Clavius, Christoph, Geometria practica

Table of contents

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[281.] PROBL. 17. PROPOS. 22.
Page: 319 (289)
[282.] FINIS LIBRI SEXTI.
Page: 320 (290)
[283.] GEOMETRIÆ PRACTICÆ LIBER SEPTIMVS.
Page: 321 (291)
[284.] De figuris Iſoperimetris diſputans: cui Appendicis loco annectitur breuis de circulo per lineas quadrando tractatiuncula.
Page: 321 (291)
[285.] DEFINITIONES.
Page: 321 (291)
[286.] I.
Page: 321 (291)
[287.] II.
Page: 322 (292)
[288.] III.
Page: 322 (292)
[289.] IIII.
Page: 322 (292)
[290.] V.
Page: 322 (292)
[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)
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          <pb o="260" file="290" n="290" rhead="GEOMETR. PRACT."/>
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        <div xml:id="echoid-div742" type="section" level="1" n="252">
          <head xml:id="echoid-head277" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s11972" xml:space="preserve">
              <emph style="sc">Dividi</emph>
            ergo poterit quælibet figura rectilinea in quotuis partes æquales
              <lb/>
              <note position="left" xlink:label="note-290-01" xlink:href="note-290-01a" xml:space="preserve">Quo pacto fi-
                <lb/>
              gura data ſe-
                <lb/>
              c{et}ur per li-
                <lb/>
              ne{as} parallel{as}
                <lb/>
              in quotuis par
                <lb/>
              t{es} æqual{es}.</note>
            per lineas, quæ datæ cuiuis rectæ lineæ æquidiſtent. </s>
            <s xml:id="echoid-s11973" xml:space="preserve">Nam ſi verbi gratia data fi-
              <lb/>
            gura ſecanda ſit in 8. </s>
            <s xml:id="echoid-s11974" xml:space="preserve">partes æquales per lineas datæ rectæ parallelas, diuidemus
              <lb/>
            eam primum in duas partes inter ſe proportionem habentes 1. </s>
            <s xml:id="echoid-s11975" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s11976" xml:space="preserve">Ita namque
              <lb/>
            prior pars erit {1/8}. </s>
            <s xml:id="echoid-s11977" xml:space="preserve">totius figuræ. </s>
            <s xml:id="echoid-s11978" xml:space="preserve">Deinde poſteriorem partem ſecabimus in pro-
              <lb/>
            portionem 1. </s>
            <s xml:id="echoid-s11979" xml:space="preserve">ad 6. </s>
            <s xml:id="echoid-s11980" xml:space="preserve">ita vt prior pars huius diuiſionis ſit {1/7}. </s>
            <s xml:id="echoid-s11981" xml:space="preserve">illius partis diuiſæ, hoc
              <lb/>
            eſt, {1/7}. </s>
            <s xml:id="echoid-s11982" xml:space="preserve">totius figuræ, cum pars illa diuiſa complectatur {7/8}. </s>
            <s xml:id="echoid-s11983" xml:space="preserve">totius figuræ. </s>
            <s xml:id="echoid-s11984" xml:space="preserve">Poſtea
              <lb/>
            partem poſt eriorem proximæ diuiſionis partiemur in proportionem 1. </s>
            <s xml:id="echoid-s11985" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s11986" xml:space="preserve">Et
              <lb/>
            poſteriorem huius diuiſionis partem in proportionem 1. </s>
            <s xml:id="echoid-s11987" xml:space="preserve">ad 4. </s>
            <s xml:id="echoid-s11988" xml:space="preserve">Atqueita dein-
              <lb/>
            ceps, minuendo ſemper, don@c ad partem deueniamus, quæ ſecanda ſit in pro-
              <lb/>
            portionem 1. </s>
            <s xml:id="echoid-s11989" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s11990" xml:space="preserve">hoc eſt, in partes æquales.</s>
            <s xml:id="echoid-s11991" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11992" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            idem effici poterit ea ratione, quam ad finem ſcholij propoſ. </s>
            <s xml:id="echoid-s11993" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11994" xml:space="preserve">expo-
              <lb/>
            ſuimus: </s>
            <s xml:id="echoid-s11995" xml:space="preserve">ſi videlicetlatus quadrati H I, quod rectilineo dato conſtructum eſt
              <lb/>
            æquale, in tot æquales partes ſecetur, in quot partes datum rectilineum diuiden-
              <lb/>
            dum eſt, & </s>
            <s xml:id="echoid-s11996" xml:space="preserve">primo rectilineum diuidatur in proportionem primæ partis ad reli-
