Clavius, Christoph, Geometria practica

Table of contents

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[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)
[361.] PROBL. 9. PROPOS. 17.
Page: 379 (351)
[362.] PROBL. 10. PROPOS. 18.
Page: 379 (351)
[363.] PROBL. 11. PROPOS. 19.
Page: 380 (352)
[364.] PROBL. 12. PROPOS. 20.
Page: 381 (353)
[365.] THEOR. 9. ROPOS. 21.
Page: 381 (353)
[366.] PROBL. 13. PROPOS. 22.
Page: 382 (354)
[367.] PROBL. 14. PROPOS. 23.
Page: 383 (355)
[368.] PROBL. 15. PROPOS. 24.
Page: 383 (355)
[369.] PROBL. 16. PROPOS. 25.
Page: 384 (356)
[370.] PROBL. 17. PROPOS. 26.
Page: 385 (357)
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          <p>
            <s xml:id="echoid-s14724" xml:space="preserve">
              <pb o="314" file="344" n="344" rhead="GEOMETR. PRACT."/>
            męſextæ, &</s>
            <s xml:id="echoid-s14725" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14726" xml:space="preserve">rectangulum conſtituere Iſoperimetrum & </s>
            <s xml:id="echoid-s14727" xml:space="preserve">æquale; </s>
            <s xml:id="echoid-s14728" xml:space="preserve">ſi li-
              <lb/>
              <note position="left" xlink:label="note-344-01" xlink:href="note-344-01a" xml:space="preserve">Semicirculo
                <lb/>
              & aliis parti-
                <lb/>
              b{us} ſubduplis
                <lb/>
              circuli æqua-
                <lb/>
              lia rectangu-
                <lb/>
              la & Iſoperi-
                <lb/>
              metra conſti-
                <lb/>
              tuere.</note>
            nea recta periphæriæ detur æqualis.</s>
            <s xml:id="echoid-s14729" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14730" xml:space="preserve">
              <emph style="sc">Sit</emph>
            ſemicirculus A B C: </s>
            <s xml:id="echoid-s14731" xml:space="preserve">Quadrans A B D, octaua pars circuli A N D, pars
              <lb/>
            ſextadecima AOD, &</s>
            <s xml:id="echoid-s14732" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14733" xml:space="preserve">conſtruatur rectangulum AE, contentum ſub ſemidia-
              <lb/>
            metro A D, & </s>
            <s xml:id="echoid-s14734" xml:space="preserve">ſub recta A F, quæ quartæ parti peripheriæ æqualis ſit; </s>
            <s xml:id="echoid-s14735" xml:space="preserve">Item re-
              <lb/>
            ctangulum A G, ſub ſemidiametro AD, & </s>
            <s xml:id="echoid-s14736" xml:space="preserve">ſub AH, octaua parte peripheriæ. </s>
            <s xml:id="echoid-s14737" xml:space="preserve">Itẽ
              <lb/>
            rectangulum A I, ſub ſemidiametro AD, & </s>
            <s xml:id="echoid-s14738" xml:space="preserve">ſub AK,
              <lb/>
              <figure xlink:label="fig-344-01" xlink:href="fig-344-01a" number="236">
                <image file="344-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/344-01"/>
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            parte decimaſexta peripherię. </s>
            <s xml:id="echoid-s14739" xml:space="preserve">Item rectangulum AL,
              <lb/>
            ſub ſemidiametro AD, & </s>
            <s xml:id="echoid-s14740" xml:space="preserve">ſub AM, parte trigeſima ſe-
              <lb/>
            cunda peripheriæ. </s>
            <s xml:id="echoid-s14741" xml:space="preserve">Erit igitur ex ijs, quę lib. </s>
            <s xml:id="echoid-s14742" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14743" xml:space="preserve">cap.
