Clavius, Christoph, Geometria practica

List of thumbnails

< >
391
391 (363) 		392
392 (364)
393
393 (365) 		394
394 (366)
395
395 (367) 		396
396 (368)
397
397 (369) 		398
398 (370)
399
399 (371) 		400
400 (372)
< >
page |< < (366) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1061" type="section" level="1" n="380">
          <p>
            <s xml:id="echoid-s17263" xml:space="preserve">
              <pb o="366" file="394" n="394" rhead="GEOMETR. PRACT."/>
              <figure xlink:label="fig-394-01" xlink:href="fig-394-01a" number="287">
                <image file="394-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/394-01"/>
              </figure>
            rectæ A B, ex lateribus æqualibus quadrati ABCD,
              <lb/>
            ipſæ inter ſe æquales erunt; </s>
            <s xml:id="echoid-s17264" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s17265" xml:space="preserve">& </s>
            <s xml:id="echoid-s17266" xml:space="preserve">earũ, quadra-
              <lb/>
            ta erunt æqualia.</s>
            <s xml:id="echoid-s17267" xml:space="preserve"> Cũ ergo quadratũ ex KH,
              <note symbol="a" position="left" xlink:label="note-394-01" xlink:href="note-394-01a" xml:space="preserve">47. primi.</note>
            ſit quadratis ex AH, AK, ipſum duplũ erit tã qua-
              <lb/>
            drati ex AH, ꝗ̃ quadrati ex AK. </s>
            <s xml:id="echoid-s17268" xml:space="preserve">Quia verò A B, dia-
              <lb/>
            meter eſt quadratiex AE, deſcripti, abſciſſaq; </s>
            <s xml:id="echoid-s17269" xml:space="preserve">eſt re-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-394-02" xlink:href="note-394-02a" xml:space="preserve">32. hui{us}.</note>
            cta BK, lateri AE, æqualis; </s>
            <s xml:id="echoid-s17270" xml:space="preserve"> erit reliqua AK, lat
              <emph style="sub">9</emph>
            qua- drati, cuius diameter GK, quæ relin quitur poſt de-
              <lb/>
            tractionem ipſius A K, bis ex diametro A B, vel ex
              <lb/>
            latere A G, ſemel. </s>
            <s xml:id="echoid-s17271" xml:space="preserve"> Igitur & </s>
            <s xml:id="echoid-s17272" xml:space="preserve">quadratum ex G K, duplum erit quadrati ex K A: </s>
            <s xml:id="echoid-s17273" xml:space="preserve">ac proinde quadrata
              <lb/>
              <note symbol="c" position="left" xlink:label="note-394-03" xlink:href="note-394-03a" xml:space="preserve">ſchol. 47.
                <lb/>
              primi.</note>
            ex K H, K G, æqualia inter ſe erunt; </s>
            <s xml:id="echoid-s17274" xml:space="preserve">ideo que & </s>
            <s xml:id="echoid-s17275" xml:space="preserve">re-
              <lb/>
            ctæ KH, KG, æquales erunt. </s>
            <s xml:id="echoid-s17276" xml:space="preserve">Eadem ratione oſten-
              <lb/>
            demus, eandem GK, æqualem eſſe rectæ G M; </s>
            <s xml:id="echoid-s17277" xml:space="preserve">& </s>
            <s xml:id="echoid-s17278" xml:space="preserve">G M, æqualem rectæ M L, & </s>
            <s xml:id="echoid-s17279" xml:space="preserve">
              <lb/>
              <note symbol="d" position="left" xlink:label="note-394-04" xlink:href="note-394-04a" xml:space="preserve">13 primi.</note>
            ſic de cæteris. </s>
            <s xml:id="echoid-s17280" xml:space="preserve">Æquilaterum ergo eſt octogonum. </s>
            <s xml:id="echoid-s17281" xml:space="preserve"> Quoniam autem
              <note symbol="e" position="left" xlink:label="note-394-05" xlink:href="note-394-05a" xml:space="preserve">4. primi.</note>
            anguliad H, K, G, M, L, I, N, F, æquales ſunt duobus rectis; </s>
            <s xml:id="echoid-s17282" xml:space="preserve"> ſuntque
              <note symbol="f" position="left" xlink:label="note-394-06" xlink:href="note-394-06a" xml:space="preserve">ſchol. 34.
