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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          <head xml:id="echoid-head332" xml:space="preserve">THEOR. 11. PROPOS. 13.</head>
          <p>
            <s xml:id="echoid-s14399" xml:space="preserve">CIRCVLVS omnibus figuris rectilineis regularibus ſibi iſoperime-
              <lb/>
              <note position="left" xlink:label="note-336-01" xlink:href="note-336-01a" xml:space="preserve">Circul{us} o-
                <lb/>
              mnium ſigu-
                <lb/>
              varum recti-
                <lb/>
              linearum re-
                <lb/>
              gularium ſibi
                <lb/>
              iſoperimetra-
                <lb/>
              rum maxi-
                <lb/>
              m{us} est.</note>
            tris maior eſt.</s>
            <s xml:id="echoid-s14400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14401" xml:space="preserve">
              <emph style="sc">Esto</emph>
            circulus ABC, figura autem regularis quotcunque laterum ei iſoperi-
              <lb/>
            metra DEF. </s>
            <s xml:id="echoid-s14402" xml:space="preserve">Dico circulum ABC, eſſe maiorem figura DEF. </s>
            <s xml:id="echoid-s14403" xml:space="preserve">Sit enim G, cen-
              <lb/>
            trum circuli A B C, & </s>
            <s xml:id="echoid-s14404" xml:space="preserve">H, centrum figuræ D E F; </s>
            <s xml:id="echoid-s14405" xml:space="preserve">Deſcribaturque circa circulum
              <lb/>
            ABC, figura BIKC, tot laterum, & </s>
            <s xml:id="echoid-s14406" xml:space="preserve">angulorum æqualium, quot continet figu-
              <lb/>
            ra DEF, per ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s14407" xml:space="preserve">16. </s>
            <s xml:id="echoid-s14408" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14409" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14410" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s14411" xml:space="preserve">docuimus. </s>
            <s xml:id="echoid-s14412" xml:space="preserve">Deinde ex
              <lb/>
              <figure xlink:label="fig-336-01" xlink:href="fig-336-01a" number="228">
                <image file="336-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/336-01"/>
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            puncto contactus A, ad centrum G, ducatur recta A G, quæ
              <note symbol="a" position="left" xlink:label="note-336-02" xlink:href="note-336-02a" xml:space="preserve">18. tertii.</note>
            erit ad IK. </s>
            <s xml:id="echoid-s14413" xml:space="preserve">Ducatur rurſus HD, ad LM, perpendicularis; </s>
            <s xml:id="echoid-s14414" xml:space="preserve"> Diuidentque
              <note symbol="b" position="left" xlink:label="note-336-03" xlink:href="note-336-03a" xml:space="preserve">3. tertii.</note>
            GA, HD, rectas IK, LM, bifariã, vt conſtat, ſi figuris BIKC, DEF, circumſcriban-
              <lb/>
            tur circuli. </s>
            <s xml:id="echoid-s14415" xml:space="preserve">Ducantur quoque rectæ GI, HL, quæ diuident angulos I, & </s>
            <s xml:id="echoid-s14416" xml:space="preserve">L, bi-
              <lb/>
            fariam, vt manifeſtum eſt ex demonſtratione propoſ. </s>
            <s xml:id="echoid-s14417" xml:space="preserve">12. </s>
            <s xml:id="echoid-s14418" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14419" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14420" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s14421" xml:space="preserve">Quo-
              <lb/>
            niam igitur toti anguli I, & </s>
            <s xml:id="echoid-s14422" xml:space="preserve">L, ſunt æquales, propter ſimilitudinem figurarum,
              <lb/>
            erunt etiamip ſorum dimidia (videlicet anguli AIG, DLH,) æqualia. </s>
            <s xml:id="echoid-s14423" xml:space="preserve">Cum er-
              <lb/>
            go & </s>
            <s xml:id="echoid-s14424" xml:space="preserve">anguli I A G, L D H, ſintæ quales, vtpote recti; </s>
            <s xml:id="echoid-s14425" xml:space="preserve"> erunt triangula A I
              <note symbol="c" position="left" xlink:label="note-336-04" xlink:href="note-336-04a" xml:space="preserve">32. primi.</note>
            DLH, æquiangula. </s>
            <s xml:id="echoid-s14426" xml:space="preserve">Quia verò ambitus figuræ B I K C, maior eſt (per 1. </s>
            <s xml:id="echoid-s14427" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s14428" xml:space="preserve">libr. </s>
            <s xml:id="echoid-s14429" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14430" xml:space="preserve">Archimedis de ſphæra, & </s>
            <s xml:id="echoid-s14431" xml:space="preserve">cylindro) ambitu circuli A B C; </s>
            <s xml:id="echoid-s14432" xml:space="preserve">Ambitus au-
              <lb/>
            tem circuli æqualis ponitur ambitui figuræ D E F; </s>
            <s xml:id="echoid-s14433" xml:space="preserve">erit quo que ambitus figuræ
              <lb/>
            BIKC, maior ambitus figuræ DEF. </s>
            <s xml:id="echoid-s14434" xml:space="preserve">Cum igitur figuræ ſint regulares, & </s>
            <s xml:id="echoid-s14435" xml:space="preserve">ſimiles,
              <lb/>
            erit etiam latus IK, latere LM, maius; </s>
            <s xml:id="echoid-s14436" xml:space="preserve">& </s>
            <s xml:id="echoid-s14437" xml:space="preserve">ideò I A, dimidium lateris IK, maius,
              <lb/>
            quam LD, dimidium lateris LM. </s>
            <s xml:id="echoid-s14438" xml:space="preserve"> Rurſus quoniam eſt, vt IA, ad G A, ita L
              <note symbol="d" position="left" xlink:label="note-336-05" xlink:href="note-336-05a" xml:space="preserve">4. ſexti.</note>
            ad D H; </s>
            <s xml:id="echoid-s14439" xml:space="preserve">Et eſt I A, maior quam L D; </s>
            <s xml:id="echoid-s14440" xml:space="preserve"> erit quo que A G, maior, quam D H.</s>
            <s xml:id="echoid-s14441" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-336-06" xlink:href="note-336-06a" xml:space="preserve">14. quinti.</note>
            Quamobrem rectangulum contentum ſub A G, & </s>
            <s xml:id="echoid-s14442" xml:space="preserve">dimidio ambitu circuli
              <lb/>
            ABC, quod circulo ABC, eſt æquale, maius eſt, quam rectangulum
              <note symbol="f" position="left" xlink:label="note-336-07" xlink:href="note-336-07a" xml:space="preserve">4. hui{us}.</note>
            tum ſub DH, & </s>
            <s xml:id="echoid-s14443" xml:space="preserve">dimidio ambitu figuræ DEF, hoc eſt, quam area figuræ DEF.</s>
            <s xml:id="echoid-s14444" xml:space="preserve">
              <note symbol="g" position="left" xlink:label="note-336-08" xlink:href="note-336-08a" xml:space="preserve">2. hui{us}.</note>
            Circulus igitur omnibus figuris rectilineis regularibus ſibi iſoperimetris maior
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s14445" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s14446" xml:space="preserve"/>
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          <head xml:id="echoid-head333" xml:space="preserve">COROLLARIVM.</head>
          <note position="left" xml:space="preserve">Circul{us} o-
            <lb/>
          mnib{us} figu-
            <lb/>
          ris rectilin{eis}
            <lb/>
          ſibi iſoperime-
            <lb/>
          tris maior eſt.</note>
          <p>
            <s xml:id="echoid-s14447" xml:space="preserve">EX omnibus iis, quæ demonſtrata ſunt, perſpicuum eſt, circulum ab-
              <lb/>
            ſolutè omnium figurarum rectilinearum ſibi iſoperimetrarum maxi-
              <lb/>
            mum eſſe.</s>
            <s xml:id="echoid-s14448" xml:space="preserve"/>
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