Clavius, Christoph, Geometria practica

Table of contents

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[301.] PROBL. 2. PROPOS. 10.
Page: 329 (299)
[302.] THEOR. 9. PROPOS. 11.
Page: 330 (300)
[303.] THEOR. 10. PROPOS. 12.
Page: 333 (303)
[304.] SCHOLIVM.
Page: 334 (304)
[305.] THEOR. 11. PROPOS. 13.
Page: 336 (306)
[306.] COROLLARIVM.
Page: 336 (306)
[307.] THEOR. 12. PROPOS. 14.
Page: 337 (307)
[308.] THEOR. 13. PROPOS. 15.
Page: 337 (307)
[309.] THEOR. 14. PROPOS. 16.
Page: 338 (308)
[310.] THEOR. 15. PROPOS. 17.
Page: 340 (310)
[311.] COROLLARIVM.
Page: 341 (311)
[312.] THEOR. 16. PROPOS. 18.
Page: 341 (311)
[313.] THEOR. 17. PROPOS. 19.
Page: 343 (313)
[314.] SCHOLIVM.
Page: 343 (313)
[315.] PROBL. 3. PROPOS. 20.
Page: 343 (313)
[316.] PROBL. 4. PROPOS. 21.
Page: 344 (314)
[317.] SCHOLIVM.
Page: 346 (316)
[318.] PROBL. 5. PROPOS. 22.
Page: 346 (316)
[319.] SCHOLIVM.
Page: 347 (317)
[320.] APPENDIX.
Page: 347 (317)
[321.] I. QVADRA TRICEM lineam deſcribere.
Page: 350 (320)
[322.] COROLLARIVM.
Page: 353 (323)
[323.] II.
Page: 354 (324)
[324.] COROLLARIVM I.
Page: 355 (325)
[325.] COROLLARIVM II.
Page: 356 (326)
[326.] COROLLARIVM III.
Page: 356 (326)
[327.] III.
Page: 357 (327)
[328.] IV.
Page: 359 (329)
[329.] COROLLARIVM.
Page: 359 (329)
[330.] V.
Page: 359 (329)
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          <p>
            <s xml:id="echoid-s12519" xml:space="preserve">
              <pb o="272" file="302" n="302" rhead="GEOMETR. PRACT."/>
            extendatur ſecans DC, productamin L. </s>
            <s xml:id="echoid-s12520" xml:space="preserve">Dico duas AK, CL, medias propor-
              <lb/>
            tionales eſſe inter AB, BC. </s>
            <s xml:id="echoid-s12521" xml:space="preserve"> Quoniam
              <note symbol="a" position="left" xlink:label="note-302-01" xlink:href="note-302-01a" xml:space="preserve">2. ſexti.</note>
            eſt LC, ad CD, vt LB, ad BK, hoc eſt, vt DA,
              <lb/>
            ad AK; </s>
            <s xml:id="echoid-s12522" xml:space="preserve">Et vt CD, ad C E, ita eſt GA, ad DA,
              <lb/>
            quod vtraque CD, GA, ſecta ſit bifariam in
              <lb/>
            E, D: </s>
            <s xml:id="echoid-s12523" xml:space="preserve">erit ex proportione perturbata LC, ad
              <lb/>
              <figure xlink:label="fig-302-01" xlink:href="fig-302-01a" number="206">
                <image file="302-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/302-01"/>
              </figure>
            CE, vt GA ad AK, vt in hac formula apparet:
              <lb/>
            </s>
            <s xml:id="echoid-s12524" xml:space="preserve">hoc eſt, vt HI, ad IK. </s>
            <s xml:id="echoid-s12525" xml:space="preserve">Cum ergo C E, ipſi I K, ſit æqualis per conſtructionem,
              <lb/>
              <note symbol="b" position="left" xlink:label="note-302-02" xlink:href="note-302-02a" xml:space="preserve">14. quinti.</note>
            erit quoque LC, ipſi HI, æqualis, & </s>
            <s xml:id="echoid-s12526" xml:space="preserve">tota LE, toti HK. </s>
            <s xml:id="echoid-s12527" xml:space="preserve"> Deinde quia
              <note symbol="c" position="left" xlink:label="note-302-03" xlink:href="note-302-03a" xml:space="preserve">6. ſecundi.</note>
            gulum ſub DK, KA, vna cum quadrato ex AF, æquale eſt quadrato FK; </s>
            <s xml:id="echoid-s12528" xml:space="preserve">addi-
              <lb/>
            to communi quadrato ex FH, eritrectangulum ſub DK, KA, vnà cum quadra-
              <lb/>
              <note symbol="d" position="left" xlink:label="note-302-04" xlink:href="note-302-04a" xml:space="preserve">47. primi.</note>
            tis ex AF, FH, hoc eſt, vna cum quadrato ex AH, vel ex CE, æquale
              <note symbol="e" position="left" xlink:label="note-302-05" xlink:href="note-302-05a" xml:space="preserve">6. ſecundi.</note>
            ex KF, FH, hoc eſt, quadrato ex HK, id eſt, ex LE, ipſi HK, æquali. </s>
            <s xml:id="echoid-s12529" xml:space="preserve"> Sed & </s>
            <s xml:id="echoid-s12530" xml:space="preserve">rectã- gulum ſub DL, LC, vna cum eodem quadrato ex CE, æquale quoq; </s>