                <lb/>
              primi.</note>
            cuti verſus angulos quadrati omnes inter ſe æquales: </s>
            <s xml:id="echoid-s17283" xml:space="preserve"> immo ſemirecti, quod KH, GM, &</s>
            <s xml:id="echoid-s17284" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17285" xml:space="preserve">ſint diametri quadratorum exlateribus AH, GB, &</s>
            <s xml:id="echoid-s17286" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17287" xml:space="preserve">deſcripto-
              <lb/>
            rum: </s>
            <s xml:id="echoid-s17288" xml:space="preserve">Erunt reliqui anguli obtuſi in octogono æquales; </s>
            <s xml:id="echoid-s17289" xml:space="preserve">ideoque octogonum
              <lb/>
            æquiangulum etiam eſt. </s>
            <s xml:id="echoid-s17290" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17291" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1063" type="section" level="1" n="381">
          <head xml:id="echoid-head408" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s17292" xml:space="preserve">
              <emph style="sc">Hæc</emph>
            praxis, quam antè aliquot annos à quo dam Architecto ſine demon-
              <lb/>
            ſtrationetamen accepi, pulcherrima eſt: </s>
            <s xml:id="echoid-s17293" xml:space="preserve">quippe quæ non requirat diuiſionem
              <lb/>
            circuli in octo partes æquales, & </s>
            <s xml:id="echoid-s17294" xml:space="preserve">deſcribat octogonum ad datam altitudinem,
              <lb/>
            latitudinemuè, vt patet. </s>
            <s xml:id="echoid-s17295" xml:space="preserve">Quam praxem vt demonſtrarem, oportuit prius de-
              <lb/>
            monſtrare præcedens theorema. </s>
            <s xml:id="echoid-s17296" xml:space="preserve">Ex eo enim facile problema propoſitum con-
              <lb/>
            ficitur, vt patuit.</s>
            <s xml:id="echoid-s17297" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1064" type="section" level="1" n="382">
          <head xml:id="echoid-head409" xml:space="preserve">PROBL. 20. PROPOS. 34.</head>
          <p>
            <s xml:id="echoid-s17298" xml:space="preserve">AMBITVM terræ ex edito aliquo monte metiri.</s>
            <s xml:id="echoid-s17299" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17300" xml:space="preserve">
              <emph style="sc">Circa</emph>
            finem cap. </s>
            <s xml:id="echoid-s17301" xml:space="preserve">1. </s>
            <s xml:id="echoid-s17302" xml:space="preserve">ſphęræ Ioan. </s>
            <s xml:id="echoid-s17303" xml:space="preserve">de Sacro boſco propoſui rationem, qua
              <lb/>
            Franciſcus Maurolycus ambitum terræ ex edito aliquo monte inueſtigare do-
              <lb/>
            cuit, quæ talis eſt. </s>
            <s xml:id="echoid-s17304" xml:space="preserve">Sit circulus terræ B C D, in quo eligatur editiſsimus aliquis
              <lb/>
            mons, (ipſe in Sicilia montem Ætnam ad hoc negotium cenſuit eligendum)
              <lb/>
            cuius altitudo AB, inquiratur vel per Quadrantem, vt lib. </s>
            <s xml:id="echoid-s17305" xml:space="preserve">2. </s>
            <s xml:id="echoid-s17306" xml:space="preserve">problem. </s>
            <s xml:id="echoid-s17307" xml:space="preserve">2. </s>
            <s xml:id="echoid-s17308" xml:space="preserve">3. </s>
            <s xml:id="echoid-s17309" xml:space="preserve">& </s>
            <s xml:id="echoid-s17310" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s17311" xml:space="preserve">
              <figure xlink:label="fig-394-02" xlink:href="fig-394-02a" number="288">
                <image file="394-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/394-02"/>
              </figure>
            docuimus, vel per Quadratum Geometricum, vt lib. </s>
            <s xml:id="echoid-s17312" xml:space="preserve">3. </s>
            <s xml:id="echoid-s17313" xml:space="preserve">pro-
              <lb/>
            blem. </s>
            <s xml:id="echoid-s17314" xml:space="preserve">6. </s>
            <s xml:id="echoid-s17315" xml:space="preserve">7. </s>
            <s xml:id="echoid-s17316" xml:space="preserve">8. </s>
            <s xml:id="echoid-s17317" xml:space="preserve">& </s>
            <s xml:id="echoid-s17318" xml:space="preserve">9. </s>
            <s xml:id="echoid-s17319" xml:space="preserve">vel potius vt in ſcholio problem. </s>
            <s xml:id="echoid-s17320" xml:space="preserve">7. </s>
            <s xml:id="echoid-s17321" xml:space="preserve">ac 9.
              <lb/>
            </s>
            <s xml:id="echoid-s17322" xml:space="preserve">tradidimus. </s>
            <s xml:id="echoid-s17323" xml:space="preserve">Deinde ex A, vertice montis menſuretur totum
              <lb/>
            illud ſpacium pelagi, ſeu terrę, (vbi tamen montes nonſint)
              <lb/>
            quod inde conſpicitur, ita vt radius AC, maris vel terræ ſu-
              <lb/>
            perficiẽ contingat in C. </s>
            <s xml:id="echoid-s17324" xml:space="preserve">Hoc autẽ fiet per ea, quæ in proble-
              <lb/>
            matib. </s>
            <s xml:id="echoid-s17325" xml:space="preserve">citatis tradita ſunt. </s>
            <s xml:id="echoid-s17326" xml:space="preserve">Ex his poſtea explorat magnitudi-
              <lb/>
            nẽ lineæ tangẽtis A C, ꝓ pterea ꝙ ei
              <emph style="sub">9</emph>
            quadrato æqualia
              <note symbol="g" position="left" xlink:label="note-394-07" xlink:href="note-394-07a" xml:space="preserve">47. primi.</note>
            quadrata AB, BC, (ſumpto ſpacio BC, ꝓ linea recta)
              <note symbol="h" position="left" xlink:label="note-394-08" xlink:href="note-394-08a" xml:space="preserve">36. tertij.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum