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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[161. Figure: Compositorum]
[162. Figure: Simpricium]
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[180. Figure: SVPERFICIALIS.]
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THEOREM. ARIT.
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                  <pb o="109" rhead="THEOREM. ARIT." n="121" file="0121" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0121"/>
                cum dimidio, ut in figura
                  <var>.C.</var>
                geometrica hic ſubſcripta videre licet, et
                  <var>.q.p.</var>
                erit .21.
                  <lb/>
                Cogitemus nunc differentiam
                  <var>.d.i.</var>
                diuiſam eſſe in puncto
                  <var>.e.</var>
                ita vt eadem proportio
                  <lb/>
                ſit ipſius
                  <var>.d.e.</var>
                ad
                  <var>.e.i.</var>
                quæ ipſius
                  <var>.q.g.</var>
                ad
                  <var>.g.p.</var>
                hoc eſt vt .1 2. ad .9. quapropter
                  <var>.d.e.</var>
                erit
                  <num value="2">.
                    <lb/>
                  2.</num>
                et
                  <var>.e.i.</var>
                erit .1. cum dimidio, vt in dicta figura
                  <var>.C.</var>
                arithmetica reperiuntur eſſe dif-
                  <lb/>
                ferentiæ ipſorum antecedentium numerorum, deinde à puncto
                  <var>.e.</var>
                ducatur imagina-
                  <lb/>
                tione
                  <var>.u.e.o.</var>
                æ quidiſtans ipſi
                  <var>.q.p.</var>
                & producatur
                  <var>.q.n.</var>
                vſque ad
                  <var>.u.</var>
                vnde ita ſe habebit
                  <lb/>
                  <var>u.e.</var>
                ad
                  <var>.e.o.</var>
                ut
                  <var>.q.g.</var>
                ad
                  <var>g.p</var>
                . </s>
                <s xml:id="echoid-s1399" xml:space="preserve">quare vt
                  <var>.d.e.</var>
                ad
                  <var>.e.i.</var>
                ideo ex .15. ſexti vel .20. ſeptimi
                  <var>.n.e.</var>
                  <lb/>
                rectangulum æquale crit ipſi
                  <var>.e.f.</var>
                qua propter rectang ulum
                  <var>.q.o.</var>
                æquale erit duobus
                  <lb/>
                rectangulis
                  <var>.f.g.</var>
                et
                  <var>.g.n</var>
                : ſed cum
                  <var>.g.i.</var>
                ſit vt .6. cum dimidio, et
                  <var>.i.e.</var>
                vt .1. cum dimidio, er
                  <lb/>
                go
                  <var>.g.e.</var>
                erit ut .8. qui quidem numerus multiplicatus cum
                  <var>.q.p.</var>
                21. producit .168. ve
                  <lb/>
                rum eſt igitur quod dictum fuit, hoc eſt
                  <reg norm="quod" type="simple">ꝙ</reg>
                maximum productum ęquale ſit reliquis
                  <lb/>
                duobus.</s>
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