Clavius, Christoph, Geometria practica

Table of contents

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[241.] GEOMETRIÆ PRACTICÆ LIBER SEXTVS.
Page: 266 (236)
[242.] THOREMA 1. PROPOSITIO 1.
Page: 267 (237)
[243.] PROBLEMA 1. PROPOSITIO 2.
Page: 269 (239)
[244.] PROBL. 2. PROPOS. 3.
Page: 276 (246)
[245.] ALITER.
Page: 276 (246)
[246.] ALITER.
Page: 277 (247)
[247.] PROBL. 3. PROPOS. 4.
Page: 278 (248)
[248.] SCHOLIVM.
Page: 282 (252)
[249.] PROBLEMA 4. PROPOSITIO 5.
Page: 283 (253)
[250.] ALITER.
Page: 284 (254)
[251.] ALITER.
Page: 286 (256)
[252.] SCHOLIVM.
Page: 290 (260)
[253.] THEOREMA 2. PROPOS. 6.
Page: 290 (260)
[254.] THEOR. 3. PROPOS. 7.
Page: 291 (261)
[255.] THEOR. 4. PROPOS. 8.
Page: 291 (261)
[256.] COROLLARIVM.
Page: 292 (262)
[257.] THEOR. 5. PROPOS. 9.
Page: 292 (262)
[258.] PROBL. 5. PROPOS. 10.
Page: 292 (262)
[259.] PROBL. 6. PROPOS. 11.
Page: 293 (263)
[260.] PROBL. 7. PROPOS. 12.
Page: 294 (264)
[261.] PROBL. 8. PROPOS. 13.
Page: 295 (265)
[262.] COROLLARIVM.
Page: 295 (265)
[263.] PROBL. 9. PROPOS. 14.
Page: 295 (265)
[264.] PROBL. 10. PROPOS. 15.
Page: 296 (266)
[265.] MODVS HERONIS IN MECHANICIS introductionibus, & telis fabricandis: qui etiam Apollo-nio Pergæo aſcribitur.
Page: 296 (266)
[266.] MODVS PHILONIS BYSANTII, qui Philoppono quoque tribuitur.
Page: 297 (267)
[267.] MODIS DIOCLIS IN LIBRO DE Piriis pulcherrimus.
Page: 298 (268)
[268.] MODVS NICOMEDIS IN libro de lineis Conchoidibus.
Page: 300 (270)
[269.] PROBL. 11. PROPOS. 16.
Page: 302 (272)
[270.] PROBL. 12. PROPOS. 17.
Page: 303 (273)
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            <s xml:id="echoid-s9943" xml:space="preserve">
              <pb o="221" file="251" n="251" rhead="LIBER QVINTVS."/>
            Contineatur autem quarta pars rectanguli G I, tam ſub {1/4}. </s>
            <s xml:id="echoid-s9944" xml:space="preserve">diametri F I, & </s>
            <s xml:id="echoid-s9945" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-251-01" xlink:href="note-251-01a" xml:space="preserve">1. ſexti.</note>
            cumferentia F G, quam ſub {1/4}. </s>
            <s xml:id="echoid-s9946" xml:space="preserve">circumferentiæ F G, & </s>
            <s xml:id="echoid-s9947" xml:space="preserve">diametro F I; </s>
            <s xml:id="echoid-s9948" xml:space="preserve">liquido con-
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            ſtat, quod proponitur.</s>
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        <div xml:id="echoid-div613" type="section" level="1" n="216">
          <head xml:id="echoid-head233" xml:space="preserve">PROPOSITIO IV.</head>
          <p>
            <s xml:id="echoid-s9950" xml:space="preserve">QVADRATVM circumferentiæ circuli maximi in ſphæra ad ſuper-
              <lb/>
            ficiem ſphæræ conuexam, maiorem proportionem habet, quam 223.
              <lb/>
            </s>
            <s xml:id="echoid-s9951" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s9952" xml:space="preserve">minorem verò, quam 22. </s>
            <s xml:id="echoid-s9953" xml:space="preserve">ad 7.</s>
            <s xml:id="echoid-s9954" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9955" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            enim per præcedentem ſit, vt quadratum circumferentiæ maximi cir-
              <lb/>
            culi ad ſuperficiem conuexam ſphærę, ita circumferentia eiuſdem circuli ad
              <lb/>
            diametrum: </s>
            <s xml:id="echoid-s9956" xml:space="preserve"> ſit autem maior proportio circumferentię ad diametrum,
              <note symbol="b" position="right" xlink:label="note-251-02" xlink:href="note-251-02a" xml:space="preserve">2. de Dimẽſ@
                <lb/>
              circuli lib. 4.</note>
            3 {10/71}. </s>
            <s xml:id="echoid-s9957" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s9958" xml:space="preserve">hoc eſt, quam 223. </s>
            <s xml:id="echoid-s9959" xml:space="preserve">ad 71. </s>
            <s xml:id="echoid-s9960" xml:space="preserve">minor verò, quam 3 {1/7}. </s>
            <s xml:id="echoid-s9961" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s9962" xml:space="preserve">hoc eſt, quam
              <lb/>
            22. </s>
            <s xml:id="echoid-s9963" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s9964" xml:space="preserve">liquetid, quod propoſitum eſt.</s>
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          <head xml:id="echoid-head234" xml:space="preserve">PROPOSITIO V.</head>
          <p>
            <s xml:id="echoid-s9966" xml:space="preserve">QVADRATVM diametri circuli in ſphæra maximi ad ſuperficiem
              <lb/>
            ſphæræ conuexam, maiorem proportionem habet, quam 7. </s>
            <s xml:id="echoid-s9967" xml:space="preserve">ad 22.