            <s xml:id="echoid-s12531" xml:space="preserve">eſt eidem
              <lb/>
            quadrato ex LE. </s>
            <s xml:id="echoid-s12532" xml:space="preserve">Igitur rectangulum ſub D K, A K, vna cum quadrato ex C E,
              <lb/>
            æquale erit rectangulo ſub DL, LC, vna cum eodem quadrato ex CE; </s>
            <s xml:id="echoid-s12533" xml:space="preserve">Et dem-
              <lb/>
            pto communi quadrato C E, reliquum rectangulum ſub D L, L C, reliquo re-
              <lb/>
            ctangulo ſub DK, A K, æquale erit. </s>
            <s xml:id="echoid-s12534" xml:space="preserve"> Igitur erit D L, ad D K, hoc eſt, AB,
              <note symbol="f" position="left" xlink:label="note-302-06" xlink:href="note-302-06a" xml:space="preserve">16. ſexti.</note>
            AK, vt AK, ad LC. </s>
            <s xml:id="echoid-s12535" xml:space="preserve"> Vtautem AB, ad A K, ita eſt quo que LC, ad CB. </s>
            <s xml:id="echoid-s12536" xml:space="preserve">
              <note symbol="g" position="left" xlink:label="note-302-07" xlink:href="note-302-07a" xml:space="preserve">4. ſexti.</note>
            erit AB, ad AK, vt AK, ad LC, & </s>
            <s xml:id="echoid-s12537" xml:space="preserve">vt LC, ad CB: </s>
            <s xml:id="echoid-s12538" xml:space="preserve">ac proinde AK, LC, medię pro-
              <lb/>
              <note symbol="h" position="left" xlink:label="note-302-08" xlink:href="note-302-08a" xml:space="preserve">4. ſexti.</note>
            portionales erunt inter datas AB, BC, quod eſt propoſitum.</s>
            <s xml:id="echoid-s12539" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12540" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi datę duę rectæ ſint nimis longę, accipi poterunt earum ſemiſſes,
              <lb/>
            vel tertię partes, &</s>
            <s xml:id="echoid-s12541" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12542" xml:space="preserve">atque inter eas duę medię inquirendę. </s>
            <s xml:id="echoid-s12543" xml:space="preserve">Nam ſi inuentę du-
              <lb/>
            plicentur, veltriplicentur, &</s>
            <s xml:id="echoid-s12544" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12545" xml:space="preserve">habebuntur duę medię inter datas duas. </s>
            <s xml:id="echoid-s12546" xml:space="preserve">Quod
              <lb/>
            etiam in aliis modis intelligendum eſt.</s>
            <s xml:id="echoid-s12547" xml:space="preserve"/>
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        <div xml:id="echoid-div783" type="section" level="1" n="269">
          <head xml:id="echoid-head294" xml:space="preserve">PROBL. 11. PROPOS. 16.</head>
          <p>
            <s xml:id="echoid-s12548" xml:space="preserve">DATAM figuram planam, vel circulum augere, vel minuere in data
              <lb/>
            proportione.</s>
            <s xml:id="echoid-s12549" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12550" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            problema, quod ad figuras planas rectilineas attinet, explicauimus
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s12551" xml:space="preserve">15. </s>
            <s xml:id="echoid-s12552" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s12553" xml:space="preserve">33. </s>
            <s xml:id="echoid-s12554" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12555" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12556" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s12557" xml:space="preserve">Nuncidem ad circulos quoque ex-
              <lb/>
            tendemus. </s>
            <s xml:id="echoid-s12558" xml:space="preserve">Sit ergo rectilineum, cuius latus A B, vel circulus, cuius diameter
              <lb/>
            AB, oporteatque conſtituere maius rectilineum, vel circulum maiorem in pro-
              <lb/>
            portione, C, ad D, nimirum ſub tripla. </s>
            <s xml:id="echoid-s12559" xml:space="preserve">Tribus lineis C, D, AB, inueniatur </s>
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