Clavius, Christoph, Geometria practica

Table of contents

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[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)
[321.] I. QVADRA TRICEM lineam deſcribere.
Page: 350 (320)
[322.] COROLLARIVM.
Page: 353 (323)
[323.] II.
Page: 354 (324)
[324.] COROLLARIVM I.
Page: 355 (325)
[325.] COROLLARIVM II.
Page: 356 (326)
[326.] COROLLARIVM III.
Page: 356 (326)
[327.] III.
Page: 357 (327)
[328.] IV.
Page: 359 (329)
[329.] COROLLARIVM.
Page: 359 (329)
[330.] V.
Page: 359 (329)
[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)
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            <image file="346-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/346-01"/>
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        <div xml:id="echoid-div905" type="section" level="1" n="317">
          <head xml:id="echoid-head344" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s14825" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi ſumatur punctum V, vtc
              <unsure/>
            unque inter R, & </s>
            <s xml:id="echoid-s14826" xml:space="preserve">O, erit rectangulum
              <lb/>
            ſub QV, VO, adhuc Iſoperimetrum triangulo ABC, ſed minus. </s>
            <s xml:id="echoid-s14827" xml:space="preserve">Si vero capia-
              <lb/>
            tur punctum X, vtcunque inter R, & </s>
            <s xml:id="echoid-s14828" xml:space="preserve">Y, (diuiſa Q O, bifariam in Y,) erit adhuc
              <lb/>
            rectangulum ſub QX, XO, Iſoperimetrum triangulo A B C, ſed maius. </s>
            <s xml:id="echoid-s14829" xml:space="preserve">Qua-
              <lb/>
            dratum denique rectæ QV, Iſoperimetrum quo que eſt triangulo A B C, & </s>
            <s xml:id="echoid-s14830" xml:space="preserve">ma-
              <lb/>
            ius, quæ omnia ita demonſtrabimus. </s>
            <s xml:id="echoid-s14831" xml:space="preserve">Prædicta rectangula, & </s>
            <s xml:id="echoid-s14832" xml:space="preserve">quadratum rectæ
              <lb/>
            QY, Iſoperimetra eſſe triangulo ABC, hoc eſt, rectangulo QS, patet: </s>
            <s xml:id="echoid-s14833" xml:space="preserve">cum bi-
              <lb/>
            na latera circa angulumrectum æqualia ſemper ſintrectæ QO, hoc eſt, binis la-
              <lb/>
            teribus rectanguli QS. </s>
            <s xml:id="echoid-s14834" xml:space="preserve">Eadem verò eſſe inæ qualia triangulo ABC, ſic oſtendo.
              <lb/>
            </s>
            <s xml:id="echoid-s14835" xml:space="preserve"> Quoniam quadrata QV, VO, maiora ſunt quadratis QR, RO, ſimul: </s>
            <s xml:id="echoid-s14836" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-346-01" xlink:href="note-346-01a" xml:space="preserve">lemma 42.
                <lb/>
              decimi.</note>
            autem tam illa duo, vna cum rectangulo ſub QV, VO, bis, quam hæc duo, vna
              <lb/>
              <note symbol="b" position="left" xlink:label="note-346-02" xlink:href="note-346-02a" xml:space="preserve">4. ſecundi.</note>
            cumrectangulo ſub QR, RO, bis, quadrato QO, æqualia; </s>
            <s xml:id="echoid-s14837" xml:space="preserve">erit rectangulum ſub
              <lb/>
            QV, VO, bis minus rectangulo ſub QR, R O, bis; </s>
            <s xml:id="echoid-s14838" xml:space="preserve">ideo que & </s>
            <s xml:id="echoid-s14839" xml:space="preserve">rectangulum ſub
              <lb/>
            QV, VO, ſemel, rectangulo ſub QR, RO, ſemel minus erit. </s>
            <s xml:id="echoid-s14840" xml:space="preserve">Non aliter oſten-
              <lb/>
            demus, rectangulum ſub QR, R O, minus eſſe rectangulo ſub QX, XO, hoc
              <lb/>
            eſt rectangulum ſub QX, XO, maius eſſe rectangulo ſub QR, R O. </s>
            <s xml:id="echoid-s14841" xml:space="preserve">Denique
              <lb/>
            quoniam rectangulum ſub QX, XO, vna cum quadrato XY, æquale eſt
              <note symbol="c" position="left" xlink:label="note-346-03" xlink:href="note-346-03a" xml:space="preserve">6. ſecundi.</note>
            drato Y O, vel QY; </s>
            <s xml:id="echoid-s14842" xml:space="preserve">erit quadratum QY, maius rectangulo ſub QX, XO, ideo-
              <lb/>
            que multo maius rectangulo ſub QR, R O, id eſt, triangulo A B C. </s>
            <s xml:id="echoid-s14843" xml:space="preserve">quæ omnia
              <lb/>
            demonſtranda erant.</s>
            <s xml:id="echoid-s14844" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14845" xml:space="preserve">EX quo conſtat, quadratum QY, ex ſemiſſæ rectæ QO, deſcriptum maxi-
              <lb/>
            mum eſſe omnium rectangulorum ſub quibuſcunque ſegmentis rectæ QO, cõ-
              <lb/>
            prehenſorum, quod etiam ex propoſ. </s>
            <s xml:id="echoid-s14846" xml:space="preserve">12. </s>
            <s xml:id="echoid-s14847" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14848" xml:space="preserve">liquet.</s>
            <s xml:id="echoid-s14849" xml:space="preserve"/>
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          <head xml:id="echoid-head345" xml:space="preserve">PROBL. 5. PROPOS. 22.</head>
          <note position="left" xml:space="preserve">Rectangulũ
            <lb/>
          datæfiguræ
            <lb/>
          Iſoperimetrũ
            <lb/>
          & æquale cõ-
            <lb/>
          ſtituere.</note>
          <p>
            <s xml:id="echoid-s14850" xml:space="preserve">DATO rectilineo parallelogrammum rectangulum æquale, & </s>
            <s xml:id="echoid-s14851" xml:space="preserve">Iſope-
              <lb/>
            rimetrum conſtituere. </s>
            <s xml:id="echoid-s14852" xml:space="preserve">Oportet autem latus quadrati rectilineo æ-
              <lb/>
            qualis, maius non eſſe ſemiſſe dimidiati ambitus dati rectilinei.</s>
            <s xml:id="echoid-s14853" xml:space="preserve"/>
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