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-div441" type="chapter" level="2" n="5">
            <div xml:id="echoid-div441" type="section" level="3" n="1">
              <div xml:id="echoid-div448" type="section" level="4" n="8">
                <pb o="200" rhead="IO. BAPT. BENED." n="212" file="0212" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0212"/>
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              <div xml:id="echoid-div449" type="section" level="4" n="9">
                <head xml:id="echoid-head336" xml:space="preserve">NONVM.</head>
                <head xml:id="echoid-head337" style="it" xml:space="preserve">Euclidis uero tertiadecima propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2424" xml:space="preserve">
                    <emph style="sc">Qvotiescvnqve</emph>
                  aliqua proportio plurium proportionum inuicem æqua-
                    <lb/>
                  lium, tertia aliqua proportione, maior aut minor fuerit, quælibet prædictarum æqua
                    <lb/>
                  lium inter ſe, tertia illa proportione maior aut minor pariter erit.</s>
                </p>
              </div>
              <div xml:id="echoid-div450" type="section" level="4" n="10">
                <head xml:id="echoid-head338" xml:space="preserve">DECIMVM.</head>
                <p>
                  <s xml:id="echoid-s2425" xml:space="preserve">
                    <emph style="sc">Qvotiescvnqve</emph>
                  fuerint ex vna parte plurestermini (ſiue coniuncti ſiue di-
                    <lb/>
                  ſiuncti ſint) æquales ſinguli vni tertio termino; </s>
                  <s xml:id="echoid-s2426" xml:space="preserve">ex altera verò parte totidem fuerint
                    <lb/>
                  alteri tertio termino æquales, proportio aggregati priorum terminorum ad
                    <reg norm="ſuum" type="context">ſuũ</reg>
                  ter-
                    <lb/>
                  tium, æqualis erit proportioni aggregati reliquorum terminorum ad ſuum tertium,
                    <lb/>
                  & è conuerſo, ita ſe habebit primus tertius terminus ad ſuos multos terminos, ſicut
                    <lb/>
                  ſe habet ſecundus tertius terminus ad ſuos ſimul ſumptos.</s>
                </p>
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              <div xml:id="echoid-div451" type="section" level="4" n="11">
                <head xml:id="echoid-head339" xml:space="preserve">VNDECIMVM.</head>
                <p>
                  <s xml:id="echoid-s2427" xml:space="preserve">Aggregatum ex partibus proportiona litatis continuæ, quod inter maximum, &
                    <lb/>
                  minimum terminum omnium terminorum proportionalium compræhenditur, ſem
                    <lb/>
                  per multiplex eſt ad ſingulas partiales proportiones, ex quibus ipſum componitur.</s>
                </p>
              </div>
              <div xml:id="echoid-div452" type="section" level="4" n="12">
                <head xml:id="echoid-head340" xml:space="preserve">DVODECIMVM.</head>
                <p>
                  <s xml:id="echoid-s2428" xml:space="preserve">Quæuis proportio quocunque modo diuiſa fuerit, ex iis partibus componitur, in
                    <lb/>
                  quas diuiditur.</s>
                </p>
                <p style="it">
                  <s xml:id="echoid-s2429" xml:space="preserve">Cum enim bæ præpoſitiones ſint ita conſpicuæ ipſi intellectui, ut
                    <reg norm="abſque" type="simple">abſq;</reg>
                  dubio inter obie
                    <lb/>
                  ct a ipſius intellectus connumerari poſſint, nullus ſanæ mentis eas negabit.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div454" type="section" level="3" n="2">
              <div xml:id="echoid-div454" type="section" level="4" n="1">
                <head xml:id="echoid-head341" xml:space="preserve">THEOR.I. II. ET III.</head>
                <p>
                  <s xml:id="echoid-s2430" xml:space="preserve">PRimum, ſecundum, & tertium theorema quinti Euclidis ab ipſo ſatis exactè de
                    <lb/>
                  monſtratur, ſtudioſus itaque autorem conſulat.</s>
                </p>
              </div>
              <div xml:id="echoid-div455" type="section" level="4" n="2">
                <head xml:id="echoid-head342" xml:space="preserve">THEOREM. IIII.</head>
                <p>
                  <s xml:id="echoid-s2431" xml:space="preserve">QVartum vero Theorema Eu-
                    <lb/>
                    <figure xlink:label="fig-0212-01" xlink:href="fig-0212-01a" number="262">
                      <image file="0212-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0212-01"/>
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                  clidis ego ſic
                    <reg norm="demonſtrarem" type="context">demonſtrarẽ</reg>
                  .
                    <lb/>
                  </s>
                  <s xml:id="echoid-s2432" xml:space="preserve">ſit, verbi gratia, proportio
                    <var>.a.</var>
                  ad
                    <var>.b.</var>
                    <lb/>
                  quæ eſt
                    <var>.c.</var>
                  ad
                    <var>.d.</var>
                  ſumptis multiplici-
                    <lb/>
                  bus
                    <var>.e.</var>
                  et
                    <var>.f.</var>
                  ad
                    <var>.a.</var>
                  et
                    <var>.c.</var>
                  æqualiter, item
                    <lb/>
                  multiplicibus
                    <var>.g.</var>
                  et
                    <var>.h.</var>
                  ad
                    <var>.b.</var>
                  et
                    <var>.d.</var>
                  dico
                    <lb/>
                  proportionem
                    <var>.e.</var>
                  ad
                    <var>.g.</var>
                  eſſe eandem
                    <lb/>
                  quæ eſt
                    <var>.f.</var>
                  ad
                    <var>.h</var>
                  . </s>
                  <s xml:id="echoid-s2433" xml:space="preserve">Habemus enim ex .10
                    <lb/>
                  poſtulato præmiſſo, eandem futuram
                    <lb/>
                  proportionem
                    <var>.e.</var>
                  ad
                    <var>.a.</var>
                  quæ eſt
                    <var>.f.</var>
                  ad
                    <var>.c.</var>
                    <lb/>
                  & ita
                    <var>.b.</var>
                  ad
                    <var>.g.</var>
                  quæ eſt
                    <var>.d.</var>
                  ad
                    <var>.h.</var>
                  ex præ-
                    <lb/>
                  ſuppoſito verò
                    <reg norm="cum" type="context">cũ</reg>
                  ſic ſe habeat
                    <var>.a.</var>
                  ad
                    <lb/>
                  b. ſicut
                    <var>.c.</var>
                  ad
                    <var>.d.</var>
                  erit ex primo poſtula-
                    <lb/>
                  to
                    <reg norm="eadem" type="context">eadẽ</reg>
                  proportio
                    <var>.e.</var>
                  ad
                    <var>.g.</var>
                  quæ eſt
                    <var>.f.</var>
                    <lb/>
                  ad
                    <var>.h</var>
                  . </s>
                  <s xml:id="echoid-s2434" xml:space="preserve">Nam proportio
                    <var>.e.</var>
                  ad
                    <var>.g.</var>
                  compo
                    <lb/>
                  nitur ex eis quæ ſunt
                    <var>.e.</var>
                  ad .a: et
                    <var>.a.</var>
                  ad
                    <var>. </var>
                  </s>
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