              <lb/>
            </s>
            <s xml:id="echoid-s14744" xml:space="preserve">7. </s>
            <s xml:id="echoid-s14745" xml:space="preserve">ad finem Num. </s>
            <s xml:id="echoid-s14746" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14747" xml:space="preserve">oſtendimus, AE, ſemicir culo ABC; </s>
            <s xml:id="echoid-s14748" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s14749" xml:space="preserve">AG. </s>
            <s xml:id="echoid-s14750" xml:space="preserve">Quadranti ABD; </s>
            <s xml:id="echoid-s14751" xml:space="preserve">& </s>
            <s xml:id="echoid-s14752" xml:space="preserve">AI, octauę parti AND: </s>
            <s xml:id="echoid-s14753" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s14754" xml:space="preserve">AL, parti ſextæ decimæ A O D, æquale, &</s>
            <s xml:id="echoid-s14755" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14756" xml:space="preserve">Dico
              <lb/>
            hæc eadem rectangula eſſe Iſoperimetra prædictis cir-
              <lb/>
            culi partibus, ſingula ſingulis. </s>
            <s xml:id="echoid-s14757" xml:space="preserve">quod quidem perſpi-
              <lb/>
            cuum eſt ex conſtructione. </s>
            <s xml:id="echoid-s14758" xml:space="preserve">Nam AD, EF, æqualia
              <lb/>
            ſunt diametro AC, & </s>
            <s xml:id="echoid-s14759" xml:space="preserve">AF, DE, ſemicircumferentiæ A-
              <lb/>
            BC, nimirum duabus quartis partibus circumferentiæ. </s>
            <s xml:id="echoid-s14760" xml:space="preserve">Item AD, GH, æqualia
              <lb/>
            ſunt ſemidiametris A D, D B, & </s>
            <s xml:id="echoid-s14761" xml:space="preserve">A H, D G, duabus partibus octauis, hoc eſt,
              <lb/>
            quartæ parti cir cumferentiæ AB. </s>
            <s xml:id="echoid-s14762" xml:space="preserve">Item AD, IK, duabus ſemidiametris AD, DN,
              <lb/>
            & </s>
            <s xml:id="echoid-s14763" xml:space="preserve">AK, DI, duabus ſextis decimis, id eſt, octauæ parti circumferentiæ AN. </s>
            <s xml:id="echoid-s14764" xml:space="preserve">Item
              <lb/>
            AD, LM, duabus ſemidiametris AD, DO, & </s>
            <s xml:id="echoid-s14765" xml:space="preserve">AM, DL, duabus partibus trigeſi-
              <lb/>
            mis ſecundis, hoc eſt, parti decimæſextæ AO; </s>
            <s xml:id="echoid-s14766" xml:space="preserve">Atque ita deinceps, ſi tam peri-
              <lb/>
            pheria AO, quam recta AM, continue ſubdiuidatur. </s>
            <s xml:id="echoid-s14767" xml:space="preserve">Dato ergo ſemicirculo,
              <lb/>
            vel Quadranti, &</s>
            <s xml:id="echoid-s14768" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14769" xml:space="preserve">rectangulum Iſoperimetrum, & </s>
            <s xml:id="echoid-s14770" xml:space="preserve">æquale conſtituimus. </s>
            <s xml:id="echoid-s14771" xml:space="preserve">quod
              <lb/>
            faciendum erat.</s>
            <s xml:id="echoid-s14772" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s14773" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            problema, quod ad ſemicirculum, ac Quadrantem attinet, aduertit
              <lb/>
            etiam nuper R. </s>
            <s xml:id="echoid-s14774" xml:space="preserve">P. </s>
            <s xml:id="echoid-s14775" xml:space="preserve">Odo Malcotius Mathematicus ingenioſus, cum problema
              <lb/>
            Mathematicum per ſuos auditores exhiberet in Collegio Romano: </s>
            <s xml:id="echoid-s14776" xml:space="preserve">quamuis
              <lb/>
            illud inſtar Theorematis propoſuerit.</s>
            <s xml:id="echoid-s14777" xml:space="preserve"/>
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          <head xml:id="echoid-head343" xml:space="preserve">PROBL. 4. PROPOS. 21.</head>
          <note position="left" xml:space="preserve">Parallelogrã-
            <lb/>
          mum dato
            <lb/>
          triangulo æ-
            <lb/>
          quale & Iſo-
            <lb/>
          perimetrum
            <lb/>
          conſtituere.</note>
          <p>
            <s xml:id="echoid-s14778" xml:space="preserve">DATO triangulo cuicunque parallelogrammum æquale, atque Iſo-
              <lb/>
            perimetrum conſtituere.</s>
            <s xml:id="echoid-s14779" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14780" xml:space="preserve">
              <emph style="sc">Sit</emph>
            datum triangulum qualecunque ABC. </s>
            <s xml:id="echoid-s14781" xml:space="preserve">Per A, ducatur AM, baſi B C,
              <lb/>
            parallela. </s>
            <s xml:id="echoid-s14782" xml:space="preserve">Et quia, ſi neuter angulorum B, C, rectus eſt, vtrumquelatus AB, @ maius eſt perpendiculariex A, vel B, C, D, in oppoſitam parallelam demiſ-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-344-03" xlink:href="note-344-03a" xml:space="preserve">coroll. 19.
                <lb/>
              primi.</note>
            ſa: </s>
            <s xml:id="echoid-s14783" xml:space="preserve">ſi verò alter angulorumrectus eſt, hoc eſt, alterutrum laterum perpendicu-
              <lb/>
            lare eſt ad dictas parallelas; </s>
            <s xml:id="echoid-s14784" xml:space="preserve">vtrumque latus AB, AC, ſimulmaius eſt, quam du-
              <lb/>
            plum prædictæ perpendicularis; </s>
            <s xml:id="echoid-s14785" xml:space="preserve">ideo que ſemiſsis aggregati ex vtro que latere
              <lb/>
            maior perpendiculari eadem; </s>
            <s xml:id="echoid-s14786" xml:space="preserve">id eſt, ſi accipiatur GH, lateri AB, & </s>
            <s xml:id="echoid-s14787" xml:space="preserve">HI, lateri AC,
              <lb/>
            ęqualis, vttota GI, ſummæ laterum AB, AC, æqualis ſit, diuidatur que GI, bifa-
              <lb/>
            riam in K, ſemiſsis GK, maior erit perpendiculari DE. </s>
            <s xml:id="echoid-s14788" xml:space="preserve">Si igitur ex D, medio </s>
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