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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IO. BAPT. BENED.
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            <div xml:id="echoid-div266" type="math:theorem" level="3" n="139">
              <p>
                <s xml:id="echoid-s1219" xml:space="preserve">
                  <pb o="94" rhead="IO. BAPT. BENED." n="106" file="0106" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0106"/>
                  <var>A.I.</var>
                vnde quadratum lineæ
                  <var>.A.I.</var>
                erit .100. idem dico de quadrato lineæ
                  <var>.I.L</var>
                . </s>
                <s xml:id="echoid-s1220" xml:space="preserve">quare
                  <lb/>
                ex penultima primi
                  <var>.A.L.</var>
                erit radix quadrata quadrati .200. ideſt .14. cum vno ſepti-
                  <lb/>
                mo ferè. </s>
                <s xml:id="echoid-s1221" xml:space="preserve">quare
                  <var>.A.L.</var>
                iuncta
                  <var>.A.O.</var>
                erit .28. cum duobus ſeptimis. </s>
                <s xml:id="echoid-s1222" xml:space="preserve">ſed
                  <var>.L.O.</var>
                ex ſuppoſi-
                  <lb/>
                to erit .20. eo quòd
                  <var>.L.I.</var>
                ęquatur ipſi
                  <var>.A.I.</var>
                ſimiliter et
                  <var>.I.O.</var>
                vt ipſe etiam probauit. </s>
                <s xml:id="echoid-s1223" xml:space="preserve">qua
                  <lb/>
                dempta ex
                  <var>.L.A.O.</var>
                relinquetur
                  <var>.H.A.M.</var>
                (nam
                  <var>.L.H.</var>
                cum
                  <var>.O.M.</var>
                æquatur ipſi
                  <var>.L.O.</var>
                ex .
                  <lb/>
                35. tertij ipſius Eucli. partium .8.
                  <reg norm="cum" type="context">cũ</reg>
                duabus ſeptimis. cuius
                  <reg norm="dimidium" type="context">dimidiũ</reg>
                hoc eſt
                  <var>.A.H.</var>
                erit
                  <lb/>
                4. cum una ſeptima, quod eſt propoſitum. </s>
                <s xml:id="echoid-s1224" xml:space="preserve">Reſpice figuram ipſius Tartaleæ.</s>
              </p>
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            <div xml:id="echoid-div268" type="math:theorem" level="3" n="140">
              <head xml:id="echoid-head159" xml:space="preserve">THEOREMA
                <num value="140">CXL</num>
              .</head>
              <p>
                <s xml:id="echoid-s1225" xml:space="preserve">QVadrageſimum nonum quæſitum ſimiliter poſſumus alio modo ſoluere, vt
                  <lb/>
                putà cum vnumquodque latus rhombi ſimul cum area cognitum, ſeu datum
                  <lb/>
                nobis ſit
                  <reg norm="cognitum" type="context">cognitũ</reg>
                ſimiliter nobis erit quadratum lateris
                  <var>.a.d.</var>
                hoc eſt ſumma duorum
                  <lb/>
                quadratorum
                  <var>.a.o.</var>
                et
                  <var>.o.d.</var>
                ex penultima primi Euclid. </s>
                <s xml:id="echoid-s1226" xml:space="preserve">cúmque nobis cognita etiam
                  <lb/>
                ſit totalis ſuperficies rhombi, cognita etiam nobis erit eius medietas, hoc eſt produ-
                  <lb/>
                ctum
                  <var>.o.d.</var>
                in
                  <var>.o.a.</var>
                vnde ex methodo .37. Theorematis cognoſcemus .a
                  <unsure/>
                  <var>.o.</var>
                et
                  <var>.o.d.</var>
                & ſic
                  <lb/>
                etiam eorum dupla, quod quærebatur.</s>
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            <div xml:id="echoid-div269" type="math:theorem" level="3" n="141">
              <head xml:id="echoid-head160" xml:space="preserve">THEOREMA
                <num value="141">CXLI</num>
              .</head>
              <p>
                <s xml:id="echoid-s1227" xml:space="preserve">PVlchrum quæſitum fuit id, quod Tartalea ponit pro .18. noni libri in quarto fo-
                  <lb/>
                lio, quod huiuſmodi eſt. </s>
                <s xml:id="echoid-s1228" xml:space="preserve">Aliquis habet dolium mero plenum, ex quo
                  <lb/>
                duas vrnas extrahit ipſius vini, ſed loco ipſius vini infundit duas vrnas aquæ. </s>
                <s xml:id="echoid-s1229" xml:space="preserve">Dein
                  <lb/>
                de poſt aliquot dies extrahit iterum alias duas vrnas illius miſti, & iterum infundit
                  <lb/>
                duas vrnas aquæ, & poſt alios aliquot dies idem facit, & hac vltima tertia vice in-
                  <lb/>
                uenit aquam tantam eſſe, quantum vinum. </s>
                <s xml:id="echoid-s1230" xml:space="preserve">Quæritur nunc quot vrnas capiat il-
                  <lb/>
                lud dolium.</s>
              </p>
              <p>
                <s xml:id="echoid-s1231" xml:space="preserve">Solutio ipſius Tartaleæ bona eſt, cum ſupponat illas quatuor quantitates vini eſſe
                  <lb/>
                inuicem continuas proportionales, vt putà primò totum vinum merum, poſteà re-
                  <lb/>
                ſiduum pro ſecunda quantitate, deinde pro tertia in ſecunda, & pro quarta in ter-
                  <lb/>
                tia extractione, hoc eſt quòd proportio totius vini meri ad vinum in prima ſit, vt hu
                  <lb/>
                ius ad vinum in ſecunda, & vt huius ad vinum in tertia miſtione. </s>
                <s xml:id="echoid-s1232" xml:space="preserve">Sed quia ipſe
                  <lb/>
                non probat hanc continuam proportionalitatem ex methodo ſcientifica, mihi
                  <reg norm="visum" type="context">visũ</reg>
                  <lb/>
                eſt hoc loco illam deſcribere.</s>
              </p>
              <p>
                <s xml:id="echoid-s1233" xml:space="preserve">Cogitemus igitur
                  <var>a.u.</var>
                pro capacitate dolij, et
                  <var>.a.i.</var>
                pro quantitate duarum vrna-
                  <lb/>
                rum. </s>
                <s xml:id="echoid-s1234" xml:space="preserve">Nunc uerò ſupponamus quamlibet partem huius miſti omogeneam eſſe ſuo
                  <lb/>
                toto, quapropter ſequetur eandem proportionem eſſe vini ad aquam in qualibet
                  <lb/>
                parte, quæ erit in toto, & ideò imaginemur
                  <var>.e.o.</var>
                æqualem
                  <var>.a.i</var>
                . </s>
                <s xml:id="echoid-s1235" xml:space="preserve">Sed in puncto
                  <var>.i.</var>
                tali
                  <lb/>
                modo diuiſam, vt proportio
                  <var>.i.e.</var>
                ad
                  <var>.i.o.</var>
                eadem ſit quæ
                  <var>.i.a.</var>
                ad
                  <var>.i.u</var>
                . </s>
                <s xml:id="echoid-s1236" xml:space="preserve">Supponamus
                  <reg norm="etiam" type="context">etiã</reg>
                </s>
              </p>
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