Clavius, Christoph, Geometria practica

Table of contents

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[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)
[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)
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            <s xml:id="echoid-s12602" xml:space="preserve">
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            monſtratum eſt: </s>
            <s xml:id="echoid-s12603" xml:space="preserve">Similiter Conus & </s>
            <s xml:id="echoid-s12604" xml:space="preserve">Cylindrus, cuius baſis diameter A, ad Co-
              <lb/>
            num & </s>
            <s xml:id="echoid-s12605" xml:space="preserve">Cylindrum ſimilem, cuius diameter E: </s>
            <s xml:id="echoid-s12606" xml:space="preserve">Necnon ſphæra diametri A, ad
              <lb/>
            ſphæram diametri E; </s>
            <s xml:id="echoid-s12607" xml:space="preserve">eſt autem, ex defin. </s>
            <s xml:id="echoid-s12608" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12609" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12610" xml:space="preserve">5. </s>
            <s xml:id="echoid-s12611" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s12612" xml:space="preserve">proportio quoque
              <lb/>
            A, ad D, triplicata proportionis A, ad E: </s>
            <s xml:id="echoid-s12613" xml:space="preserve">Erit ſolidum A, ad ſolidum E, vt A, ad
              <lb/>
            D, hoc eſt, vt B, ad C. </s>
            <s xml:id="echoid-s12614" xml:space="preserve">quod eſt propoſitum.</s>
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              <emph style="sc">Sit</emph>
            deinde ſolidum lateris, vel diametri D, minuendum in proportione da-
              <lb/>
            ta C, ad B. </s>
            <s xml:id="echoid-s12617" xml:space="preserve">Tribus C, B, D, inueniatur quarta proportionalis A; </s>
            <s xml:id="echoid-s12618" xml:space="preserve">atque inter D,
              <lb/>
            & </s>
            <s xml:id="echoid-s12619" xml:space="preserve">A, reperiantur duæ mediæ proportionales F, E. </s>
            <s xml:id="echoid-s12620" xml:space="preserve">Dico ſolidum lateris, vel dia-
              <lb/>
            metri D, ad ſolidum ſimile ſimiliter que deſcriptum ſupra F, nimirum ſupra me-
              <lb/>
            diam proportionalem, quæ lateri dato D, propinquior eſt, proportio nem habe-
              <lb/>
            re, quam C, ad B. </s>
            <s xml:id="echoid-s12621" xml:space="preserve">Quoniam enim ſolidum D, ad ſimile ſimiliter que deſcriptum
              <lb/>
            ſolidum F, proportionem habet triplicatam lateris D, ad latus F: </s>
            <s xml:id="echoid-s12622" xml:space="preserve">qualem etiam
              <lb/>
            habet ex defin. </s>
            <s xml:id="echoid-s12623" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12624" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12625" xml:space="preserve">5. </s>
            <s xml:id="echoid-s12626" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s12627" xml:space="preserve">recta D, ad rectam A: </s>
            <s xml:id="echoid-s12628" xml:space="preserve">erit ſolidum D, ad ſolidum
              <lb/>
            F, vt D, ad A, id eſt, vt C, ad B. </s>
            <s xml:id="echoid-s12629" xml:space="preserve">quod eſt propoſitum.</s>
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            <s xml:id="echoid-s12631" xml:space="preserve">
              <emph style="sc">Constat</emph>
            ex his, qua ratione Cubus non ſolum duplicandus ſit (quod
              <lb/>
            veteres inquirebant) ſed etiam augendus minuenduſue in quacunque propor-
              <lb/>
            tione: </s>
            <s xml:id="echoid-s12632" xml:space="preserve">Item quo pacto pylæ bombardarum maiores, aut minores fieri debeant
              <lb/>
            ſecundum proportionem datam.</s>
            <s xml:id="echoid-s12633" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div788" type="section" level="1" n="271">
          <head xml:id="echoid-head296" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s12634" xml:space="preserve">
              <emph style="sc">Figvras</emph>
            ſolidas ſimiliterque poſitas habere proportionem triplicatam
              <lb/>
            homologorum laterum, demonſtratum eſt de parallelepipedis quidem lib. </s>
            <s xml:id="echoid-s12635" xml:space="preserve">11.
