Clavius, Christoph, Geometria practica

Page concordance

< >
Scan Original
201 171
202 172
203 173
204 174
205 175
206 176
207 177
208 178
209 179
210 180
211 181
212 182
213 183
214 184
215 185
216 186
217 187
218 188
219 189
220 190
221 191
222 192
223 193
224 194
225 195
226 196
227 197
228 198
229 199
230 200
< >
page |< < (266) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div766" type="section" level="1" n="263">
          <pb o="266" file="296" n="296" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s12250" xml:space="preserve">
              <emph style="sc">Sit</emph>
            primò parallelo grammum A B C D, per rectam ex puncto E, exteriori
              <lb/>
            ductam ſecundum bifariam. </s>
            <s xml:id="echoid-s12251" xml:space="preserve">Ducta diametro B D, eaque ſecta bifariam in F,
              <lb/>
            ducatur ex E, per F, recta EH, quam dico parallelogrammum
              <lb/>
              <figure xlink:label="fig-296-01" xlink:href="fig-296-01a" number="201">
                <image file="296-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/296-01"/>
              </figure>
            partiri bifariam. </s>
            <s xml:id="echoid-s12252" xml:space="preserve">Nam vt in ſcholio Propoſ. </s>
            <s xml:id="echoid-s12253" xml:space="preserve">34. </s>
            <s xml:id="echoid-s12254" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12255" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12256" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s12257" xml:space="preserve">de-
              <lb/>
            monſtrauimus, recta G H, diuidens diametrum B D, in F, bifa-
              <lb/>
            riam, ſecat parallelo grammum bifariam. </s>
            <s xml:id="echoid-s12258" xml:space="preserve">Idem fiet, ſi recta IK,
              <lb/>
            latera AD, BC, ſecans bifariam, diuidatur bifariam in F, & </s>
            <s xml:id="echoid-s12259" xml:space="preserve">per
              <lb/>
            F, extendatur recta E F, propterea quod I K, diametrum ſecat
              <lb/>
            bifariam, ac proinde per F, punctum medium diametritranſit.
              <lb/>
            </s>
            <s xml:id="echoid-s12260" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-296-01" xlink:href="note-296-01a" xml:space="preserve">29. primi.</note>
            Cum enim anguli IDF, F I D, angulis alternis KBF, FKB, æquales ſint, & </s>
            <s xml:id="echoid-s12261" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-296-02" xlink:href="note-296-02a" xml:space="preserve">26. primi.</note>
            I D, KB, quibus adiacent, æqualia; </s>
            <s xml:id="echoid-s12262" xml:space="preserve"> erunt tam latera D F, quam I
              <unsure/>
            F, K F, inter æqualia.</s>
            <s xml:id="echoid-s12263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12264" xml:space="preserve">
              <emph style="sc">Eodem</emph>
            modo ex puncto interioriL; </s>
            <s xml:id="echoid-s12265" xml:space="preserve">Item ex puncto G, in latere BC, recta
              <lb/>
            ducta LF, vel GF, parallelogrammum bifariam diuidet.</s>
            <s xml:id="echoid-s12266" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div768" type="section" level="1" n="264">
          <head xml:id="echoid-head289" xml:space="preserve">PROBL. 10. PROPOS. 15.</head>
          <p>
            <s xml:id="echoid-s12267" xml:space="preserve">INTER datas duas rectas, duas medias proportionales prope verum
              <lb/>
            inuenire.</s>
            <s xml:id="echoid-s12268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12269" xml:space="preserve">
              <emph style="sc">Exposita</emph>
            Geodæſia noſtra prioribus quinq; </s>
            <s xml:id="echoid-s12270" xml:space="preserve">propoſitionibus huius lib.
