Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

Page concordance

< >
Scan Original
151 139
152 140
153 141
154 142
155 143
156 144
157 145
158 146
159 147
160 148
161 149
162 150
163 151
164 152
165 153
166 154
167 155
168 156
169 157
170 158
171 159
172 160
173 161
174 162
175 163
176 164
177 165
178 166
179 167
180 168
< >
page |< < (323) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div852" type="section" level="1" n="465">
          <p style="it">
            <s xml:id="echoid-s10269" xml:space="preserve">
              <pb o="323" file="335" n="335" rhead=""/>
            tertio lateri adiuncta offeret alteram rectam inter perpendicularem, & </s>
            <s xml:id="echoid-s10270" xml:space="preserve">
              <lb/>
            angulum acutum.</s>
            <s xml:id="echoid-s10271" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10272" xml:space="preserve">SI ergo ab vno angulo trianguli cuiuſuis notorum laterum, &</s>
            <s xml:id="echoid-s10273" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10274" xml:space="preserve">Quod fa-
              <lb/>
            ciendum erat.</s>
            <s xml:id="echoid-s10275" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div858" type="section" level="1" n="466">
          <head xml:id="echoid-head498" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s10276" xml:space="preserve">_
              <emph style="sc">VIDe</emph>
            S_ igitur, in vtraque praxi calculum ipſum monſtrare, num perpendicula
              <lb/>
            ris intra triangulum cadat, an vero extra.</s>
            <s xml:id="echoid-s10277" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10278" xml:space="preserve">_
              <emph style="sc">IDEm</emph>
            _ hoc problema abſolui poteſt per propoſ. </s>
            <s xml:id="echoid-s10279" xml:space="preserve">_13._ </s>
            <s xml:id="echoid-s10280" xml:space="preserve">aut _12._ </s>
            <s xml:id="echoid-s10281" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10282" xml:space="preserve">_2._ </s>
            <s xml:id="echoid-s10283" xml:space="preserve">
              <emph style="sc">E</emph>
            ucl. </s>
            <s xml:id="echoid-s10284" xml:space="preserve">prout per@
              <lb/>
            pendicularis intra triangulum cadit, vel extra. </s>
            <s xml:id="echoid-s10285" xml:space="preserve">Cadat enim primũ perpendicularis
              <lb/>
            _AD,_ intra, ſintq́; </s>
            <s xml:id="echoid-s10286" xml:space="preserve">latera, vt prius; </s>
            <s xml:id="echoid-s10287" xml:space="preserve">_
              <emph style="sc">Ab</emph>
            , 13. </s>
            <s xml:id="echoid-s10288" xml:space="preserve">AC, 20 BC._ </s>
            <s xml:id="echoid-s10289" xml:space="preserve">_21._ </s>
            <s xml:id="echoid-s10290" xml:space="preserve">_
              <emph style="sc">E</emph>
            _ritq; </s>
            <s xml:id="echoid-s10291" xml:space="preserve">vterq; </s>
            <s xml:id="echoid-s10292" xml:space="preserve">angulus _B, C,_
              <lb/>
            acutus, propter rectos angulos ad _D._ </s>
            <s xml:id="echoid-s10293" xml:space="preserve">cũ tam duo anguli _B,_ & </s>
            <s xml:id="echoid-s10294" xml:space="preserve">ADB, quàm duo _C,_ & </s>
            <s xml:id="echoid-s10295" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-335-01" xlink:href="note-335-01a" xml:space="preserve">17. primi.</note>
            _
              <emph style="sc">A</emph>
            DC,_ ſint duobus rectis minores. </s>
            <s xml:id="echoid-s10296" xml:space="preserve">Quoniam igitur quadratũ ex _AC,_ minus eſt, quàm
              <lb/>
            duo quadrata ex _AB,
              <emph style="sc">B</emph>