              <lb/>
            </s>
            <s xml:id="echoid-s12636" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s12637" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12638" xml:space="preserve">33. </s>
            <s xml:id="echoid-s12639" xml:space="preserve">Depyramidibus verò lib. </s>
            <s xml:id="echoid-s12640" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12641" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12642" xml:space="preserve">8. </s>
            <s xml:id="echoid-s12643" xml:space="preserve">eiuſque coroll. </s>
            <s xml:id="echoid-s12644" xml:space="preserve">& </s>
            <s xml:id="echoid-s12645" xml:space="preserve">de
              <lb/>
            Priſmatis, in eiuſdem ſcholio. </s>
            <s xml:id="echoid-s12646" xml:space="preserve">Deſphæra autem lib. </s>
            <s xml:id="echoid-s12647" xml:space="preserve">eodem 12. </s>
            <s xml:id="echoid-s12648" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12649" xml:space="preserve">18. </s>
            <s xml:id="echoid-s12650" xml:space="preserve">De
              <lb/>
            Conis deinde & </s>
            <s xml:id="echoid-s12651" xml:space="preserve">Cylindris eodem lib. </s>
            <s xml:id="echoid-s12652" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12653" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12654" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12655" xml:space="preserve">ſi pro lateribus homolo-
              <lb/>
            gis ſumantur diametri ſphærarum, & </s>
            <s xml:id="echoid-s12656" xml:space="preserve">diametribaſium Conorum, & </s>
            <s xml:id="echoid-s12657" xml:space="preserve">Cylindro-
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            rum. </s>
            <s xml:id="echoid-s12658" xml:space="preserve">Actandem de quinque corporibus regularibus in coroll. </s>
            <s xml:id="echoid-s12659" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12660" xml:space="preserve">17. </s>
            <s xml:id="echoid-s12661" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12662" xml:space="preserve">
              <lb/>
            12. </s>
            <s xml:id="echoid-s12663" xml:space="preserve">quippe cum omnia hæc corpora in ſphæris deſcribi poſsint.</s>
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              <emph style="sc">Qvamvis</emph>
            autem problema hoc deſupradictis corporibus duntaxat pro-
              <lb/>
            poſuerimus, idem tamen etiam locum habet in aliis cuiuſque generis corpori-
              <lb/>
            bus ſimilibus, ſimiliter que poſitis, vt perſpicuum eſt; </s>
            <s xml:id="echoid-s12666" xml:space="preserve">propterea quod diuidi
              <lb/>
            poſſunt in pyramides ſimiles, æquales numero; </s>
            <s xml:id="echoid-s12667" xml:space="preserve"> quæ quidem
              <note symbol="a" position="left" xlink:label="note-304-01" xlink:href="note-304-01a" xml:space="preserve">8. duodec.
                <lb/>
              eiuſ coroll.</note>
            habent laterum homologorum triplicatam. </s>
            <s xml:id="echoid-s12668" xml:space="preserve"> Cum ergo ſit, vt vna pyramis ad vnam pyramidem, ita omnes ad omnes, id eſt, ita ſolidum ad ſolidum; </s>
            <s xml:id="echoid-s12669" xml:space="preserve">ſint-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-304-02" xlink:href="note-304-02a" xml:space="preserve">12. quinti.</note>
            que eadem latera homologa ſolidorum, quæ pyramidum ſimilium, conſtat
              <lb/>
            propoſitum.</s>
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          <head xml:id="echoid-head297" xml:space="preserve">PROBL. 13. PROPOS. 18.</head>
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            <s xml:id="echoid-s12671" xml:space="preserve">INTER duos numeros datos tum vnum, tum duos medios propor-
              <lb/>
            tionales reperire.</s>
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          </p>
          <p>
            <s xml:id="echoid-s12673" xml:space="preserve">
              <emph style="sc">Non</emph>
            rarò figura ſiue plana, ſiue ſolida augenda, vel minuenda eſt per nume-
              <lb/>
            ros, quod quidem ſine inuentione vnius medij proportionalis, vel duorum
              <lb/>
            mediorum inter datos duos numeros perfici nonpoteſt: </s>
            <s xml:id="echoid-s12674" xml:space="preserve">idcirco artem </s>
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