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-div230" type="math:theorem" level="3" n="120">
              <pb o="82" rhead="IO. BAPT. BENED." n="94" file="0094" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0094"/>
              <p>
                <s xml:id="echoid-s1083" xml:space="preserve">Pro cuius ratione conſideremus triangulum hic ſubnotatum
                  <var>.a.b.c.</var>
                cuius
                  <lb/>
                unumquodque latus ſignificet ſummam duorum ſociorum, vtputa latus
                  <var>.a.b.</var>
                ſignifi-
                  <lb/>
                cet ſummam primi cum ſecundo, latus verò
                  <var>.b.c.</var>
                ſummam ſecundi cum tertio, la-
                  <lb/>
                rus autem
                  <var>.a.c.</var>
                ſummam primi cum tertio, et
                  <var>.a.e.</var>
                ſeu
                  <var>.a.o.</var>
                ſit numerus primi ſocij, et
                  <var>.
                    <lb/>
                  e.b.</var>
                vel
                  <var>.b.u.</var>
                ſit ſecundi ſocij, et
                  <var>.c.u.</var>
                ſeu
                  <var>.c.o.</var>
                ſit tertij, cum autem
                  <var>.a.e.</var>
                æqualis ſit
                  <var>.a.o.</var>
                  <lb/>
                  <figure xlink:label="fig-0094-01" xlink:href="fig-0094-01a" number="128">
                    <image file="0094-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0094-01"/>
                  </figure>
                et
                  <var>.b.e</var>
                :æ qualis
                  <var>.b.u.</var>
                et
                  <var>.c.u.</var>
                æqualis
                  <var>.c.o.</var>
                  <lb/>
                ex ſuppoſito ſi
                  <reg norm="dempta" type="context">dẽpta</reg>
                fuerit ſumma ſeu
                  <lb/>
                latus
                  <var>.a.c.</var>
                datum ex aggregato laterum
                  <var>.
                    <lb/>
                  a.b.</var>
                cum
                  <var>.b.c.</var>
                reliquarum ſummarum, re
                  <lb/>
                linquet nobis cognitum aggregatum
                  <lb/>
                ex
                  <var>.b.e.</var>
                cum
                  <var>.b.u</var>
                . </s>
                <s xml:id="echoid-s1084" xml:space="preserve">Quare & eius medic-
                  <lb/>
                tas
                  <var>.b.e.</var>
                ſiue
                  <var>.b.u.</var>
                nobis cognita erit, qua
                  <lb/>
                detracta exſumma
                  <var>.b.a.</var>
                relinquetur no
                  <lb/>
                bis cognitus numerus
                  <var>.a.e.</var>
                detracto ve-
                  <lb/>
                ro numero
                  <var>.a.e.</var>
                hoc eſt
                  <var>.a.o.</var>
                ex
                  <var>.a.c.</var>
                ſum-
                  <lb/>
                ma, ſeu latus, aut
                  <var>.b.u.</var>
                ex
                  <var>.b.c.</var>
                remanebit
                  <lb/>
                  <var>o.c.</var>
                ſeu
                  <var>.c.u.</var>
                cognitus.</s>
              </p>
            </div>
            <div xml:id="echoid-div232" type="math:theorem" level="3" n="121">
              <head xml:id="echoid-head139" xml:space="preserve">THEOREMA
                <num value="121">CXXI</num>
              .</head>
              <p>
                <s xml:id="echoid-s1085" xml:space="preserve">HAC etiam methodo hoc facere poſſumus non
                  <reg norm="ſolum" type="context">ſolũ</reg>
                de tribus ſocijs, ſed
                  <reg norm="etiam" type="context">etiã</reg>
                  <lb/>
                de omnibus quotquot volueris, vt exempli gratia,
                  <lb/>
                  <figure xlink:label="fig-0094-02" xlink:href="fig-0094-02a" number="129">
                    <image file="0094-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0094-02"/>
                  </figure>
                ſint ſex ſocij
                  <var>.a.b.c.d.e.f.</var>
                quorum ſumma per binos co-
                  <lb/>
                gnita, vtputà ſumma numeri
                  <var>.a.</var>
                cum
                  <var>.b.</var>
                cognita nobis ſit,
                  <lb/>
                & ſumma numeri
                  <var>.b.</var>
                cum
                  <var>.c.</var>
                & ſumma
                  <var>.c.</var>
                cum
                  <var>.d.</var>
                & ſum-
                  <lb/>
                ma
                  <var>.d.</var>
                cum
                  <var>.e.</var>
                & ſumma
                  <var>.e.</var>
                cum
                  <var>.f.</var>
                neceſle eft etiam ſcire
                  <lb/>
                ſummam duorum vno relicto, vtputa ſummam
                  <var>.a.</var>
                cum
                  <lb/>
                c. vt poſſimus triangulum
                  <var>.a.b.c.</var>
                conſtituere. </s>
                <s xml:id="echoid-s1086" xml:space="preserve">Vnde ex
                  <lb/>
                præmiffa, cognitus numerus nobis erit vniuſcuiuſque
                  <var>.a.
