Clavius, Christoph, Geometria practica

Table of contents

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[211.] COROLLARIVM.
Page: 249 (219)
[212.] PROPOSITIO II.
Page: 249 (219)
[213.] COROLLARIVM.
Page: 249 (219)
[214.] PROPOSITIO III.
Page: 250 (220)
[215.] COROLLARIVM.
Page: 250 (220)
[216.] PROPOSITIO IV.
Page: 251 (221)
[217.] PROPOSITIO V.
Page: 251 (221)
[218.] PROPOSITIO VI.
Page: 251 (221)
[219.] PROPOSITIO VII.
Page: 252 (222)
[220.] I.
Page: 253 (223)
[221.] II.
Page: 253 (223)
[222.] ALITER.
Page: 255 (225)
[223.] ALITER.
Page: 255 (225)
[224.] I.
Page: 256 (226)
[225.] II.
Page: 257 (227)
[226.] III.
Page: 257 (227)
[227.] IIII.
Page: 257 (227)
[228.] I.
Page: 258 (228)
[229.] II.
Page: 258 (228)
[230.] III.
Page: 258 (228)
[231.] IIII.
Page: 258 (228)
[232.] DE AREA SEGMENTO-rum ſphæræ. Capvt VI.
Page: 259 (229)
[233.] ALITER.
Page: 261 (231)
[234.] DE AREA SPHÆROIDIS, EIVSDEM-que portionum. Capvt VII.
Page: 262 (232)
[235.] DE AREA CONOIDIS parabolici. Capvt VIII.
Page: 262 (232)
[236.] DE AREA CONOIDIS Hyperbolici. Capvt IX.
Page: 263 (233)
[237.] DE AREA DOLIORVM. Capvt X.
Page: 263 (233)
[238.] DE AREA CORPORVM. omnino irregularium. Capvt XI.
Page: 264 (234)
[239.] DE SVPERFICIE CONVEXA coni & cylindri recti. Capvt XII.
Page: 265 (235)
[240.] FINIS LIBRI QVINTI.
Page: 265 (235)
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              <pb o="182" file="212" n="212" rhead="GEOMETR. PRACT."/>
            dubitamus etiam, quin res hæc ſtudioſo lectorigrata, ac iucunda ſit futura.</s>
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          <head xml:id="echoid-head184" xml:space="preserve">PROPOSITIO I.</head>
          <p>
            <s xml:id="echoid-s7713" xml:space="preserve">AREA cuiuslibet circuli æqualis eſt triangulo rectangulo, cuius vnum
              <lb/>
            quidem latus circa angulum rectum ſemidiametro circuli, alterũ ve-
              <lb/>
            rò peripheriæ eiuſdem circuli æquale eſt.</s>
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          </p>
          <p>
            <s xml:id="echoid-s7715" xml:space="preserve">
              <emph style="sc">Sit</emph>
            circulus ABCD, cuius centrum E, ſemidiameter EA: </s>
            <s xml:id="echoid-s7716" xml:space="preserve">ſitque triangulum
              <lb/>
            rectangulum FGH, angulum habens rectum G, latus verò F G, ſemidiametro
              <lb/>
            circuli EA, & </s>
            <s xml:id="echoid-s7717" xml:space="preserve">latus GH, peripheriæ eiuſdem circuli æquale. </s>
            <s xml:id="echoid-s7718" xml:space="preserve">Dico circulum AB-
              <lb/>
            CD, triangulo FGH, æqualem eſſe. </s>
            <s xml:id="echoid-s7719" xml:space="preserve">Si enim dicatur non eſſe æqualis, ſit primũ,
              <lb/>
            ſi fieri poteſt, circulus maior quam triangulum, magnitu dinez: </s>
            <s xml:id="echoid-s7720" xml:space="preserve">adeo vt circulus
              <lb/>
            æqualis ſit triangulo, & </s>
            <s xml:id="echoid-s7721" xml:space="preserve">magnitudiniz. </s>
            <s xml:id="echoid-s7722" xml:space="preserve">ſimul; </s>
            <s xml:id="echoid-s7723" xml:space="preserve">propterea que maior, quam z. </s>
            <s xml:id="echoid-s7724" xml:space="preserve">Si
              <lb/>
            igitur ex circulo auferatur plus, quàm dimidium, & </s>
            <s xml:id="echoid-s7725" xml:space="preserve">à reſiduo plus etiam, quam
              <lb/>
            dimidium, & </s>
            <s xml:id="echoid-s7726" xml:space="preserve">ita deinceps: </s>
            <s xml:id="echoid-s7727" xml:space="preserve"> relinquetur tandem magnitudo minor, quam z.</s>
            <s xml:id="echoid-s7728" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-212-01" xlink:href="note-212-01a" xml:space="preserve">1. decimi.</note>
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          <p style="it">
            <s xml:id="echoid-s7729" xml:space="preserve">Hæc autem detractio continua fiet, ſi primo loco auferatur ex circulo quadr atum in-
              <lb/>
