Clavius, Christoph, Geometria practica

List of thumbnails

< >
281
281 (251) 		282
282 (252)
283
283 (253) 		284
284 (254)
285
285 (255) 		286
286 (256)
287
287 (257) 		288
288 (258)
289
289 (259) 		290
290 (260)
< >
page |< < (257) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div730" type="section" level="1" n="251">
          <p>
            <s xml:id="echoid-s11840" xml:space="preserve">
              <pb o="257" file="287" n="287" rhead="LIBER SEXTVS."/>
            literque poſita: </s>
            <s xml:id="echoid-s11841" xml:space="preserve"> Vt autem C G, ad C H, ita quoque eſt idem triangulum C B
              <note symbol="a" position="right" xlink:label="note-287-01" xlink:href="note-287-01a" xml:space="preserve">1. ſexti.</note>
            ad triangulum C B H; </s>
            <s xml:id="echoid-s11842" xml:space="preserve"> æqualia erunt triangula C I K, C B H: </s>
            <s xml:id="echoid-s11843" xml:space="preserve">ideoque & </s>
            <s xml:id="echoid-s11844" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-287-02" xlink:href="note-287-02a" xml:space="preserve">9. quinti.</note>
              <figure xlink:label="fig-287-01" xlink:href="fig-287-01a" number="190">
                <image file="287-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/287-01"/>
              </figure>
            quum trapezium I K B A, reliquo triangulo H B A, æquale erit. </s>
            <s xml:id="echoid-s11845" xml:space="preserve"> Quocirca
              <note symbol="c" position="right" xlink:label="note-287-03" xlink:href="note-287-03a" xml:space="preserve">7. quinti.</note>
            triangulum C I K, ad trapezium I K B A, vt triangulum C B H, ad triangulum H B A,
              <lb/>
            hoc eſt, vt C H, ad H A, vel vt E, ad D. </s>
            <s xml:id="echoid-s11846" xml:space="preserve">quod faciendum erat.</s>
            <s xml:id="echoid-s11847" xml:space="preserve"/>
          </p>
          <note symbol="d" position="right" xml:space="preserve">1. ſexti.</note>
          <p>
            <s xml:id="echoid-s11848" xml:space="preserve">
              <emph style="sc">Fiet</emph>
            idem quoque aliter, ſi cadente puncto diuiſionis L, inter A, & </s>
            <s xml:id="echoid-s11849" xml:space="preserve">G,
              <lb/>
            conſtruatur trapezium G N, per parallelam M N, æquale triangulo B G L; </s>
            <s xml:id="echoid-s11850" xml:space="preserve">
              <note symbol="e" position="right" xlink:label="note-287-05" xlink:href="note-287-05a" xml:space="preserve">2. hui{us}.</note>
            dente verò puncto diuiſionis H, inter G, & </s>
            <s xml:id="echoid-s11851" xml:space="preserve">C, trapezium conſtituatur B I, æqua-
              <lb/>
            le triangulo B G H, per parallelam I K, &</s>
            <s xml:id="echoid-s11852" xml:space="preserve">c.</s>
            <s xml:id="echoid-s11853" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11854" xml:space="preserve">
              <emph style="sc">Præterea</emph>
            quadrilaterum A B C D, diuidendum ſit per lineam lateri
              <lb/>
            C D, parallelam in duas partes, vt pars verſus A, ad reliquam habeat datam pro-
              <lb/>
            portionem E, ad F. </s>
            <s xml:id="echoid-s11855" xml:space="preserve">Per ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s11856" xml:space="preserve">14. </s>
            <s xml:id="echoid-s11857" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11858" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11859" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s11860" xml:space="preserve">vel potius per
              <lb/>
            ea, quæ Num. </s>
            <s xml:id="echoid-s11861" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11862" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s11863" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11864" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11865" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11866" xml:space="preserve">huius tradidimus, quadrilatero A B C D, conſtrua-
              <lb/>
            tur quadratum æquale G H I K; </s>
            <s xml:id="echoid-s11867" xml:space="preserve">ſecetur que latus G K, in L, in proportionem E,
              <lb/>
            ad F, datam, & </s>
            <s xml:id="echoid-s11868" xml:space="preserve">per L, ipſi G H, parallela agatur L M. </s>