            C,_ rectangulo bis cõprehenſo ſub _
              <emph style="sc">Cb, b</emph>
            D;_ </s>
            <s xml:id="echoid-s10297" xml:space="preserve">ſi quadratũ lateris
              <lb/>
              <note position="right" xlink:label="note-335-02" xlink:href="note-335-02a" xml:space="preserve">13. ſecundi.</note>
            _AC,_ nempe 400. </s>
            <s xml:id="echoid-s10298" xml:space="preserve">auferatur ex ſumma quadratorum laterum _AB,
              <emph style="sc">B</emph>
            C,_ nimirum ex
              <lb/>
            _610._ </s>
            <s xml:id="echoid-s10299" xml:space="preserve">reliquum erit rectangulũ ſub _
              <emph style="sc">Cb</emph>
            , BD,_ bis com-
              <lb/>
              <figure xlink:label="fig-335-01" xlink:href="fig-335-01a" number="180">
                <image file="335-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/335-01"/>
              </figure>
            prehẽſum _210._ </s>
            <s xml:id="echoid-s10300" xml:space="preserve">Semiſsis ergo huius, vtpote _105._ </s>
            <s xml:id="echoid-s10301" xml:space="preserve">erit re-
              <lb/>
            ctangulum ſub _
              <emph style="sc">Cb, b</emph>
            D,_ comprehenſum: </s>
            <s xml:id="echoid-s10302" xml:space="preserve">quo diuiſ@
              <lb/>
            per latus _BC,_ hoc eſt, per _21._ </s>
            <s xml:id="echoid-s10303" xml:space="preserve">exibit ſegmentum _
              <emph style="sc">B</emph>
            D,_
              <lb/>
            _5._ </s>
            <s xml:id="echoid-s10304" xml:space="preserve">Reliquum ergo _CD,_ erit _16._ </s>
            <s xml:id="echoid-s10305" xml:space="preserve">Quod tamen eodem mo
              <lb/>
            do reperirs poteſt, ſi quadratum lateris _AB,_ ex qua-
              <lb/>
            dratis laterum _AC,
              <emph style="sc">C</emph>
            B,_ ſubducatur, &</s>
            <s xml:id="echoid-s10306" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10307" xml:space="preserve">_
              <emph style="sc">E</emph>
            _ſt enim
              <lb/>
              <note position="right" xlink:label="note-335-03" xlink:href="note-335-03a" xml:space="preserve">13. ſecundi.</note>
            & </s>
            <s xml:id="echoid-s10308" xml:space="preserve">illud minus, quàm hæc duo, rectangulo ſub _
              <emph style="sc">Bc</emph>
            ,_
              <lb/>
            _
              <emph style="sc">C</emph>
            D,_ bis comprehenſo.</s>
            <s xml:id="echoid-s10309" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10310" xml:space="preserve">_
              <emph style="sc">CA</emph>
            DAT_ deinde perpendicularis _AD,_ extra, ſintq́;
              <lb/>
            </s>
            <s xml:id="echoid-s10311" xml:space="preserve">latera, vt prius; </s>
            <s xml:id="echoid-s10312" xml:space="preserve">_AB, 13. </s>
            <s xml:id="echoid-s10313" xml:space="preserve">
              <emph style="sc">Ac</emph>
            , 20. </s>
            <s xml:id="echoid-s10314" xml:space="preserve">
              <emph style="sc">Bc</emph>
            , 11._ </s>
            <s xml:id="echoid-s10315" xml:space="preserve">_E_ritq́; </s>
            <s xml:id="echoid-s10316" xml:space="preserve">
              <lb/>
            angulus _
              <emph style="sc">A</emph>
              <emph style="sc">Bc</emph>
            ,_ obtuſus: </s>
            <s xml:id="echoid-s10317" xml:space="preserve">propterea quod duo _D,_ & </s>
            <s xml:id="echoid-s10318" xml:space="preserve">
              <lb/>
            _ABD,_ ſunt duobus rectis minores; </s>
            <s xml:id="echoid-s10319" xml:space="preserve">ac proinde _