            ſcriptum A B C D. </s>
            <s xml:id="echoid-s7730" xml:space="preserve">Hoc enim cum dimidium ſit quadrati I K L M, circulo circumſcri-
              <lb/>
            pti, vt in ſchol. </s>
            <s xml:id="echoid-s7731" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s7732" xml:space="preserve">9. </s>
            <s xml:id="echoid-s7733" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7734" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7735" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s7736" xml:space="preserve">oſtendim{us}: </s>
            <s xml:id="echoid-s7737" xml:space="preserve">circul{us} autem ipſi{us} quadrati I K L M,
              <lb/>
            pars ſit: </s>
            <s xml:id="echoid-s7738" xml:space="preserve">erit quadratum inſcriptum A B C D mai{us} quam dimidium circuli. </s>
            <s xml:id="echoid-s7739" xml:space="preserve">Deinde ſi
              <lb/>
            auferantur à
              <unsure/>
            reſiduis quatuor ſegmentis quatuor triangula Iſoſcelia AOB, BPC, CQD,
              <lb/>
            DNA, ductis rectis ad media puncta arcuum. </s>
            <s xml:id="echoid-s7740" xml:space="preserve">Hæc enim ſimul maiora ſunt, quam di-
              <lb/>
              <figure xlink:label="fig-212-01" xlink:href="fig-212-01a" number="133">
                <image file="212-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/212-01"/>
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            midium quatuor ſegmentorum ſimul, cum vnum quod
              <lb/>
            mai{us} ſit, quam dimidium ſegmenti, in quo exiſtit. </s>
            <s xml:id="echoid-s7741" xml:space="preserve">Com-
              <lb/>
            pleto enim rectangulo A R, erit ei{us} dimidium
              <note symbol="b" position="left" xlink:label="note-212-02" xlink:href="note-212-02a" xml:space="preserve">41. primi.</note>
            lum A N D: </s>
            <s xml:id="echoid-s7742" xml:space="preserve">ac proinde idem triangulum mai{us} erit
              <lb/>
            quam dimidium ſegmenti A N D. </s>
            <s xml:id="echoid-s7743" xml:space="preserve">Eademque ratio est
              <lb/>
            de aliis. </s>
            <s xml:id="echoid-s7744" xml:space="preserve">Pari ratione, ſi à reſiduis octo ſegmentis aufe-
              <lb/>
            rantur octo alia triangula Iſoſcelia in illis conſtituta, &</s>
            <s xml:id="echoid-s7745" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s7746" xml:space="preserve">atque ita deinceps.</s>
            <s xml:id="echoid-s7747" xml:space="preserve"/>
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            <image file="212-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/212-02"/>
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            <s xml:id="echoid-s7748" xml:space="preserve">Ponantur ergo iam octo ſegmenta A O, O B, B P, P C, C Q, Q D, D N, N A,
              <lb/>
            relicta eſſe minora magnitudine z. </s>
            <s xml:id="echoid-s7749" xml:space="preserve">& </s>
            <s xml:id="echoid-s7750" xml:space="preserve">quoniam circulus æqualis conceditur tri-
              <lb/>
            angulo F G H, & </s>
            <s xml:id="echoid-s7751" xml:space="preserve">magnitudiniz, ſimul: </s>
            <s xml:id="echoid-s7752" xml:space="preserve">ſi demantur inæqualia@, nimirum iſta ſe-
              <lb/>
            gmenta ex circulo, & </s>
            <s xml:id="echoid-s7753" xml:space="preserve">magnitudo z, ex aggregato trianguli cum z, reliqua erit
              <lb/>
            figura inſcripta, Octo gona videlicet, maior triangulo F G H, quod eſt abſu@ dũ,
              <lb/>
            quippe cum multo minor ſit. </s>
            <s xml:id="echoid-s7754" xml:space="preserve">Sinamque ex centro E, ad latus B O, ducatur
              <lb/>
            perpendicularis E T, & </s>
            <s xml:id="echoid-s7755" xml:space="preserve">in triangulo ſumatur G K, ipſi E T, & </s>
            <s xml:id="echoid-s7756" xml:space="preserve">recta G i, </s>
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