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-div443" type="section" level="4" n="3">
                <pb o="199" rhead="IN QVINT. LIB. EVCLI." n="211" file="0211" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0211"/>
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              <div xml:id="echoid-div444" type="section" level="4" n="4">
                <head xml:id="echoid-head326" xml:space="preserve">QVARTVM.</head>
                <head xml:id="echoid-head327" style="it" xml:space="preserve">εuclidis uerò nona propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2417" xml:space="preserve">
                    <emph style="sc">Qvotiescvnqve</emph>
                  proportio vnius plurium terminorum collatorum cum ali
                    <lb/>
                  quo tertio eiuſdem generis, eadem fuerit cum ea quæ eſt cuiuſuis alterius dictorum
                    <lb/>
                  terminorum cum eodem tertio, aut proportio dicti tertij, cum aliquo dictorum, ea-
                    <lb/>
                  dem fuerit cum ea quæ ipſius eſt ad aliquem alium eorundem
                    <reg norm="terminorum" type="context">terminorũ</reg>
                  , tunc eiuſ-
                    <lb/>
                  modi termini, æquales erunt inter ſe.</s>
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              <div xml:id="echoid-div445" type="section" level="4" n="5">
                <head xml:id="echoid-head328" xml:space="preserve">QVINTVM.</head>
                <head xml:id="echoid-head329" style="it" xml:space="preserve">Euclidis uerò octaua propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2418" xml:space="preserve">
                    <emph style="sc">Qvoties</emph>
                  plures erunt termini, quorum vnus fuerit maior altero, ſi compa-
                    <lb/>
                  rentur alicui tertio eiuſdem generis, proportio maioris adtertium illum, maior erit
                    <lb/>
                  ea, quæ eſt minoris ad prædictum tertium, & proportio illius tertij ad maiorem, mi-
                    <lb/>
                  nor erit ea quæ eiuſdem tertij ad minorem terminum comparati.</s>
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              <div xml:id="echoid-div446" type="section" level="4" n="6">
                <head xml:id="echoid-head330" xml:space="preserve">SEXTVM.</head>
                <head xml:id="echoid-head331" style="it" xml:space="preserve">εuclidis uerò decima propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2419" xml:space="preserve">
                    <emph style="sc">Qvoties</emph>
                  proportio vnius, ex pluribus terminis comparatis ad aliquem ter-
                    <lb/>
                  tium, maior fuerit proportione alicuius alterius dictorum cum eodem tertio, primus
                    <lb/>
                  ille terminus, altero maior erit. </s>
                  <s xml:id="echoid-s2420" xml:space="preserve">Et quoties proportio tertij termini ad vnum
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  ad alterum terminum maior fuerit, eiuſmodi terminus altero minor erit.</s>
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              <div xml:id="echoid-div447" type="section" level="4" n="7">
                <head xml:id="echoid-head332" xml:space="preserve">SEPTIMVM.</head>
                <head xml:id="echoid-head333" style="it" xml:space="preserve">Euclidis uerò undecima propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2421" xml:space="preserve">
                    <emph style="sc">Proportiones</emph>
                  , quarum vnaquęque cum aliqua tertia æqualis eſt, ipſæ quo-
                    <lb/>
                  que inter ſe ſunt æquales. </s>
                  <s xml:id="echoid-s2422" xml:space="preserve">Vtillud, Quæ vni & eidem ſunt æqualia, ſibi inuicem
                    <lb/>
                  ſunt æqualia.</s>
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              <div xml:id="echoid-div448" type="section" level="4" n="8">
                <head xml:id="echoid-head334" xml:space="preserve">OCTAVVM.</head>
                <head xml:id="echoid-head335" style="it" xml:space="preserve">εuclidis uerò duodecima propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2423" xml:space="preserve">
                    <emph style="sc">Qvotiescvnqve</emph>
                  proportio vnius ex pluribus antecedentibus cum ſuo ex
                    <lb/>
                  pluribus conſequentibus, æqualis fuerit ei cuiuſuis alterius dictorum
                    <reg norm="antecedentium" type="context">antecedentiũ</reg>
                  ,
                    <lb/>
                  cum ſuo plurium
                    <reg norm="conſequentium" type="context">cõſequentium</reg>
                  , proportio totius aggregati antecedentium cum to-
                    <lb/>
                  to aggregato conſequentium, dictæ primę proportioni ęqualis erit, nempe illius an
                    <lb/>
                  tecedentis ad ſuum conſequens.</s>
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