Clavius, Christoph, Geometria practica

Table of contents

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[301.] PROBL. 2. PROPOS. 10.
Page: 329 (299)
[302.] THEOR. 9. PROPOS. 11.
Page: 330 (300)
[303.] THEOR. 10. PROPOS. 12.
Page: 333 (303)
[304.] SCHOLIVM.
Page: 334 (304)
[305.] THEOR. 11. PROPOS. 13.
Page: 336 (306)
[306.] COROLLARIVM.
Page: 336 (306)
[307.] THEOR. 12. PROPOS. 14.
Page: 337 (307)
[308.] THEOR. 13. PROPOS. 15.
Page: 337 (307)
[309.] THEOR. 14. PROPOS. 16.
Page: 338 (308)
[310.] THEOR. 15. PROPOS. 17.
Page: 340 (310)
[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)
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            <s xml:id="echoid-s12559" xml:space="preserve">
              <pb o="273" file="303" n="303" rhead="LIBER SEXTVS."/>
            ta proportionalis E atque inter AB, & </s>
            <s xml:id="echoid-s12560" xml:space="preserve">E, reperiatur media proportionalis FG,
              <lb/>
            & </s>
            <s xml:id="echoid-s12561" xml:space="preserve">ſupra FG, figura conſtruatur ſimilis datæ figuræ AB, ſimiliterque poſita. </s>
            <s xml:id="echoid-s12562" xml:space="preserve">Item
              <lb/>
            circulus deſcribatur circa diametrnm FG. </s>
            <s xml:id="echoid-s12563" xml:space="preserve">Dico tam rectilineum A B, eſſe ter-
              <lb/>
            tiam partem rectilinei FG, quam circulum AB, circuli FG, nimirum eandem ha-
              <lb/>
            bere proportionem AB, ad FG, quam habet C, ad D. </s>
            <s xml:id="echoid-s12564" xml:space="preserve">Quoniam enim tres rectę
              <lb/>
            AB, FG, & </s>
            <s xml:id="echoid-s12565" xml:space="preserve">E, continuè proportionales ſunt, erit figura A B, ad figuram
              <note symbol="a" position="right" xlink:label="note-303-01" xlink:href="note-303-01a" xml:space="preserve">coroll. 19.
                <lb/>
              vel 20. ſexti.</note>
            vt AB, ad E, hoc eſt, vt C, ad D. </s>
            <s xml:id="echoid-s12566" xml:space="preserve"> Quia verò eſt, vt quadratum ex A B, ad qua- dratum FG, ita circulus AB, ad circulum FG; </s>
            <s xml:id="echoid-s12567" xml:space="preserve">eſtque quadratum AB, ad quadra-
              <lb/>
              <note symbol="b" position="right" xlink:label="note-303-02" xlink:href="note-303-02a" xml:space="preserve">2. duodec.</note>
            tum FG, vt AB, ad E; </s>
            <s xml:id="echoid-s12568" xml:space="preserve">erit quoque circulus AB, ad circulum FG, vt AB, ad E, vel
              <lb/>
            vt C, ad D.</s>
            <s xml:id="echoid-s12569" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12570" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde figura, vel circulus H I, oporteatque conſtruere minorem figu-
              <lb/>
            ram, vel circulum in proportione K, ad L, nimirum tripla. </s>
            <s xml:id="echoid-s12571" xml:space="preserve">Tribus rectis K, L, H
              <lb/>
            I, inueniatur quarta proportionalis M: </s>
            <s xml:id="echoid-s12572" xml:space="preserve">atque inter HI, & </s>
            <s xml:id="echoid-s12573" xml:space="preserve">M, media proportio-
              <lb/>
            nalis inueniatur N O, ſupra quam conſtruatur figura ſimilis ſimiliter que poſita
              <lb/>
            figuræ HI: </s>
            <s xml:id="echoid-s12574" xml:space="preserve">Item circulus deſcribatur circa diametrum NO. </s>
            <s xml:id="echoid-s12575" xml:space="preserve">Dico tam figuram
              <lb/>
            HI, ad figuram NO, quam circulum HI, ad circulum NO, habereproportionem
              <lb/>
            triplam, eandem videlicet, quam habet K, ad L. </s>
            <s xml:id="echoid-s12576" xml:space="preserve">Quoniam enim tres rectæ HI,
              <lb/>
              <note symbol="c" position="right" xlink:label="note-303-03" xlink:href="note-303-03a" xml:space="preserve">coroll. 19. vel
                <lb/>
              20. ſexti.</note>
            NO, & </s>
            <s xml:id="echoid-s12577" xml:space="preserve">M, continuè ſunt proportionales; </s>