            <s xml:id="echoid-s11869" xml:space="preserve">Deinde ſuper C D, inter re-
              <lb/>
            ctas C B, D A, fiat rectilineo L I, æquale quadrilaterum D O, habenslatus N
              <note symbol="f" position="right" xlink:label="note-287-06" xlink:href="note-287-06a" xml:space="preserve">2. hui{us}.</note>
            lateri C D, parallelum: </s>
            <s xml:id="echoid-s11870" xml:space="preserve">Et ſi quidem punctum O, cadit in latus C B, vel in ipſum
              <lb/>
            punctum B, recta N O, problema efficiet. </s>
            <s xml:id="echoid-s11871" xml:space="preserve">Cum enim quadratum G I, toti qua-
              <lb/>
            drilatero A C, æquale ſit, & </s>
            <s xml:id="echoid-s11872" xml:space="preserve">rectangulum ablatum L I, quadril atero ablato D O;
              <lb/>
            </s>
            <s xml:id="echoid-s11873" xml:space="preserve">erit quoque reliquum rectangulum G M, reliquo rectilineo A N O, æquale. </s>
            <s xml:id="echoid-s11874" xml:space="preserve">
              <lb/>
              <note symbol="g" position="right" xlink:label="note-287-07" xlink:href="note-287-07a" xml:space="preserve">7. quinti.</note>
            Quapropter erit A N O, ad D O, vt G M, ad M K; </s>
            <s xml:id="echoid-s11875" xml:space="preserve"> hoc eſt, vt G L, ad L K,
              <note symbol="h" position="right" xlink:label="note-287-08" xlink:href="note-287-08a" xml:space="preserve">1. ſexti.</note>
            vt E, ad F. </s>
            <s xml:id="echoid-s11876" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s11877" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11878" xml:space="preserve">
              <emph style="sc">Si</emph>
            verò punctum O, cadit in C B, latus productum, (quod hic fiet, ſi propor-
              <unsure/>
              <lb/>
            tio data ſit Q, ad R. </s>
            <s xml:id="echoid-s11879" xml:space="preserve">Diuiſo enim latere G K, in S, in datam proportionem Q. </s>
            <s xml:id="echoid-s11880" xml:space="preserve">ad
              <lb/>
            R; </s>
            <s xml:id="echoid-s11881" xml:space="preserve">ductaque S T, parallela lateri G H; </s>
            <s xml:id="echoid-s11882" xml:space="preserve">ſi ſuper C D, inter rectas D A, C B,
              <note symbol="i" position="right" xlink:label="note-287-09" xlink:href="note-287-09a" xml:space="preserve">2. hui{us}.</note>
            ctangulo K T, æquale quadrilaterum D O, cadet O, vltra B & </s>
            <s xml:id="echoid-s11883" xml:space="preserve">parallela N O, ſe-
              <lb/>
            cabit latus A B, in P.) </s>
            <s xml:id="echoid-s11884" xml:space="preserve"> conſtituemus ſuper N P, inter rectas N A, P A, per
              <note symbol="k" position="right" xlink:label="note-287-10" xlink:href="note-287-10a" xml:space="preserve">2 hui{us}.</note>
            lam V X, trapezium N V, triangulo B O P, æquale, factum erit, quod iubetur. </s>
            <s xml:id="echoid-s11885" xml:space="preserve">Ad-
              <lb/>
            dito enim communi rectilineo C D N P B; </s>
            <s xml:id="echoid-s11886" xml:space="preserve">erit totum rectilineum C D X V B, toti
              <lb/>
            rectilineo D O, hoc eſt, rectangulo K T, æquale; </s>
            <s xml:id="echoid-s11887" xml:space="preserve">ideoque & </s>
            <s xml:id="echoid-s11888" xml:space="preserve">reliquum triangu-
              <lb/>
            lum A V X, reliquo rectangulo G T, æquale. </s>
            <s xml:id="echoid-s11889" xml:space="preserve"> Quare erit triangulum A V X,
              <note symbol="l" position="right" xlink:label="note-287-11" xlink:href="note-287-11a" xml:space="preserve">7. quinti.</note>
            rectilineum C D X V B, vt G T, ad K T, hoc eſt, vt G S, ad S K, vel vt Q, ad R.</s>
            <s xml:id="echoid-s11890" xml:space="preserve">
              <note symbol="m" position="right" xlink:label="note-287-12" xlink:href="note-287-12a" xml:space="preserve">1. ſexti.</note>
            quod erat faciendum.</s>
            <s xml:id="echoid-s11891" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11892" xml:space="preserve">
              <emph style="sc">Non</emph>
            alia ratione problema abſoluemus, ſi antecedens proportionis </s>
          </p>
        </div>
      </text>
    </echo>
Impressum