Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

Table of Notes

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            <s xml:id="echoid-s2459" xml:space="preserve">
              <pb o="75" file="527.01.075" n="75" rhead="*DE* S*TATICÆ PRINCIPIIS*."/>
            ſolidi ex inſcriptis cylindris compoſiti à dato minus erit. </s>
            <s xml:id="echoid-s2460" xml:space="preserve">Itaque infinita hac in-
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            ſcriptione tandem eò adſcenditur ut ſolidum factitium à conoïdali abl
              <unsure/>
            it diffe-
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            rentiâ, quæ ſolido dato quocunque minor ſit, cui conſequens eſt AD dati co-
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            noïdalis gravitatis eſſe diametrum, itaque gravitas ſitus unius lateris à gravita-
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            te lateris alterius minus aberit, quam vel minimi ponderis differentiâ. </s>
            <s xml:id="echoid-s2461" xml:space="preserve">Quod
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            legittimo ſyllogiſmi judicio ita concludam.</s>
            <s xml:id="echoid-s2462" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s2463" xml:space="preserve">Ponderum ſitu gravium differentiâ minus pondus dari poteſt.
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            </s>
            <s xml:id="echoid-s2464" xml:space="preserve">Sed borum ſegmentorum ſitu gravium differentiâ pondus minus nullu dari poteſt. </s>
            <s xml:id="echoid-s2465" xml:space="preserve">
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            Itaque borum conoïdalis ſegmentorum ſitu gravium differentia nullaeſt.</s>
            <s xml:id="echoid-s2466" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2467" xml:space="preserve">Et AD gravitatis erit diameter. </s>
            <s xml:id="echoid-s2468" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2469" xml:space="preserve">Quamobrem conoïda-
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            lis gravitatis centrum eſt in axe. </s>
            <s xml:id="echoid-s2470" xml:space="preserve">quod demonſtraſſe oportuit.</s>
            <s xml:id="echoid-s2471" xml:space="preserve"/>
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        <div xml:id="echoid-div358" type="section" level="1" n="255">
          <head xml:id="echoid-head269" xml:space="preserve">10 PROBLEMA. 23 PROPOSITIO.</head>
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            <s xml:id="echoid-s2472" xml:space="preserve">Conoïdalis gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2473" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2474" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2475" xml:space="preserve">ABC conoïdale, A vertex, AD axis.</s>
            <s xml:id="echoid-s2476" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2477" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2478" xml:space="preserve">Gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2479" xml:space="preserve"/>
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        <div xml:id="echoid-div359" type="section" level="1" n="256">
          <head xml:id="echoid-head270" xml:space="preserve">CONSTRVCTIO.</head>
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            <s xml:id="echoid-s2480" xml:space="preserve">A D axis ſecetur in E ratione dupla videlicet ut ſegmentum vertici conter-
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            minum reliqui ſit duplum, ajo E eſſe centrum quæſitum cujus demonſtrario-
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            nem ſolers & </s>
            <s xml:id="echoid-s2481" xml:space="preserve">ſubtilis Mathematicus Fredericus Commandinus de ſolidorũ cen-
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            trobaricis propoſ. </s>
            <s xml:id="echoid-s2482" xml:space="preserve">29 exhibet, quæ noſtro more & </s>
            <s xml:id="echoid-s2483" xml:space="preserve">modo digeſta ita habet.</s>
            <s xml:id="echoid-s2484" xml:space="preserve"/>
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          <head xml:id="echoid-head271" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s2485" xml:space="preserve">Conoïdale ſecetur plano FG axem in H biſecante, baſiq́ue BC parallelo,
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            atque planiſecantis & </s>
            <s xml:id="echoid-s2486" xml:space="preserve">ſuperficiei ſectio eſto in I, K, deinde BCGF, IKLM
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            cylindri circa conoïdale circumſcribantur, quorum gravitatis centra N, O:
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            </s>
            <s xml:id="echoid-s2487" xml:space="preserve">præterea intra ipſum cylindri IKPQ inſcripti O itidem gravitatis erit centrũ. </s>
            <s xml:id="echoid-s2488" xml:space="preserve">
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            Cum per 20 prop. </s>
            <s xml:id="echoid-s2489" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s2490" xml:space="preserve">Apoll. </s>
            <s xml:id="echoid-s2491" xml:space="preserve">& </s>
            <s xml:id="echoid-s2492" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2493" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s2494" xml:space="preserve">12. </s>
            <s xml:id="echoid-s2495" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2496" xml:space="preserve">
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              <figure xlink:label="fig-527.01.075-01" xlink:href="fig-527.01.075-01a" number="122">
                <image file="527.01.075-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.075-01"/>
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            Eucl. </s>
            <s xml:id="echoid-s2497" xml:space="preserve">igitur ſit ut DA ad AH videlicet 2
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            ad 1, ſic circulus BC ad circulũ IK, etiam
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            cylindri BC ad cylindrum IL (propter æ-
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            qualĕ altitudinem) ratio dupla erit, quam
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            obrem ſi BG 2 librarum ſtatu@ur IL erit
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            1 libræ, ſed centra gravitatis ſunt N, O,
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            ideoq́ue NO jugo in R ſecto ut NR
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            radii RO duplus ſit, ipſum circumſcripto-
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            rum cylindrorum gravitatis erit centrum,
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            ſed & </s>
            <s xml:id="echoid-s2498" xml:space="preserve">O inſcripti cylindri eſt centrum, E verò ab O & </s>
            <s xml:id="echoid-s2499" xml:space="preserve">ab R eodem intervallo
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            diſtat, videlicet {1/12} totius AD. </s>
            <s xml:id="echoid-s2500" xml:space="preserve">Acſimilis erit cæterorum ſimilium paradigma-
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            r
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            um eventus. </s>
            <s xml:id="echoid-s2501" xml:space="preserve">Verumenimverò quo res ſit manifeſtior, altero exemplo idem ex-
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            plicabimus.</s>
            <s xml:id="echoid-s2502" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2503" xml:space="preserve">Denuò iſta axis biſegmenta AH, HD, bifariam dividantur, unde tres cy-
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            lindri inſcribantur & </s>
            <s xml:id="echoid-s2504" xml:space="preserve">quatuor circumſcribantur, ut in ſecundo diagrammate
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            ubi AD conoïdalis axis ſit, centra verò cylindrorum I, K, L, M, AE verò
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            dupla ſit ipſius ED ut ſupra. </s>
            <s xml:id="echoid-s2505" xml:space="preserve">Itaque cum ſit ut AD ad AN (nempe ut 4 ad 3)
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            ſic circulus BC ad circulum OP, erit quoque cylindrus BF ad OQ in </s>
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