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]

Page concordance

< >
Scan Original
121 109
122 110
123 111
124 112
125 113
126 114
127 115
128 116
129 117
130 118
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
< >
page |< < (203) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div441" type="chapter" level="2" n="5">
            <div xml:id="echoid-div454" type="section" level="3" n="2">
              <div xml:id="echoid-div469" type="section" level="4" n="10">
                <p>
                  <s xml:id="echoid-s2474" xml:space="preserve">
                    <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/>
                    <figure xlink:label="fig-0215-01" xlink:href="fig-0215-01a" number="268">
                      <image file="0215-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0215-01"/>
                    </figure>
                  bebit
                    <var>.a.</var>
                  ad
                    <var>.c</var>
                  , ſicut
                    <var>.b.</var>
                  ad
                    <var>.d</var>
                  . </s>
                  <s xml:id="echoid-s2476" xml:space="preserve">Quare ſic ſe habebit
                    <lb/>
                  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>
                </p>
              </div>
              <div xml:id="echoid-div471" type="section" level="4" n="11">
                <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
                    <reg norm="quod" type="simple">ꝙ</reg>
                  ſi
                    <var>.a.</var>
                  maius fuerit
                    <var>.e.</var>
                  pariter
                    <var>.c.</var>
                  maius
                    <lb/>
                    <figure xlink:label="fig-0215-02" xlink:href="fig-0215-02a" number="269">
                      <image file="0215-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0215-02"/>
                    </figure>
                  erit
                    <var>.f.</var>
                  & 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>
                </p>
              </div>
              <div xml:id="echoid-div473" type="section" level="4" n="12">
                <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-
                    <lb/>
                  ſcripto nunc modo demonſtrari poterit.</s>
                </p>
              </div>
              <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>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum