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-div387" type="chapter" level="2" n="4">
            <div xml:id="echoid-div439" type="section" level="3" n="39">
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          <div xml:id="echoid-div441" type="chapter" level="2" n="5">
            <head xml:id="echoid-head321" xml:space="preserve">IN QVINTVM
              <lb/>
            EVCLIDIS LIBRVM</head>
            <p type="title" style="it">
              <s xml:id="echoid-s2404" xml:space="preserve">QVamuis omnia libri quinti Euclid. uerißima ſint.
                <lb/>
              </s>
              <s xml:id="echoid-s2405" xml:space="preserve">Animaduertimus tamen permultos ſumma
                <reg norm="cum" type="context">cũ</reg>
                <lb/>
              difficultate
                <reg norm="eorum" type="context">eorũ</reg>
              demonstr ationes percipere. </s>
              <s xml:id="echoid-s2406" xml:space="preserve">Prœ
                <unsure/>
              -
                <lb/>
              cipuè ubi quint a, aut ſeptima deffinitiones eiuſ-
                <lb/>
              dem libri neceſſariœ
                <unsure/>
              ſunt. </s>
              <s xml:id="echoid-s2407" xml:space="preserve">Illœ enim adeo obſcurœ
                <lb/>
              uidentur, ut longè facilius admißuri ſint hœc no-
                <lb/>
              ſtra poſtulat at anquam clarior a. </s>
              <s xml:id="echoid-s2408" xml:space="preserve">At que etiam tanquam intellectui
                <lb/>
              commodiora, quam ſit illud quintum
                <reg norm="idemque" type="simple">idemq́ꝫ</reg>
              ultimum postulatum
                <lb/>
              eiuſdem in primo libro poſitum, de line a duas alias ſecante. </s>
              <s xml:id="echoid-s2409" xml:space="preserve">Quan-
                <lb/>
              doquidem
                <reg norm="ijs" type="lig">ijs</reg>
              noſtris postulatis admißis, ſequentia Theoremata per
                <lb/>
              facillima reddentur.</s>
            </p>
            <div xml:id="echoid-div441" type="section" level="3" n="1">
              <div xml:id="echoid-div441" type="section" level="4" n="1">
                <head xml:id="echoid-head322" style="it" xml:space="preserve">Horum autem primum est.</head>
                <p>
                  <s xml:id="echoid-s2410" xml:space="preserve">
                    <emph style="sc">Qvod</emph>
                  tota compoſita ex æquali numero partium æqualium, ſunt inuicem
                    <lb/>
                  æqualia.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2411" xml:space="preserve">Vtſi quis diceret omnes proportiones quæ
                    <reg norm="compoſitæ" type="context">cõpoſitæ</reg>
                  ſunt ex æquali numero alia-
                    <lb/>
                  rum proportionum inuicem æqualium, ſunt etiam inuicem æquales, quod Eucli-
                    <lb/>
                  des conatur demonſtrare in .22. et .23. quinti libri.</s>
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              <div xml:id="echoid-div442" type="section" level="4" n="2">
                <head xml:id="echoid-head323" xml:space="preserve">SECVNDVM.</head>
                <p>
                  <s xml:id="echoid-s2412" xml:space="preserve">
                    <emph style="sc">Qvod</emph>
                  ſi à totis æqualibus detractæ fuerint æquales partes, quæ remanent erunt
                    <lb/>
                  partes inuicem æquales.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2413" xml:space="preserve">Et è conuerſo ſi æqualibus æqualia addas compoſita erunt inuicem æqualia.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2414" xml:space="preserve">Quod in ipſis proportionibus hoc loco ſemper intelligendum eſt.</s>
                </p>
              </div>
              <div xml:id="echoid-div443" type="section" level="4" n="3">
                <head xml:id="echoid-head324" xml:space="preserve">TERTIVM.</head>
                <head xml:id="echoid-head325" style="it" xml:space="preserve">Quę est εuclidis ſeptima propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2415" xml:space="preserve">
                    <emph style="sc">Qvod</emph>
                  ſi fuerint plures termini æquales inuicem, ratio ſeu proportio vnius ip-
                    <lb/>
                  ſorum ad alium tertium terminum maiorem, minoremúe, ſed eiuſdem generis, erit
                    <lb/>
                  cadem quæ cuiuſuis alterius termini ad eundem tertium. </s>
                  <s xml:id="echoid-s2416" xml:space="preserve">Et è conuerſo, quæ fuerit
                    <lb/>
                  proportio tertij termini ad vnum prædictorum æqualium, eadem erit, ſpecie, cum
                    <lb/>
                  alio eorundem terminorum.</s>
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