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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          <pb o="307" file="337" n="337" rhead="LIBER SEPTIMVS."/>
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            <s xml:id="echoid-s14449" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            enim ex propoſitione 5. </s>
            <s xml:id="echoid-s14450" xml:space="preserve">habetur, regularium figurarum iſope-
              <lb/>
            rimetrarum eam, quæ plura latera continet, eſſe maiorem: </s>
            <s xml:id="echoid-s14451" xml:space="preserve">Rurſus ex propoſi-
              <lb/>
            tione 12. </s>
            <s xml:id="echoid-s14452" xml:space="preserve">conſtat, inter omnes figuras iſoperimetras æqualia numero latera ha-
              <lb/>
            bentes, eam maximam eſſe, quæ regularis eſt: </s>
            <s xml:id="echoid-s14453" xml:space="preserve">Ex hac denique 13. </s>
            <s xml:id="echoid-s14454" xml:space="preserve">propoſitio-
              <lb/>
            ne perſpicuum eſt, circulum omnium figurarum iſoperimetrarum regularium
              <lb/>
            eſſe maximum: </s>
            <s xml:id="echoid-s14455" xml:space="preserve">Manifeſtè concluditur, circulum abſolutè ac ſimpliciter o-
              <lb/>
            mnium figurarum rectilinearum ſibi iſoperimetrarum maximum eſſe. </s>
            <s xml:id="echoid-s14456" xml:space="preserve">quod eſt
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s14457" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div880" type="section" level="1" n="307">
          <head xml:id="echoid-head334" xml:space="preserve">THEOR. 12. PROPOS. 14.</head>
          <p>
            <s xml:id="echoid-s14458" xml:space="preserve">AREA cuiuslibet pyramidis æqualis eſt ſolido rectangulo contento
              <lb/>
              <note position="right" xlink:label="note-337-01" xlink:href="note-337-01a" xml:space="preserve">Pyramis quæ-
                <lb/>
              lib{et} cui pa-
                <lb/>
              rallelepipedo
                <lb/>
              ſit æqualis.</note>
            ſub perpendiculari à vertice ad baſim protracta, & </s>
            <s xml:id="echoid-s14459" xml:space="preserve">tertia parte baſis.</s>
            <s xml:id="echoid-s14460" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14461" xml:space="preserve">
              <emph style="sc">Sit</emph>
            pyramis, cuius baſis quotcunque laterum ABCDE, & </s>
            <s xml:id="echoid-s14462" xml:space="preserve">vertex F. </s>
            <s xml:id="echoid-s14463" xml:space="preserve">Soli-
              <lb/>
            dum autem rectangulum G N, cuius baſis G H I K, æqualis ſit tertiæ parti baſis
              <lb/>
            A B C D E; </s>
            <s xml:id="echoid-s14464" xml:space="preserve">altitudo verò ſiue perpendicularis
              <lb/>
              <figure xlink:label="fig-337-01" xlink:href="fig-337-01a" number="229">
                <image file="337-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/337-01"/>
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            GL, æqualis altitudini pyramidis, ſiue perpen-
              <lb/>
            diculari à vertice pyramidis ad eius baſim pro-
              <lb/>
            ductæ. </s>
            <s xml:id="echoid-s14465" xml:space="preserve">Dico ſolidum rectangulum GN, æqua-
              <lb/>
            le eſſe, pyramidi A B C D E F. </s>
            <s xml:id="echoid-s14466" xml:space="preserve">Ducantur enim
              <lb/>
            ab omnibus angulis baſis G H I K, ad aliquod
              <lb/>
            punctum baſis oppoſitæ, nimirum ad L, lineæ
              <lb/>
            rectæ, ita vt conſtituatur pyramis G H I K L,
              <lb/>
            eandem habens baſim cum ſolido G N, ean-
              <lb/>
            demque altitudinem & </s>
            <s xml:id="echoid-s14467" xml:space="preserve">cum eodem ſolido
              <lb/>
            G N, & </s>
            <s xml:id="echoid-s14468" xml:space="preserve">cum pyramide A B C D E F. </s>
            <s xml:id="echoid-s14469" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-337-02" xlink:href="note-337-02a" xml:space="preserve">ſchol. 6.
                <lb/>
              duodec.</note>
            niam igitur pyramis A B C D E F, tripla eſt py-
              <lb/>
            ramidis GHIKL; </s>
            <s xml:id="echoid-s14470" xml:space="preserve"> Et ſolidum G N,
              <note symbol="b" position="right" xlink:label="note-337-03" xlink:href="note-337-03a" xml:space="preserve">coroll. 7.
                <lb/>
              duodec.</note>
            quo que eſt eiuſdem pyramidis GHIKL: </s>
            <s xml:id="echoid-s14471" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-337-04" xlink:href="note-337-04a" xml:space="preserve">9. quinti.</note>
            ſolidum G N, pyramidi A B C D E F, æquale.
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            </s>
            <s xml:id="echoid-s14472" xml:space="preserve">Quapropter area cuiuslibet pyramidis æqua-
              <lb/>
            lis eſt ſolido rectangulo, &</s>
            <s xml:id="echoid-s14473" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14474" xml:space="preserve">quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s14475" xml:space="preserve"/>
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          <head xml:id="echoid-head335" xml:space="preserve">THEOR. 13. PROPOS. 15.</head>
          <note position="right" xml:space="preserve">Corp{us} quod-
            <lb/>
          libet, in qua
            <lb/>
          ſphæra deſcri-
            <lb/>
          bipotest, cui
            <lb/>
          parallelepipe-
            <lb/>
          do æquale ſit.</note>
          <p>
            <s xml:id="echoid-s14476" xml:space="preserve">AREA cuiuslibet corporis planis ſuperficiebus contenti, & </s>
            <s xml:id="echoid-s14477" xml:space="preserve">circa
              <lb/>
            ſphæram aliquam circumſcriptibilis, hoc eſt, à cuius puncto aliquo
              <lb/>
            medio omnes perpendiculares ad baſes eius productæ ſunt æquales,
              <lb/>
            æqualis eſt ſolido rectangulo contento ſub vna perpendicularium,
              <lb/>
            & </s>
            <s xml:id="echoid-s14478" xml:space="preserve">tertia parte ambitus corporis.</s>
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