Clavius, Christoph, Geometria practica

Table of contents

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[331.] FINIS LIBRI SEPTIMI.
Page: 359 (329)
[332.] GEOMETRIÆ PRACTICÆ LIBER OCTAVVS.
Page: 360 (330)
[333.] Varia Theoremata, ac problemata Geometrica demonſtrans.
Page: 360 (330)
[334.] THEOR. 1. PROPOS. 1.
Page: 360 (330)
[335.] SCHOLIVM.
Page: 361 (331)
[336.] LEMMA I.
Page: 361 (331)
[337.] LEMMA II.
Page: 362 (332)
[338.] EEMMA III.
Page: 362 (332)
[339.] THEOR. 2. PROPOS. 2.
Page: 364 (334)
[340.] SCHOLIVM.
Page: 365 (335)
[341.] THEOR. 3. PROPOS. 3.
Page: 365 (335)
[342.] COROLLARIVM.
Page: 366 (336)
[343.] PROBL. 1. PROPOS. 4.
Page: 366 (336)
[344.] PROBL. 2. PROPOS. 5.
Page: 367 (339)
[345.] ALITER.
Page: 367 (339)
[346.] PROBL. 3. PROPOS. 6.
Page: 367 (339)
[347.] THEOR. 4. PROPOS. 7.
Page: 368 (340)
[348.] SCHOLIVM.
Page: 368 (340)
[349.] PROBL. 4. PROPOS. 8.
Page: 369 (341)
[350.] PROBL. 5. PROPOS. 9.
Page: 370 (342)
[351.] THEOR. 5. PROPOS. 10.
Page: 371 (343)
[352.] THEOR. 6. PROPOS. 11.
Page: 371 (343)
[353.] COROLLARIVM.
Page: 372 (344)
[354.] THEOR. 7. PROPOS. 12.
Page: 372 (344)
[355.] PROBL. 6. PROPOS. 13.
Page: 372 (344)
[356.] PROBL. 7. PROPOS. 14.
Page: 373 (345)
[357.] THEOR. 8. PROPOS. 15.
Page: 376 (348)
[358.] PROBL. 8. PROPOS. 16.
Page: 377 (349)
[359.] COROLLARIVM.
Page: 378 (350)
[360.] SCHOLIVM.
Page: 379 (351)
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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"/>
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          <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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