis ſit pri-
                  <lb/>
                mæ & ſecundæ cum .3. vnitatibus iunctis,
                  <lb/>
                quarta poſteà maior ſit prima ſecunda, &
                  <lb/>
                tertia per .4. vnitates, quinta demum ſu-
                  <lb/>
                peret reliquas omnes per quinque vnita
                  <lb/>
                tes, vt in figura
                  <var>.E.</var>
                videre eſt, quæ quidem
                  <lb/>
                partes compoſitæ (ſumpta vnitate pro
                  <lb/>
                prima) ita diſpoſitæ erunt .1. 4. 8. 17. 35.
                  <lb/>
                quarum ſumma erit .65. ſimplices autem
                  <lb/>
                cum diſpoſitæ fuerint erunt .1. 2. 3. 6. 12.
                  <lb/>
                quarum ſumma erit .24. dempta igitur
                  <lb/>
                cum fuerit hæc ſimplex ſumma .24. à com
                  <lb/>
                poſita .65. reſiduum erit .41. hoc eſt ſum-
                  <lb/>
                ma numerorum propoſitorum cum ſuis
                  <lb/>
                iterationibus in ipſis partibus, quod cum
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                per ſe clariſſimum ſit, ſuperſluum eſt
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                ſummam annatomizare per ſingulas par-
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                tes, niſi quis habuerit eius cerebrum à fi-
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                gura Omega
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                , cui tamen poſ-
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                ſemus dicere dictam ſummam .41. in .4.
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                partes diuidi, cuius prima eſſet .2. pro ad
                  <lb/>
                ditione ad
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                partem ſimplicium, </s>
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