Clavius, Christoph, Geometria practica

Table of handwritten notes

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              <pb o="202" file="232" n="232" rhead="GEOMETR. PRACT."/>
            duplicatæ proportionis, quam videlicet circulus, vel figura ad minorem habet
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            Vt ſi diameter vnius circuli ſit 56. </s>
            <s xml:id="echoid-s8992" xml:space="preserve">& </s>
            <s xml:id="echoid-s8993" xml:space="preserve">circumſerentia 176. </s>
            <s xml:id="echoid-s8994" xml:space="preserve">Alterius autem circuli
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            diameter 14.</s>
            <s xml:id="echoid-s8995" xml:space="preserve">| & </s>
            <s xml:id="echoid-s8996" xml:space="preserve">| circumferentia 44. </s>
            <s xml:id="echoid-s8997" xml:space="preserve">Diuiſis 56. </s>
            <s xml:id="echoid-s8998" xml:space="preserve">per 14. </s>
            <s xml:id="echoid-s8999" xml:space="preserve">vel 176. </s>
            <s xml:id="echoid-s9000" xml:space="preserve">per 44. </s>
            <s xml:id="echoid-s9001" xml:space="preserve">fit Quo-
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            tiens 4. </s>
            <s xml:id="echoid-s9002" xml:space="preserve">qui ductus in ſe producit 16. </s>
            <s xml:id="echoid-s9003" xml:space="preserve">denominatorem proportionis maioris cir-
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            culi ad minorem. </s>
            <s xml:id="echoid-s9004" xml:space="preserve">Eandemque proportionem habebitfigura ad minorem ſimi-
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            lem, ſimiliter que poſitam, ſi latera homologa ſint 56. </s>
            <s xml:id="echoid-s9005" xml:space="preserve">& </s>
            <s xml:id="echoid-s9006" xml:space="preserve">14. </s>
            <s xml:id="echoid-s9007" xml:space="preserve">vel 176. </s>
            <s xml:id="echoid-s9008" xml:space="preserve">& </s>
            <s xml:id="echoid-s9009" xml:space="preserve">44.</s>
            <s xml:id="echoid-s9010" xml:space="preserve"/>
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        <div xml:id="echoid-div549" type="section" level="1" n="198">
          <head xml:id="echoid-head211" xml:space="preserve">IV.</head>
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            <s xml:id="echoid-s9011" xml:space="preserve">DATIS pluribus circulis, quorum diametri, vel circumferentiæ co-
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            gnitæ ſint: </s>
            <s xml:id="echoid-s9012" xml:space="preserve">Item pluribus figuris ſimilibus ſimiliterque poſitis, quarũ
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            latera homologa ſint nota: </s>
            <s xml:id="echoid-s9013" xml:space="preserve">Inuenire diametrum, vel circumferenti-
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            am, cuius circulus omnibus circulis propoſitis æqualis ſit. </s>
            <s xml:id="echoid-s9014" xml:space="preserve">Item latus
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            reperire, cuius figura ſimilis, ſimiliterque poſita æqualis ſit omnibus
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            propoſitis figuris.</s>
            <s xml:id="echoid-s9015" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s9016" xml:space="preserve">
              <emph style="sc">Mvltiplicentvr</emph>
            diametri, vel circumferentiæ, aut latera homologa
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            in ſe, & </s>
            <s xml:id="echoid-s9017" xml:space="preserve">numeri producti in vnam ſummam colligantur. </s>
            <s xml:id="echoid-s9018" xml:space="preserve">Radix enim quadrata
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            huius ſummæ erit diameter, circumferentiaue, aut latus homologum quæſitum.