              <emph style="sc">AB</emph>
            D,_
              <lb/>
              <note position="right" xlink:label="note-335-04" xlink:href="note-335-04a" xml:space="preserve">17. primi</note>
            acutus, cum _D,_ rectus ſit. </s>
            <s xml:id="echoid-s10320" xml:space="preserve">Quia ergo quadratum ex
              <lb/>
            _
              <emph style="sc">AC</emph>
            ,_ maius eſt, quàm duo quadrataex _
              <emph style="sc">A</emph>
            B,
              <emph style="sc">BC</emph>
            ,_ re-
              <lb/>
              <note position="right" xlink:label="note-335-05" xlink:href="note-335-05a" xml:space="preserve">12. ſecundi.</note>
            ctangulo bis comprehenſo ſub _
              <emph style="sc">C</emph>
            B, BD;_ </s>
            <s xml:id="echoid-s10321" xml:space="preserve">ſi ſumma quadratorum laterum _
              <emph style="sc">Ab, bc</emph>
            ,_
              <lb/>
            id eſt, _290._ </s>
            <s xml:id="echoid-s10322" xml:space="preserve">auferatur ex _400._ </s>
            <s xml:id="echoid-s10323" xml:space="preserve">quadrato lateris _
              <emph style="sc">Ac</emph>
            ,_ relinquetur rectangulum bis
              <lb/>
            comprehenſum ſub _
              <emph style="sc">CB, B</emph>
            D, 110._ </s>
            <s xml:id="echoid-s10324" xml:space="preserve">Semiſsis ergo huius, nimirum _55._ </s>
            <s xml:id="echoid-s10325" xml:space="preserve">erit rectangulum
              <lb/>
            ſub _
              <emph style="sc">CB, B</emph>
            D,_ contentum: </s>
            <s xml:id="echoid-s10326" xml:space="preserve">quo diuiſo per 11. </s>
            <s xml:id="echoid-s10327" xml:space="preserve">latus _
              <emph style="sc">BC</emph>
            ,_ prodibit recta _
              <emph style="sc">B</emph>
            D,_ extra
              <lb/>
            triangulum, _5._ </s>
            <s xml:id="echoid-s10328" xml:space="preserve">quæcum _11._ </s>
            <s xml:id="echoid-s10329" xml:space="preserve">latere _
              <emph style="sc">BC</emph>
            ,_ componet rectam _
              <emph style="sc">C</emph>
            D, 16._</s>
            <s xml:id="echoid-s10330" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10331" xml:space="preserve">ITAQVE, cadente perpendiculari intra triangulum; </s>
            <s xml:id="echoid-s10332" xml:space="preserve">Siſemiſſis
              <lb/>
              <note position="right" xlink:label="note-335-06" xlink:href="note-335-06a" xml:space="preserve">Praxis.</note>
            differentiæinter quadratum vtriusuis laterum ambientium angulum, à
              <lb/>
            quo perpendicularis demiſſa eſt, & </s>
            <s xml:id="echoid-s10333" xml:space="preserve">ſummam quadratorum ex reliquis
              <lb/>
            duobus lateribus deſcriptorum, diuidatur per latus, in quod perpendicu-
              <lb/>
            laris cadit, producetur ſegmentum baſis prope angulum, quem continent
              <lb/>
            latera, quorum ſumma quadratorum accepta fuit: </s>
            <s xml:id="echoid-s10334" xml:space="preserve">Hoc autem ſegmentum
              <lb/>
            ex eadem-baſe det ractum relinquet alterum ſegmentum.</s>
            <s xml:id="echoid-s10335" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10336" xml:space="preserve">CADENTE ver o perpendiculari extra triangulum; </s>
            <s xml:id="echoid-s10337" xml:space="preserve">Si ſe miſſis
              <lb/>
            diffcrentiæinter quadratum lateris angulo obtuſo oppoſiti, & </s>
            <s xml:id="echoid-s10338" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum