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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IN QVINT. LIB. EVCLI.
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                    <pb o="203" rhead="IN QVINT. LIB. EVCLI." n="215" file="0215" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0215"/>
                  portio
                    <var>.a.</var>
                  ad
                    <var>.b.</var>
                  quæ eſt
                    <var>.c.</var>
                  ad
                    <var>.d.</var>
                  probabo ita ſe habituram proportionem
                    <var>.b.</var>
                  ad
                    <var>.a.</var>
                  ſicut
                    <lb/>
                  ſe habet
                    <var>.d.</var>
                  ad
                    <var>.c.</var>
                  hoc argumento: </s>
                  <s xml:id="echoid-s2475" xml:space="preserve">ſi
                    <var>.a.</var>
                  ad
                    <var>.b.</var>
                  ita ſe
                    <lb/>
                  habet ſicut
                    <var>.c.</var>
                  ad
                    <var>.d.</var>
                  ex .16. theoremate ita ſe ha
                    <lb/>
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                  bebit
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                  , ſicut
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                  ad
                    <var>.d</var>
                  . </s>
                  <s xml:id="echoid-s2476" xml:space="preserve">Quare ſic ſe habebit
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                  b. ad
                    <var>.d.</var>
                  ſicut
                    <var>.a.</var>
                  ad
                    <var>.c</var>
                  . </s>
                  <s xml:id="echoid-s2477" xml:space="preserve">Itaque ex eodem .16. ita ſe
                    <lb/>
                  ſe habebit
                    <var>.b.</var>
                  ad
                    <var>.a.</var>
                  ſicut
                    <var>.d.</var>
                  ad
                    <var>.c</var>
                  .</s>
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                  <figure xlink:label="fig-0215-01" xlink:href="fig-0215-01a">
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                <head xml:id="echoid-head351" xml:space="preserve">THEOREM. XX.</head>
                <p>
                  <s xml:id="echoid-s2478" xml:space="preserve">QVamuis .20. theorema apud Eucli. perfectè demonſtratum fuerit, poteſt ni-
                    <lb/>
                  hilominus & hac via demonſtrari. </s>
                  <s xml:id="echoid-s2479" xml:space="preserve">Sic ſe habeat proportio
                    <var>.a.</var>
                  ad
                    <var>.b.</var>
                  ſicut ſe
                    <lb/>
                  habet
                    <var>.c.</var>
                  ad
                    <var>.d.</var>
                  & proportio
                    <var>.b.</var>
                  ad
                    <var>.e.</var>
                  ſicut
                    <var>.d.</var>
                  ad
                    <var>.
                      <lb/>
                    f</var>
                  . </s>
                  <s xml:id="echoid-s2480" xml:space="preserve">Dico
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                  ſi
                    <var>.a.</var>
                  maius fuerit
                    <var>.e.</var>
                  pariter
                    <var>.c.</var>
                  maius
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                    <anchor type="figure" xlink:label="fig-0215-02a" xlink:href="fig-0215-02"/>
                  erit
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                  & ſi
                    <var>.a.</var>
                  minus fuerit .e: c.
                    <reg norm="quoque" type="simple">quoq;</reg>
                  minus erit
                    <lb/>
                  f. ſin verò ęquale,
                    <reg norm="ent" type="context">ẽt</reg>
                  æquale erit. </s>
                  <s xml:id="echoid-s2481" xml:space="preserve">Nam ex pri
                    <lb/>
                  mo poſtulato certi ſumus ita ſe habere pro
                    <lb/>
                    <reg norm="portionem" type="context">portionẽ</reg>
                    <var>.a.</var>
                  ad
                    <var>.e.</var>
                  ſicut ſe habet proportio
                    <var>.c.</var>
                  ad
                    <lb/>
                  p. </s>
                  <s xml:id="echoid-s2482" xml:space="preserve">Quare ex .12. theor
                    <reg norm="propoſitum" type="simple context">ꝓpoſitũ</reg>
                    <reg norm="manifeſtum" type="context">manifeſtũ</reg>
                  erit.</s>
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                <head xml:id="echoid-head352" xml:space="preserve">THEOREM. XXI.</head>
                <p>
                  <s xml:id="echoid-s2483" xml:space="preserve">VIgeſimum primum theorema, ſatis apud Eucli. probatum, nihilominus præ-
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                  ſcripto nunc modo demonſtrari poterit.</s>
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              <div xml:id="echoid-div474" type="section" level="4" n="13">
                <head xml:id="echoid-head353" xml:space="preserve">THEOREM. XXII. XXIII.</head>
                <p>
                  <s xml:id="echoid-s2484" xml:space="preserve">DVO hæc theoremata in primum poſtulatum collegimus.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s2485" xml:space="preserve">Sequentia verò cum exactè apud Eucli. demonſtrentur non eſt cur nos in
                    <lb/>
                  ijs immoremur.</s>
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