Clavius, Christoph, Geometria practica

Table of contents

< >
[271.] SCHOLIVM.
Page: 304 (274)
[272.] PROBL. 13. PROPOS. 18.
Page: 304 (274)
[273.] LEMMA.
Page: 305 (275)
[274.] PROBL. 14. PROPOS. 19. RADICEM cuiuslibet generis extrahere.
Page: 306 (276)
[275.] EXTRACTIO RADICIS Quadratæ.
Page: 309 (279)
[276.] EXTRACTIO RADICIS CVBICE.
Page: 310 (280)
[277.] EXTRACTIO RADICIS Surdeſolidæ.
Page: 311 (281)
[278.] REGVLA PROPRIA EXTRA-ctionis radicis cubicæ.
Page: 313 (283)
[279.] PROBL. 15. PROPOS. 20.
Page: 314 (284)
[280.] PROBL. 16. PROPOS. 21.
Page: 316 (286)
[281.] PROBL. 17. PROPOS. 22.
Page: 319 (289)
[282.] FINIS LIBRI SEXTI.
Page: 320 (290)
[283.] GEOMETRIÆ PRACTICÆ LIBER SEPTIMVS.
Page: 321 (291)
[284.] De figuris Iſoperimetris diſputans: cui Appendicis loco annectitur breuis de circulo per lineas quadrando tractatiuncula.
Page: 321 (291)
[285.] DEFINITIONES.
Page: 321 (291)
[286.] I.
Page: 321 (291)
[287.] II.
Page: 322 (292)
[288.] III.
Page: 322 (292)
[289.] IIII.
Page: 322 (292)
[290.] V.
Page: 322 (292)
[291.] THEOR. 1. PROPOS. 1.
Page: 322 (292)
[292.] PROBL. 2. PROPOS. 2.
Page: 323 (293)
[293.] THEOR. 3. PROPOS. 3.
Page: 324 (294)
[294.] THEOR. 4. PROPOS. 4.
Page: 324 (294)
[295.] THEOR. 5. PROPOS. 5.
Page: 325 (295)
[296.] THEOR. 6. PROPOS. 6.
Page: 326 (296)
[297.] PROBL. 1. PROPOS. 7.
Page: 327 (297)
[298.] SCHOLIVM.
Page: 327 (297)
[299.] THEOR. 7. PROPOS. 8.
Page: 327 (297)
[300.] THEOR. 8. PROPOS. 9.
Page: 328 (298)
< >
page |< < (289) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div822" type="section" level="1" n="280">
          <pb o="289" file="319" n="319" rhead="LIBER SEXTVS."/>
          <p>
            <s xml:id="echoid-s13778" xml:space="preserve">
              <emph style="sc">Demonstro</emph>
            vtrumque hunc modum hac ratione. </s>
            <s xml:id="echoid-s13779" xml:space="preserve">Quando numerator
              <lb/>
            in quadratum denominatoris ducitur, erit producti numeriradix cubica vnus
              <lb/>
            duorum mediorum proportionalium inter numeratorem ac denominatorem
              <lb/>
            collo candus iuxta denominatorem, vt conſtat ex iis, quæ propoſ. </s>
            <s xml:id="echoid-s13780" xml:space="preserve">18. </s>
            <s xml:id="echoid-s13781" xml:space="preserve">huius lib.
              <lb/>
            </s>
            <s xml:id="echoid-s13782" xml:space="preserve">demonſtrata ſunt. </s>
            <s xml:id="echoid-s13783" xml:space="preserve"> Erit igitur proportio numeratoris ad denominatorem
              <note symbol="a" position="right" xlink:label="note-319-01" xlink:href="note-319-01a" xml:space="preserve">10. defiu.