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            </s>
            <s xml:id="echoid-s9019" xml:space="preserve">Verbigratia, ſi ſint quatuor diametri, circumferentiæue circulorum, autlatera
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            homologa ſimilium figurarum, ſimiliter que poſitarum, 84. </s>
            <s xml:id="echoid-s9020" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9021" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9022" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9023" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s9024" xml:space="preserve">in ſe mul-
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            tiplicentur, gignentur numeri 7056. </s>
            <s xml:id="echoid-s9025" xml:space="preserve">9. </s>
            <s xml:id="echoid-s9026" xml:space="preserve">16. </s>
            <s xml:id="echoid-s9027" xml:space="preserve">144. </s>
            <s xml:id="echoid-s9028" xml:space="preserve">quorum ſumma 7225. </s>
            <s xml:id="echoid-s9029" xml:space="preserve">Radix er-
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            go quadrata huius ſummæ 85. </s>
            <s xml:id="echoid-s9030" xml:space="preserve">erit diameter, circumferentiaue circuli, aut latus
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            homologum, quod quæritur: </s>
            <s xml:id="echoid-s9031" xml:space="preserve">ita vt circulus, cuius diameter, vel circumferen-
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            tia eſt 85. </s>
            <s xml:id="echoid-s9032" xml:space="preserve">autfigura ſupra rectam 85. </s>
            <s xml:id="echoid-s9033" xml:space="preserve">ſimilis, ſimiliterq; </s>
            <s xml:id="echoid-s9034" xml:space="preserve">poſita figuris datis, æqua-
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            lis ſit quatuor circulis, aut figuris propoſitis. </s>
            <s xml:id="echoid-s9035" xml:space="preserve">Nam cum quadratum 7225. </s>
            <s xml:id="echoid-s9036" xml:space="preserve">radicis
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              <note symbol="a" position="left" xlink:label="note-232-01" xlink:href="note-232-01a" xml:space="preserve">2. duodec.</note>
            85. </s>
            <s xml:id="echoid-s9037" xml:space="preserve">æquale ſit quatuor quadratis 7056. </s>
            <s xml:id="echoid-s9038" xml:space="preserve">9. </s>
            <s xml:id="echoid-s9039" xml:space="preserve">16. </s>
            <s xml:id="echoid-s9040" xml:space="preserve">144. </s>
            <s xml:id="echoid-s9041" xml:space="preserve">radicũ 84. </s>
            <s xml:id="echoid-s9042" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9043" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9044" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9045" xml:space="preserve"> Circuli au- tem eandem habeant proportionem, quam quadrata diametrorum: </s>
            <s xml:id="echoid-s9046" xml:space="preserve">ac proin-
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            de quam quadrata circumferẽtiarum; </s>
            <s xml:id="echoid-s9047" xml:space="preserve">quod circumferentiæ diametris ſint pro-
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            portionales. </s>
            <s xml:id="echoid-s9048" xml:space="preserve">Item figuræ ſimiles, ſimiliter que poſitæ inter ſe ſint, vt quadrata
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            laterum homologorum, propterea quod tam quadrata, quam figuræ
              <note symbol="b" position="left" xlink:label="note-232-02" xlink:href="note-232-02a" xml:space="preserve">20. ſexti.</note>
            duplicatam proportionem laterum: </s>
            <s xml:id="echoid-s9049" xml:space="preserve">erit quo que tam circulus, cuius diameter,
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            circumferentiauẽ 85. </s>
            <s xml:id="echoid-s9050" xml:space="preserve">æqualis quatuor circulis, quorum diametri circumferen-
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            tiæue 84. </s>
            <s xml:id="echoid-s9051" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9052" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9053" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9054" xml:space="preserve">quam figura ſupra latus 85. </s>
            <s xml:id="echoid-s9055" xml:space="preserve">ſimilis ſimiliter que poſita, quatuor
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            figuris, quarum lateta 84. </s>
            <s xml:id="echoid-s9056" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9057" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9058" xml:space="preserve">12. </s>
            <s xml:id="echoid-s9059" xml:space="preserve">æqualis, quod eſt propoſitum.</s>
            <s xml:id="echoid-s9060" xml:space="preserve"/>
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        <div xml:id="echoid-div551" type="section" level="1" n="199">
          <head xml:id="echoid-head212" xml:space="preserve">V.</head>
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            <s xml:id="echoid-s9061" xml:space="preserve">AREAM propoſitæ Elipſis indagare.</s>
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            <s xml:id="echoid-s9063" xml:space="preserve">
              <emph style="sc">Lvbet</emph>
            denique librum hunc quartum duobus problematibus terminare,
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            quæ ab Archimede Syracuſano accutiſsimè inuenta ſunt, ac demonſtrata. </s>
            <s xml:id="echoid-s9064" xml:space="preserve">Vnũ
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            eſt de area Ellipſis; </s>
            <s xml:id="echoid-s9065" xml:space="preserve">alterum de area Parabolæ. </s>
            <s xml:id="echoid-s9066" xml:space="preserve">Sit ergo Ellipſis A B C D, cuius
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            maior diameter BD, & </s>
            <s xml:id="echoid-s9067" xml:space="preserve">minor AC, ſecans maiorem in E, bifariam. </s>
            <s xml:id="echoid-s9068" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-232-03" xlink:href="note-232-03a" xml:space="preserve">13. ſexti.</note>
            HI, media proportionalis inter BD, & </s>
            <s xml:id="echoid-s9069" xml:space="preserve">AC: </s>
            <s xml:id="echoid-s9070" xml:space="preserve">& </s>
            <s xml:id="echoid-s9071" xml:space="preserve">circuli circa diametrum HI, deſcri-
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            pti area in quiratur, per ea, quæ c. </s>
            <s xml:id="echoid-s9072" xml:space="preserve">7. </s>
            <s xml:id="echoid-s9073" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s9074" xml:space="preserve">ſcripſimus. </s>
            <s xml:id="echoid-s9075" xml:space="preserve">Dico hanc aream </s>
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