              <lb/>
            </s>
            <s xml:id="echoid-s9968" xml:space="preserve">minorem verò, quam 71. </s>
            <s xml:id="echoid-s9969" xml:space="preserve">ad 223.</s>
            <s xml:id="echoid-s9970" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9971" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            enim per propoſ. </s>
            <s xml:id="echoid-s9972" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9973" xml:space="preserve">ſit, vt quadratum diametri ad ſuperficiem ſphærę,
              <lb/>
            ita diameter ad circumferentiam: </s>
            <s xml:id="echoid-s9974" xml:space="preserve"> Sit autem maior proportio diametri ad
              <note symbol="c" position="right" xlink:label="note-251-03" xlink:href="note-251-03a" xml:space="preserve">26. quinti.</note>
            cumferentiam, quam 7. </s>
            <s xml:id="echoid-s9975" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s9976" xml:space="preserve">( quod minor ſit proportio circumferentię
              <note symbol="d" position="right" xlink:label="note-251-04" xlink:href="note-251-04a" xml:space="preserve">2. de Dimẽſ.
                <lb/>
              circuli lib. 4.</note>
            diametrum, quam 22. </s>
            <s xml:id="echoid-s9977" xml:space="preserve">ad 7.) </s>
            <s xml:id="echoid-s9978" xml:space="preserve">minor verò, quam 71. </s>
            <s xml:id="echoid-s9979" xml:space="preserve">ad 223. </s>
            <s xml:id="echoid-s9980" xml:space="preserve">( quod maior ſit proportio circumferentię ad diametrum, quam 223. </s>
            <s xml:id="echoid-s9981" xml:space="preserve">ad 71.) </s>
            <s xml:id="echoid-s9982" xml:space="preserve">patet verum eſſe,
              <lb/>
            quod proponitur.</s>
            <s xml:id="echoid-s9983" xml:space="preserve"/>
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          <head xml:id="echoid-head235" xml:space="preserve">PROPOSITIO VI.</head>
          <p>
            <s xml:id="echoid-s9984" xml:space="preserve">PROPORTIO cubi ex circumferentia maximi in ſphæra circuli de-
              <lb/>
            ſcripti, ad ſphæram maior eſt, quam 298374. </s>
            <s xml:id="echoid-s9985" xml:space="preserve">ad 5041. </s>
            <s xml:id="echoid-s9986" xml:space="preserve">minor autem,
              <lb/>
            quam 2904. </s>
            <s xml:id="echoid-s9987" xml:space="preserve">ad 49.</s>
            <s xml:id="echoid-s9988" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9989" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            enim ſit per propoſ. </s>
            <s xml:id="echoid-s9990" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9991" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s9992" xml:space="preserve">7. </s>
            <s xml:id="echoid-s9993" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9994" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9995" xml:space="preserve">vt circumferentia maximi circuli in
              <lb/>
            quauis ſphæra, ad circumferentiam maximi circuli in quauis alia ſphęra, ita dia-
              <lb/>
            meter ad diametrum: </s>
            <s xml:id="echoid-s9996" xml:space="preserve"> habeat autem cubus circumferentię prioris ſphærę ad cubum circumferentię ſphærę poſterioris, proportionem triplicatam circum-
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              <note symbol="e" position="right" xlink:label="note-251-05" xlink:href="note-251-05a" xml:space="preserve">33. vndec.</note>
            ferentię ad circumferentiam; </s>
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            <s xml:id="echoid-s9998" xml:space="preserve">erit vt cubus ex circumfe-
              <lb/>
              <note position="right" xlink:label="note-251-06" xlink:href="note-251-06a" xml:space="preserve">18. duodec.</note>
            rentia prioris ſphærę deſcriptus ad cubum ex poſterioris ſphærę circumferen-
              <lb/>
            tia deſcriptum, ita ſphæra prior ad poſteriorem ſphęram; </s>
            <s xml:id="echoid-s9999" xml:space="preserve">Et permutando, vt cu-
              <lb/>
            bus circumferentię ſphærę prioris ad priorem ſphęram, ita cubus circumferen-
              <lb/>
            tiæ poſterioris ſphęrę ad ſphęram poſteriorem.</s>
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