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-div237" type="math:theorem" level="3" n="124">
              <p>
                <s xml:id="echoid-s1103" xml:space="preserve">
                  <pb o="84" rhead="IO. BAPT. BENED." n="96" file="0096" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0096"/>
                rum ſpecierum materiæ, tertium verò corpus maius, vel minus ſit in quantitate vtro-
                  <lb/>
                que illorum, ſed eiuſdem materiæ vnius quod vis illorum, ponderis verò alterius,
                  <lb/>
                  <reg norm="semper" type="context">sẽper</reg>
                eadem proportio erit inter pondera æqualium corporum, quæ inter
                  <reg norm="quantita- tem" type="context">quãtita-
                    <lb/>
                  tem</reg>
                corporis inæqualis, & eam quæ vnius cuiuſuis æqualium.</s>
              </p>
              <p>
                <s xml:id="echoid-s1104" xml:space="preserve">Exempli gratia, ſit
                  <var>.b.</var>
                corpus aliquod aureum æquale corpori
                  <var>.u.</var>
                argenteo, ſit
                  <lb/>
                etiam corpus
                  <var>.a.</var>
                argenteum maius corpore
                  <var>.b.</var>
                vel
                  <var>.u.</var>
                ſed ponderis eiuſdem, quod au-
                  <lb/>
                ri
                  <var>.b</var>
                . </s>
                <s xml:id="echoid-s1105" xml:space="preserve">Tunc dico eandem eſſe proportionem ponde-
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0096-01a" xlink:href="fig-0096-01"/>
                ris
                  <var>.b.</var>
                ad pondus
                  <var>.u.</var>
                quæ eſt magnitudinis
                  <var>.a.</var>
                ad ma-
                  <lb/>
                gnitudinem
                  <var>.u</var>
                . </s>
                <s xml:id="echoid-s1106" xml:space="preserve">Quod ratiocinemur hoc modo, nam
                  <lb/>
                cum proportio corporeitatis
                  <var>.a.</var>
                ad corporeitatem
                  <var>.u.</var>
                  <lb/>
                eadem ſit, quæ ponderis
                  <var>.a.</var>
                ad pondus
                  <var>.u.</var>
                ex ratione
                  <lb/>
                omogeneitatis, ponderis verò
                  <var>.b.</var>
                ad pondus
                  <var>.u.</var>
                ex .7.
                  <lb/>
                quinti, eadem quæ ponderis
                  <var>.a.</var>
                ad pondus
                  <var>.u.</var>
                ideo ex
                  <lb/>
                11. eiuſdem proportio ponderis
                  <var>.b.</var>
                ad pondus
                  <var>.u.</var>
                eadem erit, quæ corporeitatis
                  <var>.a.</var>
                  <lb/>
                ad corporeitatem
                  <var>.u.</var>
                vel ad corporeitatem
                  <var>.b.</var>
                quæ æqualis eſt alteri.</s>
              </p>
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                <figure xlink:label="fig-0096-01" xlink:href="fig-0096-01a">
                  <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0096-01"/>
                </figure>
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            <div xml:id="echoid-div239" type="math:theorem" level="3" n="125">
              <head xml:id="echoid-head143" xml:space="preserve">THEOREMA
                <num value="125">CXXV</num>
              .</head>
              <p>
                <s xml:id="echoid-s1107" xml:space="preserve">QVotieſcunque nobis propoſita fuerint duo corpora cuiuſuis magnitudinis æ-
                  <lb/>
                que ponderantia, ſed diuerſarum ſpecierum materiæ, cum ſcire volueri-
                  <lb/>
                mus proportionem ponderum illarum ſpecierum inter ipſas hoc modo faciemus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1108" xml:space="preserve">Sint exempli gratia, duo nobis propoſita corpora
                  <var>.a.</var>
                et
                  <var>.b.</var>
                (vt dictum eſt) quæ ſi
                  <lb/>
                fuerint æqualium magnitudinum inter ſe, clarum erit quod quæritur, ſed inæqua-
                  <lb/>
                lia erunt, immergatur
                  <reg norm="unumquodque" type="simple">unumquodq;</reg>
                eorum in vas aqua plenum, & collecta ſit aqua
                  <lb/>
                effuſa ab vnoquoque illorum, </s>
                <s xml:id="echoid-s1109" xml:space="preserve">tunc
                  <reg norm="vnaquæque" type="simple">vnaquæq;</reg>
                iſtarum aquarum æqualis magnitudi-
                  <lb/>
                nis erit ſui corporis impellentis, & proportio ponderoſitatis illarum eadem erit,
                  <lb/>
                quæ earum magnitudinum ex omogeneitate, quapropter ſi vnamquamque illarum
                  <lb/>
                ponderabimus, habebimus propoſitum ex præcedenti theoremate.</s>
              </p>
            </div>
            <div xml:id="echoid-div240" type="math:theorem" level="3" n="126">
              <head xml:id="echoid-head144" xml:space="preserve">THEOREMA
                <num value="126">CXXVI</num>
              .</head>
              <p>
                <s xml:id="echoid-s1110" xml:space="preserve">SED cum ſcire voluerimus pondus alicuius magnitudinis aquæ æqualis alicui
                  <lb/>
                corpori ponderoſo, breuiſſimus modus erit ponderando ipſum corpus tam in ae-
                  <lb/>
                re, quàm in aqua, & quia ſemper leuius erit in aqua, </s>
                <s xml:id="echoid-s1111" xml:space="preserve">tunc differentia ponderum ip-
                  <lb/>
                ſius corporis, erit pondus quæſitum, hoc eſt vnius corporis aquei æqualis magnitu-
                  <lb/>
                dinis magnitudini corporis propoſiti ex
                  <ref id="ref-0014">.7. propoſitione lib. Archimedis de inſi-
                    <lb/>
                  dentibus aquæ</ref>
                . </s>
              </p>
              <p>
                <s xml:id="echoid-s1112" xml:space="preserve">Quare ex præmiſſis quotieſcunque immerſa fuerint in aquam dicti vaſis duo cor
                  <lb/>
                pora æquè ponderantia, ſed diuerſarum ſpecierum, vt dictum eſt, proportio pon-
                  <lb/>
                deris aquæ maioris ad pondus aquæ minoris magnitudinis eadem ſemper erit, quæ
                  <lb/>
                ponderis minoris corporis ad pondus alicuius corporis eidem æqualis, ſpeciei verò
                  <lb/>
                maioris, vel eadem proportio ponderis alicuius corporis æqualis maiori, ſpeciei ve
                  <lb/>
                rò minoris ad pondus ipſius maioris.</s>
              </p>
              <p>
                <s xml:id="echoid-s1113" xml:space="preserve">Vt puta ſit corpus
                  <var>.a.</var>
                argenteum æqualis ponderis corpori
                  <var>.b.</var>
                aurei, & corpus
                  <var>.u.</var>
                  <lb/>
                argenteum æqualis magnitudinis corpori
                  <var>.b.</var>
                aurei, corpus verò
                  <var>.n.</var>
                aureum æqualis
                  <lb/>
                magnitudinis corpori
                  <var>.a.</var>
                argentei, corpus verò
                  <var>.f.</var>
                aqueum æqualis magnitudinis cor- </s>
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