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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            <div xml:id="echoid-div81" type="math:theorem" level="3" n="37">
              <pb o="24" rhead="IO. BAPT. BENED." n="36" file="0036" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0036"/>
              <p>
                <s xml:id="echoid-s334" xml:space="preserve">Hoc ipſum & alia ratione perfici poteſt, nempe, iuncta ſumma
                  <var>.k.b</var>
                :
                  <var>b.d</var>
                : ec
                  <unsure/>
                  <var>.
                    <lb/>
                  b.t.</var>
                alteri rectangulo æquali
                  <var>.b.d.</var>
                quod ſit
                  <var>.b.c.</var>
                ex quo totum quadratum lineæ
                  <var>.d.k.</var>
                  <lb/>
                cognitum erit,
                  <reg norm="atque" type="simple">atq;</reg>
                ita etiam conſequenter eius radicem
                  <var>.d.k.</var>
                cognoſcemus, cuius
                  <lb/>
                ope ac producti
                  <var>.d.b.</var>
                cognoſcemus
                  <var>.d.p.</var>
                et
                  <var>.p.k.</var>
                prout ex theoremate quadrageſi-
                  <lb/>
                moquinto huius libri patebit.</s>
              </p>
              <p>
                <s xml:id="echoid-s335" xml:space="preserve">Michael Stifelius, vndecimo cap. tertij libri, problema eiuſmodi proponit,
                  <lb/>
                quod tamen ipſe via algebræ diſsoluit.</s>
              </p>
              <figure position="here" number="50">
                <image file="0036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0036-01"/>
              </figure>
            </div>
            <div xml:id="echoid-div83" type="math:theorem" level="3" n="38">
              <head xml:id="echoid-head54" xml:space="preserve">THEOREMA
                <num value="38">XXXVIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s336" xml:space="preserve">CVR ij, qui duos numeros inuenire volunt, quorum productum alicui nu-
                  <lb/>
                mero propoſito æquetur, & quadratorum eorundem differentia alteri nu-
                  <lb/>
                mero propoſito æqualis ſir. </s>
                <s xml:id="echoid-s337" xml:space="preserve">Rectè dimidium ſecundi numeri propoſiti in ſeipſum
                  <lb/>
                multiplicent, cui quidem numero differentia quadratorum æquari debet; </s>
                <s xml:id="echoid-s338" xml:space="preserve">porrò
                  <lb/>
                huic quadrato primi propoſiti numeri, cui æquandum eſt productum numerorum
                  <lb/>
                quæſitorum, quadratum adiungant; </s>
                <s xml:id="echoid-s339" xml:space="preserve">tum radicem quadratam huius ſummæ co-
                  <lb/>
                pulet dimidio ſecundi numeri propoſiti, ei inquam, cui differentia quadratorum
                  <lb/>
                æqualis eſſe debet, ex quo quadratum maius conſurgit, à quo, detracto ſecundo
                  <lb/>
                numero, ſupereſt quadratum minus.</s>
              </p>
              <p>
                <s xml:id="echoid-s340" xml:space="preserve">Exempli gratia, ſi proponeretur primo loco numerus .8. cui æquandum eſt
                  <lb/>
                productum numerorum quæſitorum, tum proponeretur numerus .12. cui, detra-
                  <lb/>
                cto minore à maiore, differentia quadratorum vtriuſque quæſiti numeri æqualis
                  <lb/>
                eſſe debet, oportet huius vltimi numeri .12. dimidium in ſeipſum multiplicare,
                  <reg norm="fient- q́ue" type="context">fiẽt-
                    <lb/>
                  q́ue</reg>
                .36. quadratum dimidij, vnde in ſummam colligeremus quadratum primi
                  <lb/>
                numeri .8. quod eſſet .64. quæ cum .36. efficerent .100. cuius centenarij radice, nem
                  <lb/>
                pe .10. collecta in ſummam cum dimidio ſecundi numeri, nempe .6. daretur qua-
                  <lb/>
                dratum maius, nempe .16. ex quo, detracto ſecundo numero, nempe .12. rema-
                  <lb/>
                neret quadratum minus .4.</s>
              </p>
              <p>
                <s xml:id="echoid-s341" xml:space="preserve">Cuius ſpeculationis cauſa, maius quadratum
                  <lb/>
                  <figure xlink:label="fig-0036-02" xlink:href="fig-0036-02a" number="51">
                    <image file="0036-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0036-02"/>
                  </figure>
                incognitum ſignificetur linea
                  <var>.q.g.</var>
                minus verò
                  <lb/>
                pariter incognitum linea
                  <var>.g.i.</var>
                </s>
                <s xml:id="echoid-s342" xml:space="preserve">quare
                  <var>.q.i.</var>
                eorum
                  <lb/>
                differentia, tanquam data remanebit cognita,
                  <lb/>
                vnà etiam
                  <var>.b.i.</var>
                et
                  <var>.q.b.</var>
                ſua dimidia; </s>
                <s xml:id="echoid-s343" xml:space="preserve">tunc cogite-
                  <lb/>
                tur quadratum
                  <var>.y.g.</var>
                ſuper
                  <var>.b.g.</var>
                et
                  <reg norm="parallelogram- mum" type="context">parallelogrã-
                    <lb/>
                  mum</reg>
                rectangu
                  <unsure/>
                lum
                  <var>.g.r.</var>
                deſignatum, & ita etiam
                  <lb/>
                gnomon
                  <var>.u.g.t.</var>
                prout ſexta ſecundi Euclidis pro
                  <lb/>
                ponitur, ex quo quadratum
                  <var>.b.i.</var>
                nempe
                  <var>.u.t.</var>
                co-
                  <lb/>
                gnitum erit, ſed gnomon æqualis eſt rectangulo
                  <var>.g.r.</var>
                ex prædicta, aut ex .8. poſt .16. </s>
              </p>
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