Clavius, Christoph, Geometria practica

Table of contents

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[191.] II. EX diametro aream circuli vera minorem inueſtigare.
[192.] III. EX circumferentia aream circuli vera maiorem colligere.
[193.] IV. EX circumferentia aream circuli vera minorem concludere.
[194.] DE AREA SEGMENTORVM CIRCVLI. Capvt VIII.
[196.] II.
[197.] III.
[198.] IV.
[200.] VI.
[201.] FINIS LIBRI QVARTI.
[202.] GEOMETRIÆ PRACTICÆ LIBER QVINTVS.
[203.] AREAS Solidorum, corporumue perſcrutans.
[204.] DE AREA PARALLELEPIP EDO-rum, Priſmatum, & Cylindrorum. Capvt I.
[205.] DE AREA PYRAMIDVM & Conorum. Capvt II.
[206.] DL AREA FRVSTI PYRA-midis, & Coni. Capvt III.
[207.] SCHOLIVM.
[208.] DE AREA QVINQVE COR-porum regularium. Capvt IV.
[209.] Capvt V.
[210.] PROPOSITIO I.
[211.] COROLLARIVM.
[212.] PROPOSITIO II.
[213.] COROLLARIVM.
[214.] PROPOSITIO III.
[215.] COROLLARIVM.
[216.] PROPOSITIO IV.
[217.] PROPOSITIO V.
[218.] PROPOSITIO VI.
[219.] PROPOSITIO VII.
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          <p>
            <s xml:id="echoid-s9809" xml:space="preserve">
              <pb o="218" file="248" n="248" rhead="GEOMETR. PRACT."/>
            in triangulo inclinato, & </s>
            <s xml:id="echoid-s9810" xml:space="preserve">lateri @coſaedri inter angulum ſupremum pentagoni
              <lb/>
            prædicti, & </s>
            <s xml:id="echoid-s9811" xml:space="preserve">angulum trianguli inclinati. </s>
            <s xml:id="echoid-s9812" xml:space="preserve">Ex quo fit, punctump, in plano ſupre@
              <lb/>
              <figure xlink:label="fig-248-01" xlink:href="fig-248-01a" number="160">
                <image file="248-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/248-01"/>
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            mæ baſis exiſtere: </s>
            <s xml:id="echoid-s9813" xml:space="preserve">ac ꝓinde perpendicularem p q, ad planũ baſis per m n, du-
              <lb/>
            ctũ demiſſam, æqualẽ eſſe altitudini Icoſaedri, eiuſq; </s>
            <s xml:id="echoid-s9814" xml:space="preserve">ſemiſſem r q, altitudini v-
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            nius pyramidis trigoni eſſe æqualem. </s>
            <s xml:id="echoid-s9815" xml:space="preserve">Quæ omnia facilè percipientur, ſi adhibe-
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            atur materiale aliquod Icoſaedrum. </s>
            <s xml:id="echoid-s9816" xml:space="preserve">Inuenta porrò hocmodo altitudine pyra-
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            midis, cognoſcenda eadem ſumma diligentia e@it, beneficio inſtrumentiparti-
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            um, in partibus lateris corporis regularis propoſiti.</s>
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          </p>
          <p>
            <s xml:id="echoid-s9818" xml:space="preserve">DE AREA SPHÆRÆ, INVENTIONE-
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            que ſuperficiei conuexæ eiuſdem ſphæræ.</s>
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        <div xml:id="echoid-div599" type="section" level="1" n="209">
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            <emph style="sc">Capvt</emph>
          V.</head>
          <p>
            <s xml:id="echoid-s9820" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9821" xml:space="preserve">VT ſphæræ aream, ſoliditatemue pluribus poſsimus vijs aſſequi, demõ-
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            ſtranda prius erunt nonnulla ad eamrem valdè neceſſaria, atq; </s>
            <s xml:id="echoid-s9822" xml:space="preserve">vtilia.
              <lb/>
            </s>
            <s xml:id="echoid-s9823" xml:space="preserve">quodſequentibus 7. </s>
            <s xml:id="echoid-s9824" xml:space="preserve">propoſitionibus effi ciemus.</s>
            <s xml:id="echoid-s9825" xml:space="preserve"/>
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          <head xml:id="echoid-head227" xml:space="preserve">PROPOSITIO I.</head>
          <p>
            <s xml:id="echoid-s9826" xml:space="preserve">QVAM proportionem habent duæ quælibet partes aliquotæ magni-
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            tudinis cuiuſcunque, eandem habent duæ ſimiles partes alterius cu-
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            iuſuis magnitudinis.</s>
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              <emph style="sc">Sit</emph>
            enim A, eadem pars magnitudinis B, quæ C, magnitudinis D: </s>
            <s xml:id="echoid-s9829" xml:space="preserve">Item E,
              <lb/>
              <figure xlink:label="fig-248-02" xlink:href="fig-248-02a" number="161">
                <image file="248-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/248-02"/>
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            eadẽ pars magnitudinis B, quæ F, ma-
              <lb/>
            g@itudinis D. </s>
            <s xml:id="echoid-s9830" xml:space="preserve">Dico eſſe, vt A, ad E, ita
              <lb/>
            C, ad F, Quoniam enim eſt, vt A, ad B,
              <lb/>
            ita C, ad D, quod vtrobiq@ eadem pro-
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            portio ſubmultiplex poſita ſit. </s>
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