              <lb/>
            quas: </s>
            <s xml:id="echoid-s11997" xml:space="preserve">Deinde poſterior pars rectilinei in proportionem ſecundæ partis lateris
              <lb/>
            H I, ad reliquas: </s>
            <s xml:id="echoid-s11998" xml:space="preserve">at que ita deinceps, &</s>
            <s xml:id="echoid-s11999" xml:space="preserve">c.</s>
            <s xml:id="echoid-s12000" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12001" xml:space="preserve">
              <emph style="sc">Atqve</emph>
            hic finem habet noſtra Geodæſia complectens diuiſionem omnium
              <lb/>
            figurarum rectilinearum: </s>
            <s xml:id="echoid-s12002" xml:space="preserve">ſequuntur iam particulares nonnullæ diuiſiones qua-
              <lb/>
            rundam figurarum, quæ tum, quia ſubtiles acutaſque demonſtrationes conti-
              <lb/>
            nent, tum quia pleraſque earum eruditi quo que Geometræ, vt Leonardus Pi-
              <lb/>
            ſanus, Frater Lucas Pacciolus, & </s>
            <s xml:id="echoid-s12003" xml:space="preserve">Nicolaus Tartalea tradiderunt, omittendæ
              <lb/>
            nullo modo viſæ ſunt: </s>
            <s xml:id="echoid-s12004" xml:space="preserve">Vt autem Geometricè eas demonſtremus, præmittenda
              <lb/>
            ſunt Theoremata nonnulla, quorum primum ſit hoc.</s>
            <s xml:id="echoid-s12005" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div744" type="section" level="1" n="253">
          <head xml:id="echoid-head278" xml:space="preserve">THEOREMA 2. PROPOS. 6.</head>
          <p>
            <s xml:id="echoid-s12006" xml:space="preserve">SI duo triangula æqualia habeant vnum latus commune, & </s>
            <s xml:id="echoid-s12007" xml:space="preserve">in diuerſas
              <lb/>
            partes vergant: </s>
            <s xml:id="echoid-s12008" xml:space="preserve">Recta oppoſitos angulos connectens à latere illo
              <lb/>
            communi bifariam ſecatur.</s>
            <s xml:id="echoid-s12009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12010" xml:space="preserve">
              <emph style="sc">Sint</emph>
            æqualia duo triangula A B C, A B D, habentia latus A B, commune, & </s>
            <s xml:id="echoid-s12011" xml:space="preserve">in
              <lb/>
            diuerſas partes vergentia. </s>
            <s xml:id="echoid-s12012" xml:space="preserve">Dico rectam C D, oppoſitos angulos C, D, iungentem
              <lb/>
            ſecari in E, bifariam à latere com̃uni A B. </s>
            <s xml:id="echoid-s12013" xml:space="preserve"> Quoniã enim eſt tá
              <unsure/>
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                <image file="290-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/290-01"/>
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              <note symbol="a" position="left" xlink:label="note-290-02" xlink:href="note-290-02a" xml:space="preserve">1. ſexti.</note>
            triangulum A C E, ad triangulum A D E, quàm triangulum B C E,
              <lb/>
            ad triangulum B D E, vt C E, ad E D; </s>
            <s xml:id="echoid-s12014" xml:space="preserve"> erit triangulum A C E,
              <note symbol="b" position="left" xlink:label="note-290-03" xlink:href="note-290-03a" xml:space="preserve">11. quinti.</note>
            triangulum A D E, vt triangulum B C E, ad triangulum B D E.
              <lb/>
            </s>
            <s xml:id="echoid-s12015" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-290-04" xlink:href="note-290-04a" xml:space="preserve">12. quinti.</note>
            Igitur erunt quo que duo triangula ſimul A C E, B C E, hoc eſt, totum triangulum A B C, ad duo triangula ſimul A D E, B D E, id
              <lb/>
            eſt, ad totum triangulum A B D, vt A C E, ad A D E, hoc eſt, vt
              <lb/>
            C E, ad E D. </s>
            <s xml:id="echoid-s12016" xml:space="preserve">Cum ergo triangula A B C, A B D, ponantur æqualia; </s>
            <s xml:id="echoid-s12017" xml:space="preserve">erunt quo-
              <lb/>
            que rectæ C E, E D, æquales, ac proinde C D, in E, ſecta eſt bifariam. </s>
            <s xml:id="echoid-s12018" xml:space="preserve">quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s12019" xml:space="preserve"/>
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