            <s xml:id="echoid-s12578" xml:space="preserve"> erit figura HI, ad figuram NO, vt recta HI, ad M, hoc eſt, vt K, ad L. </s>
            <s xml:id="echoid-s12579" xml:space="preserve"> Et quia eſt, vt quadratum HI, ad
              <note symbol="d" position="right" xlink:label="note-303-04" xlink:href="note-303-04a" xml:space="preserve">2. duodec.</note>
            tum NO, ita circulus HI, ad circulum NO, eſt que quadratum HI, ad quadra-
              <lb/>
            tum NO, vt recta HI, ad M; </s>
            <s xml:id="echoid-s12580" xml:space="preserve">erit quoque circulus HI, ad circulum NO, vtre-
              <lb/>
            cta HI, ad M, vel vt K, ad L.</s>
            <s xml:id="echoid-s12581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12582" xml:space="preserve">Ex his conſtat, qua ratione, dato foramine rotundo, vel etiam quadrato ali-
              <lb/>
            cuius fontis, aliud foramen rotundum, vel quadratum maius, vel minus in qua-
              <lb/>
            cunque proportione conſtruendum ſit.</s>
            <s xml:id="echoid-s12583" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div786" type="section" level="1" n="270">
          <head xml:id="echoid-head295" xml:space="preserve">PROBL. 12. PROPOS. 17.</head>
          <p>
            <s xml:id="echoid-s12584" xml:space="preserve">DATAM figuram ſolidam qualemcunque ex iis, de quibus Eucl. </s>
            <s xml:id="echoid-s12585" xml:space="preserve">in
              <lb/>
            lib. </s>
            <s xml:id="echoid-s12586" xml:space="preserve">Stereometriæ agit, augere vel minuere in proportione data.</s>
            <s xml:id="echoid-s12587" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12588" xml:space="preserve">
              <emph style="sc">Hvivsmodi</emph>
            figuræ ſolidæ ſunt parallelepipedum, Pyra-
              <lb/>
              <figure xlink:label="fig-303-01" xlink:href="fig-303-01a" number="207">
                <image file="303-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/303-01"/>
              </figure>
            mis, Priſma, ſphæra, Conus, Cylindrus, & </s>
            <s xml:id="echoid-s12589" xml:space="preserve">quinque corporare-
              <lb/>
            gularia.</s>
            <s xml:id="echoid-s12590" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12591" xml:space="preserve">
              <emph style="sc">Sit</emph>
            ergo figura ſolida, cuius latus A, vel ſphæra, cuius dia-
              <lb/>
            meter A, augenda primum in proportione B, ad C. </s>
            <s xml:id="echoid-s12592" xml:space="preserve">Tribus re-
              <lb/>
            ctis B, C, A, inueniatur quarta proportionalis D: </s>
            <s xml:id="echoid-s12593" xml:space="preserve">atque inter A,
              <lb/>
            & </s>
            <s xml:id="echoid-s12594" xml:space="preserve">D, reperiantur duæ mediæ proportionales E, F. </s>
            <s xml:id="echoid-s12595" xml:space="preserve">Dico ſoli-
              <lb/>
            dum lateris A, ad ſolidum ſupra latus E, nimirum ſupra me-
              <lb/>
            diam proportionalem, quæ propinquior eſt lateri dato A,
              <lb/>
            conſtructum ſimile, ſimiliter que poſitum ſolido ſupra latus A,
              <lb/>
            conſtituto, habere proportionem, quam B, habet ad C. </s>
            <s xml:id="echoid-s12596" xml:space="preserve">Item
              <lb/>
            ſphæram datam diametri A, ad ſphæram diametri E, eſſe, vt B,
              <lb/>
            ad C. </s>
            <s xml:id="echoid-s12597" xml:space="preserve">Quoniam enim figura ſolida lateris A, ad figuram ſoli-
              <lb/>
            dam lateris E, ſimilem ſimiliter que poſitam habet proportio-
              <lb/>
            nem triplicatam lateris A, ad latus E, vt lib. </s>
            <s xml:id="echoid-s12598" xml:space="preserve">11. </s>
            <s xml:id="echoid-s12599" xml:space="preserve">& </s>
            <s xml:id="echoid-s12600" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12601" xml:space="preserve">Eucl. </s>
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