                    <lb/>
                  b.c</var>
                . </s>
                <s xml:id="echoid-s1087" xml:space="preserve">Quapropter dempto numero
                  <var>.c.</var>
                ex ſumma
                  <var>.c.</var>
                cum
                  <lb/>
                d. & numero
                  <var>.d.</var>
                ex ſumma
                  <var>.d.</var>
                cum
                  <var>.e.</var>
                & numero
                  <var>.e.</var>
                ex ſum
                  <lb/>
                ma
                  <var>.e.</var>
                cum
                  <var>.f.</var>
                habebimus intentum.</s>
              </p>
            </div>
            <div xml:id="echoid-div234" type="math:theorem" level="3" n="122">
              <head xml:id="echoid-head140" xml:space="preserve">THEOREMA
                <num value="122">CXXII</num>
              ,</head>
              <p>
                <s xml:id="echoid-s1088" xml:space="preserve">CVM aliquando, illud quod Archimedes inuenit, vt furtum Regiab aurifa-
                  <lb/>
                bro in regia corona factum, quemadmodum ſcribit Vitruuius, proderet, con-
                  <lb/>
                templarer, mihi etiam viſum eſt, vt aliquem modum ſcientiſicum inueſtigarem, quo
                  <lb/>
                proportio auri ad argentum, quod in aliquo propoſito corpore exipſis miſto cogni
                  <lb/>
                ti ponderis cognoſci poſſet. </s>
                <s xml:id="echoid-s1089" xml:space="preserve">Et cum multos diuerſis temporibus excogitarim offi-
                  <lb/>
                cio meo deeſſe nolui in ijſdem literarum monumentis mandandis, quorum hic
                  <lb/>
                vnus erit: </s>
                <s xml:id="echoid-s1090" xml:space="preserve">propoſita nobis ſint tria corpora
                  <var>.A.M.V.</var>
                æqualia inter ſe, ſed diuer-
                  <lb/>
                ſarum ſpecierum materiei, vtputa quod
                  <var>.A.</var>
                ſit argenteum, & omogeneum
                  <var>.V.</var>
                ve-
                  <lb/>
                rò aureum omogeneum, & M. mixtum exauro, & argento, ideſt heterogeneum,
                  <lb/>
                cupimusergo ſcire
                  <reg norm="iuſtam" type="context">iuſtã</reg>
                quantitatem auri & argenti, quæ eſt in ipſo corpore
                  <var>.M.</var>
                  <lb/>
                miſto. </s>
                <s xml:id="echoid-s1091" xml:space="preserve">Ita igitur faciamus. </s>
                <s xml:id="echoid-s1092" xml:space="preserve">Videamus primum quantum ſit pondus vniuſcuiuſque
                  <lb/>
                ipſorum corporum, ponamus autem pondus corporis
                  <var>.V.</var>
                auri eſſe vt .234. pondus </s>
              </p>
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