                <lb/>
              quinti.</note>
            plicata proportionis radicis cubicæ inuentæ ad denominatorem: </s>
            <s xml:id="echoid-s13784" xml:space="preserve"> Eſt autem eadem proportio numeratoris ad denominatorem, tanquam cubi ad cubum,
              <lb/>
              <note symbol="b" position="right" xlink:label="note-319-02" xlink:href="note-319-02a" xml:space="preserve">12. octaui.</note>
            triplicata quoque proportionis radicis cubicæ numeratoris ad radicem cubi-
              <lb/>
            cam denominatoris. </s>
            <s xml:id="echoid-s13785" xml:space="preserve">Igitur erit radix cubica inuenta ad denominatorem, vt
              <lb/>
            radix cubica numeratoris ad radicem cubicam denominatoris: </s>
            <s xml:id="echoid-s13786" xml:space="preserve"> ac
              <note symbol="c" position="right" xlink:label="note-319-03" xlink:href="note-319-03a" xml:space="preserve">7. minutia-
                <lb/>
              rum ad finem
                <lb/>
              lib. 9.</note>
            minutia, cuius numerator radix cubica inuenta, ac denominator ipſe denomi-
              <lb/>
            nator, æqualis erit minutiæ, cuius numerator radix cubica numeratoris, ac
              <lb/>
            denominator radix cubica denominatoris. </s>
            <s xml:id="echoid-s13787" xml:space="preserve">Quam ob rem ſicut hæc minu-
              <lb/>
            tia eſt radix cubica fractionis propoſitæ, ita quoque illa eritradix cubica eiuſ-
              <lb/>
            dem fractionis. </s>
            <s xml:id="echoid-s13788" xml:space="preserve">Diuiſa ergo radice illa cubica inuenta per denominatorem
              <lb/>
            fractionis propoſitæ (quæ diuiſio fit, quia illa radix cubica inuenta eſt fractio,
              <lb/>
            ac proinde, vt cognoſcatur val or minutiæ, cuius numerator radix illa inuen-
              <lb/>
            ta, ac denominator ipſemet denominator fractionis propoſitæ, diuidendus eſt
              <lb/>
            numerator huius minutiæ per eius denominatorem: </s>
            <s xml:id="echoid-s13789" xml:space="preserve">alio quin ſi illa radix cu-
              <lb/>
            bica inuenta foret numerus integer, diuiſio facienda non eſſet) producetur ra-
              <lb/>
            dix cubica fractionis propoſitæ: </s>
            <s xml:id="echoid-s13790" xml:space="preserve">quemadmodum ex diuiſione radicis cubicæ
              <lb/>
            numeratoris per radicem cubicam denominatoris procreatur radix cubica fra-
              <lb/>
            ctionis propoſitæ: </s>
            <s xml:id="echoid-s13791" xml:space="preserve">quippe cum minutia nil aliud ſit, niſi numerator per deno-
              <lb/>
            minatorem diuiſus.</s>
            <s xml:id="echoid-s13792" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13793" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            verò denominator in quadratum numeratoris ducitur, erit
              <lb/>
            numeri producti radix cubica vnus duorum mediorum proportionalium in-
              <lb/>
            ter numeratorem, ac denominatorem, collocandus iuxta numeratorem, vt
              <lb/>
            ex demonſtratis propoſ. </s>
            <s xml:id="echoid-s13794" xml:space="preserve">18. </s>
            <s xml:id="echoid-s13795" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s13796" xml:space="preserve">manifeſtum eſt. </s>
            <s xml:id="echoid-s13797" xml:space="preserve">Ergo rurſus erit propor-
              <lb/>
            tio numeratoris ad denominatorem triplicata proportionis numeratoris ad il-
              <lb/>
            lam radicem cubicam inuentam, quemadmodum & </s>
            <s xml:id="echoid-s13798" xml:space="preserve">proportionis radicis cu-
              <lb/>
            bicæ numeratoris ad radicem cubicam denominatoris, eadem illa proportio
              <lb/>
            numeratoris ad denominatorem, tanquam cubi ad cubum, triplicata eſt: </s>
            <s xml:id="echoid-s13799" xml:space="preserve">Ac
              <lb/>
            propterea, vt ſupra, minutia, cuius numerator ipſemet numerator fractio-
              <lb/>
            nis propoſitæ, denominator verò radix illa cubica inuenta, æqualis erit mi-
              <lb/>
            nutiæ, cuius numerator, radix cubica numeratoris fractionis propoſitæ, & </s>
            <s xml:id="echoid-s13800" xml:space="preserve">de-
              <lb/>
            nominator radix cubica denominatoris eiuſdem fractionis. </s>
            <s xml:id="echoid-s13801" xml:space="preserve">Quocirca diuiſo
              <lb/>
            numeratore per illam inuentam radicem cubicam, prodibit radix cubica fra-
              <lb/>
            ctionis propoſitæ.</s>
            <s xml:id="echoid-s13802" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div826" type="section" level="1" n="281">
          <head xml:id="echoid-head307" xml:space="preserve">PROBL. 17. PROPOS. 22.</head>
          <p>
            <s xml:id="echoid-s13803" xml:space="preserve">RADICEM quadratam & </s>
            <s xml:id="echoid-s13804" xml:space="preserve">cubicam in numeris non quadratis, & </s>
            <s xml:id="echoid-s13805" xml:space="preserve">
              <lb/>
            non cubicis per lineas Geometrice inuenire.</s>
            <s xml:id="echoid-s13806" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13807" xml:space="preserve">
              <emph style="sc">Sit</emph>
            datus numerus 10. </s>
            <s xml:id="echoid-s13808" xml:space="preserve">repræſentans quadratum 10. </s>
            <s xml:id="echoid-s13809" xml:space="preserve">palmorum, vel </s>
          </p>
        </div>
      </text>
    </echo>
Impressum