              <lb/>
            </s>
            <s xml:id="echoid-s12271" xml:space="preserve">& </s>
            <s xml:id="echoid-s12272" xml:space="preserve">nouem alijs propoſitionibus, ijs demonſtratis, quæ addenda eſſe cenſuimus
              <lb/>
            adidem argumentum ſpectantia: </s>
            <s xml:id="echoid-s12273" xml:space="preserve">agendumiam eſſet de augendis minuendiſq; </s>
            <s xml:id="echoid-s12274" xml:space="preserve">
              <lb/>
            figuris in data proportione, vt in titulo huius lib. </s>
            <s xml:id="echoid-s12275" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12276" xml:space="preserve">propoſuimus. </s>
            <s xml:id="echoid-s12277" xml:space="preserve">Verum quia
              <lb/>
            ſicutid in planis figuris effi ci non poteſt ſine inuentione medię proportionalis
              <lb/>
            inter duasrectas propoſitas, quam inuentionem Euclid. </s>
            <s xml:id="echoid-s12278" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12279" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12280" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12281" xml:space="preserve">13. </s>
            <s xml:id="echoid-s12282" xml:space="preserve">nobis
              <lb/>
            tradidit: </s>
            <s xml:id="echoid-s12283" xml:space="preserve">ita idem abſolui in figuris ſolidis nulla ratione poteſt, niſi inter duas
              <lb/>
            rectas datas duæ mediæ reperiantur proportionales. </s>
            <s xml:id="echoid-s12284" xml:space="preserve">Quo circa prius in hac pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s12285" xml:space="preserve">in medium afferemus, quæ antiqui Geometræ nobis hac de reſcripta relin-
              <lb/>
            querunt. </s>
            <s xml:id="echoid-s12286" xml:space="preserve">Multorum enim ingenia res hęc exercuit, at qu
              <unsure/>
            e torſit, quamuis ne-
              <lb/>
            mo ad hanc vſque diem, verè, ac Geometricè duas medias proportionales inter
              <lb/>
            duas rectas datas inuenerit. </s>
            <s xml:id="echoid-s12287" xml:space="preserve">Prætermi@sis autem modis Eratoſthenis; </s>
            <s xml:id="echoid-s12288" xml:space="preserve">Plato-
              <lb/>
            nis; </s>
            <s xml:id="echoid-s12289" xml:space="preserve">Pappi Alexandrini; </s>
            <s xml:id="echoid-s12290" xml:space="preserve">Spori; </s>
            <s xml:id="echoid-s12291" xml:space="preserve">menechmi tum beneficio Hyperbolę, ac para-
              <lb/>
            bolę, tum ope duarum parabolarum; </s>
            <s xml:id="echoid-s12292" xml:space="preserve">& </s>
            <s xml:id="echoid-s12293" xml:space="preserve">Architæ Tarentini, quamuis acutiſsi-
              <lb/>
            mis ſubtiliſsimiſque: </s>
            <s xml:id="echoid-s12294" xml:space="preserve">ſolum quatu or ab Herone, Apollonio Pergæo, Philone
              <lb/>
            Byſantio, Philoppono, Diocle, & </s>
            <s xml:id="echoid-s12295" xml:space="preserve">Nicomede traditos explicabimus, quos cõ-
              <lb/>
            modiores, facilioreſque, & </s>
            <s xml:id="echoid-s12296" xml:space="preserve">errori minus obnoxiosiudicauimus. </s>
            <s xml:id="echoid-s12297" xml:space="preserve">Qui aliorum
              <lb/>
            rationes deſiderat, legere eas poterit in Commentarijs Euto cij Aſcalonitæ in li-
              <lb/>
            brum 2. </s>
            <s xml:id="echoid-s12298" xml:space="preserve">Archimedis de Sphęra, & </s>
            <s xml:id="echoid-s12299" xml:space="preserve">Cylindro: </s>
            <s xml:id="echoid-s12300" xml:space="preserve">Item in libello Ioannis Verneri
              <lb/>
            Norimbergenſis de ſectionibus Conicis. </s>
            <s xml:id="echoid-s12301" xml:space="preserve">Hinc ita que exor diamur.</s>
            <s xml:id="echoid-s12302" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div769" type="section" level="1" n="265">
          <head xml:id="echoid-head290" xml:space="preserve">MODVS HERONIS IN MECHANICIS
            <lb/>
          introductionibus, & telis fabricandis: qui etiam Apollo-
            <lb/>
          nio Pergæo aſcribitur.</head>
          <p>
            <s xml:id="echoid-s12303" xml:space="preserve">
              <emph style="sc">Sint</emph>
            duæ lineęrectę AB, BC, inter quas oporteat duas medias proportio-
              <lb/>
            nales in quirere. </s>
            <s xml:id="echoid-s12304" xml:space="preserve">Conſtituautur ad angulumrectum B, & </s>
            <s xml:id="echoid-s12305" xml:space="preserve">perficiatur </s>
          </p>
        </div>
      </text>
    </echo>
Impressum