Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of figures

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        <div xml:id="echoid-div220" type="section" level="1" n="74">
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              <pb o="84" file="120" n="121" rhead="Comment. in I. Cap. Sphæræ"/>
            diculari, & </s>
            <s xml:id="echoid-s4203" xml:space="preserve">medietate baſis A B, (ꝑ 1. </s>
            <s xml:id="echoid-s4204" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4205" xml:space="preserve">huius) æquale eſt triangulo A B G;
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            </s>
            <s xml:id="echoid-s4206" xml:space="preserve">ſi ſumantur tot huiuſmodi rectangula, in quot triangula diuiſa eſt figura regu-
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            laris, erunt omnia ſimul ſiguræ A B C D E F, æqualia; </s>
            <s xml:id="echoid-s4207" xml:space="preserve">propterea quòd omnia
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            triangula oſtenſa ſint æqualia triangulo A B G. </s>
            <s xml:id="echoid-s4208" xml:space="preserve">Cum igitur eadem ſimul æ-
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            qualia ſint rectangulo I K L M; </s>
            <s xml:id="echoid-s4209" xml:space="preserve">propterea quòd K L, æqualis ponitur dimidio
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            ambitus A B C D E F, hoc eſt, omnibus medietatibus baſium ſimul, & </s>
            <s xml:id="echoid-s4210" xml:space="preserve">recta
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            I K, perpendiculari G H; </s>
            <s xml:id="echoid-s4211" xml:space="preserve">erit figura regularis A B C D E F, æqualis rectangu
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            lo I K L M. </s>
            <s xml:id="echoid-s4212" xml:space="preserve">Area igitur cuiuslibet figuræ regularis æqualis eſt, &</s>
            <s xml:id="echoid-s4213" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4214" xml:space="preserve">quod erat
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            demonſtrandum.</s>
            <s xml:id="echoid-s4215" xml:space="preserve"/>
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        <div xml:id="echoid-div223" type="section" level="1" n="75">
          <head xml:id="echoid-head79" style="it" xml:space="preserve">THEOR. 3. PROPOS. 3.</head>
          <note position="left" xml:space="preserve">Regularis
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          figura quæ
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          cunque cui
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          triangulo
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          rectangulo
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          æqualis ſit.</note>
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              <emph style="sc">Area</emph>
            cuiuslibet figuræregularis æqualis eſt triangulo rectangulo,
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            cuius unum latus circa angulum rectum æquale eſt perpendiculari à centro
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            figuræ ad unum latus ductæ, alterum uero æquale ambitui eiuſdem figuræ.</s>
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              <emph style="sc">Sit</emph>
            rurſus figura regularis A B C, cuius centrum D, à quo perpendicula-
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            ris ad latus A B, ducta ſit D E; </s>
            <s xml:id="echoid-s4219" xml:space="preserve">triangulum uero rectangulum D E F, habens
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              <figure xlink:label="fig-120-01" xlink:href="fig-120-01a" number="21">
                <image file="120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/120-01"/>
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            angulum E, rectum, & </s>
            <s xml:id="echoid-s4220" xml:space="preserve">latus D E, æquale perpendiculari D E, latus autẽ E F,
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            æquale ambitui figuræ A B C. </s>
            <s xml:id="echoid-s4221" xml:space="preserve">Dico triangulum D E F, figuræ A B C, æquale
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            eſſe. </s>
            <s xml:id="echoid-s4222" xml:space="preserve">Compleatur enim rectangulum D E F G; </s>
            <s xml:id="echoid-s4223" xml:space="preserve">& </s>
            <s xml:id="echoid-s4224" xml:space="preserve">diuiſa E F, bifa@iam in pun-
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            cto H, ducatur H I, æquidiſtans rectæ D E. </s>
            <s xml:id="echoid-s4225" xml:space="preserve">Erit igitur (per 2. </s>
            <s xml:id="echoid-s4226" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4227" xml:space="preserve">huius)
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            rectangulum D E H I, contentum ſub D E, perpendiculari, & </s>
            <s xml:id="echoid-s4228" xml:space="preserve">ſub E H, dimi-
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            dio ambitus figuræ, æquale figuræ A B C: </s>
            <s xml:id="echoid-s4229" xml:space="preserve">At rectangulo D E H I, æquale eſt
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            triangulum D E F. </s>
            <s xml:id="echoid-s4230" xml:space="preserve">Nam rectangulum D E H I, eſt dimidium rectanguli
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            D E F G; </s>
            <s xml:id="echoid-s4231" xml:space="preserve">propterea quod æqualia ſunt rectangula D E H I, I H F G; </s>
            <s xml:id="echoid-s4232" xml:space="preserve">Triangu-
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              <note position="left" xlink:label="note-120-02" xlink:href="note-120-02a" xml:space="preserve">38
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              . primi.</note>
            lum quoque D E F, dimidium eſt eiuſdem rectanguli D E F G. </s>
            <s xml:id="echoid-s4233" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s4234" xml:space="preserve">trian-
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              <note position="left" xlink:label="note-120-03" xlink:href="note-120-03a" xml:space="preserve">41. primi.</note>
            gulum D E F, æquale erit figuræ A B C. </s>
            <s xml:id="echoid-s4235" xml:space="preserve">Area ergo cuiuslibet figuræ regula
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            ris æqualis eſt triangulo rectangulo, &</s>
            <s xml:id="echoid-s4236" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4237" xml:space="preserve">quod demonſtrandum erat.</s>
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