Clavius, Christoph, Geometria practica

Table of contents

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[291.] THEOR. 1. PROPOS. 1.
Page: 322 (292)
[292.] PROBL. 2. PROPOS. 2.
Page: 323 (293)
[293.] THEOR. 3. PROPOS. 3.
Page: 324 (294)
[294.] THEOR. 4. PROPOS. 4.
Page: 324 (294)
[295.] THEOR. 5. PROPOS. 5.
Page: 325 (295)
[296.] THEOR. 6. PROPOS. 6.
Page: 326 (296)
[297.] PROBL. 1. PROPOS. 7.
Page: 327 (297)
[298.] SCHOLIVM.
Page: 327 (297)
[299.] THEOR. 7. PROPOS. 8.
Page: 327 (297)
[300.] THEOR. 8. PROPOS. 9.
Page: 328 (298)
[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)
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            <s xml:id="echoid-s12115" xml:space="preserve">
              <pb o="263" file="293" n="293" rhead="LIBER SEXTVS."/>
            part
              <unsure/>
            es æquales, detrahenda primum erit per lineam rectam ex dato puncto du-
              <lb/>
            ctam pars denominata à numero partium, in quas diuidendum eſt triangulum.
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            <s xml:id="echoid-s12116" xml:space="preserve">
              <figure xlink:label="fig-293-01" xlink:href="fig-293-01a" number="197">
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            Deinde duæ tales partes: </s>
            <s xml:id="echoid-s12117" xml:space="preserve">poſtea tres, atque ita deinceps, donec tot partes, vna
              <lb/>
            minus, detractæ ſint, in quot partes diuidendum proponitur triangulum. </s>
            <s xml:id="echoid-s12118" xml:space="preserve">Vt ſi
              <lb/>
            triangulum ABC, ex puncto D, diuidendum ſit in quinque partes æquales, diui-
              <lb/>
            demus latus BC, in quo datum punctum eſt, in quinque partes æquales, in pun-
              <lb/>
            ctis E, F, G, H. </s>
            <s xml:id="echoid-s12119" xml:space="preserve">Iuncta deinderecta DA, ducemus ei parallelas EI, FK, GL, HM.
              <lb/>
            </s>
            <s xml:id="echoid-s12120" xml:space="preserve">Sinamque connectantur rectæ D I, D K, D L, D M, diuiſum erit triangulum in
              <lb/>
            quinque partes æquales. </s>
            <s xml:id="echoid-s12121" xml:space="preserve">Nam vt in dicta propoſ. </s>
            <s xml:id="echoid-s12122" xml:space="preserve">14. </s>
            <s xml:id="echoid-s12123" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s12124" xml:space="preserve">33. </s>
            <s xml:id="echoid-s12125" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12126" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12127" xml:space="preserve">
              <lb/>
            Euclid. </s>
            <s xml:id="echoid-s12128" xml:space="preserve">oſtenſum eſt, triangulum DBI, eſt {@/5}. </s>
            <s xml:id="echoid-s12129" xml:space="preserve">totius trianguli, hoc eſt, ita ſe ha-
              <lb/>
            bet DBI, ad ABC, vt BE, ad BC. </s>
            <s xml:id="echoid-s12130" xml:space="preserve">Triangulum autem DBK, continet {2/3}. </s>
            <s xml:id="echoid-s12131" xml:space="preserve">totius
              <lb/>
            trianguli, id eſt, ita ſe habet D B K, ad A B C, vt B F, ad B C. </s>
            <s xml:id="echoid-s12132" xml:space="preserve">At vero triangulum
              <lb/>
            DBL, complectitur {3/5}. </s>
            <s xml:id="echoid-s12133" xml:space="preserve">totius trianguli, id eſt, ita ſe habet DBL, ad ABC, vt BG,
              <lb/>
            ad BC. </s>
            <s xml:id="echoid-s12134" xml:space="preserve">Quadrilaterum denique ABDM, comprehendit {4/5}. </s>
            <s xml:id="echoid-s12135" xml:space="preserve">totius trianguli, hoc
              <lb/>
            eſt, ita ſe habet ABDM, ad ABC, vt B H, ad B C. </s>
            <s xml:id="echoid-s12136" xml:space="preserve">Ex quo fit, reliquum triangu-
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            lum DMC, eſſe {1/5}. </s>
            <s xml:id="echoid-s12137" xml:space="preserve">eiuſdem trianguli ABC.</s>
            <s xml:id="echoid-s12138" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12139" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            punctum datum eſt in vno angulo, manifeſtum eſt, ſi latus op-
              <lb/>
            poſitum in tot partes ſecetur, in quot triangulum diuidendum eſt, rectas
              <note symbol="a" position="right" xlink:label="note-293-01" xlink:href="note-293-01a" xml:space="preserve">1. ſexti.</note>
            eo angulo ad puncta diuiſionum eductas ſecare triangulum in propoſitas par-
              <lb/>
            tes æquales.</s>
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          <head xml:id="echoid-head284" xml:space="preserve">PROBL. 6. PROPOS. 11.</head>
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            <s xml:id="echoid-s12141" xml:space="preserve">DATVM triangulum per lineas vni lateri parallelas in quotlibet æ-
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            quales partes diuidere,</s>
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          <p>
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              <emph style="sc">Sit</emph>
            triangulum A B C, diuidendum verbi gratia in quatuor partes æquales
              <lb/>
            perlineas lateri BC, æquidiſtantes. </s>
            <s xml:id="echoid-s12143" xml:space="preserve">Secetur vtrumuis reliquorum laterum ni-
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                <image file="293-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/293-02"/>
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            mirum A B, in 4. </s>
            <s xml:id="echoid-s12144" xml:space="preserve">partes æquales, in tot videlicet, in quot triangulũ diuidendum
              <lb/>
            eſt, in punctis D, E, F. </s>
            <s xml:id="echoid-s12145" xml:space="preserve">Etinter A B, A D, inuenta media proportionali A E;</s>
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