Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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              <pb o="475" file="0195" n="205" rhead="AD RESP. JAC. GREG."/>
            ctum quam præcedentem {16c + 2d - 3a/15}, ſequetur, cubum c - a non
              <unsure/>
              <lb/>
            fore majorem nihilo, & </s>
            <s xml:id="echoid-s4256" xml:space="preserve">c non majorem quam a contra hypo-
              <lb/>
            theſin, uti facile videre eſt per calculum analyticum, obſervan-
              <lb/>
            do quod d ſit = {cc/a}.</s>
            <s xml:id="echoid-s4257" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4258" xml:space="preserve">Poſſunt etiam a & </s>
            <s xml:id="echoid-s4259" xml:space="preserve">c ſumi pro circumferentiis Polygono-
              <lb/>
            rum inſcriptorum, quorum unum ſubduplum laterum ha-
              <lb/>
            bet numerum; </s>
            <s xml:id="echoid-s4260" xml:space="preserve">Et tum terminus a + {10cc - 10aa/6c + 9a} eſt longitu-
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            do circumferentiæ Circuli, aut arcus ſectoris parum admo-
              <lb/>
            dum excedens, ut ſi notarum triens in a & </s>
            <s xml:id="echoid-s4261" xml:space="preserve">c ſit eadem, er-
              <lb/>
            ror dari non poterit niſi in ultima nota, & </s>
            <s xml:id="echoid-s4262" xml:space="preserve">ſæpius nequi-
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            dem in quatuor vel quinque notis ſequentibus ultra illas quæ
              <lb/>
            dantur in numeris a vel c.</s>
            <s xml:id="echoid-s4263" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4264" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s4265" xml:space="preserve">ut illi, qui contem plationes has negligunt, tamen
              <lb/>
            quid commodi ex noſtra controverſia capiant, addam hic
              <lb/>
            Geometricam conſtructionem ex ultimâ approximatione
              <lb/>
            deductam qua invenitur longitudo arcus Circuli dati adeo
              <lb/>
            acurata quam ad uſum deſideratur.</s>
            <s xml:id="echoid-s4266" xml:space="preserve"/>
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            <s xml:id="echoid-s4267" xml:space="preserve">Sit arcus Circuli, qui non excedat ſemicircumferentiam
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              <note position="right" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">TAB. XLIV.
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              fig. 3.</note>
            A B C, cujus ſubtenſa ſit A C; </s>
            <s xml:id="echoid-s4268" xml:space="preserve">dividat hanc ut & </s>
            <s xml:id="echoid-s4269" xml:space="preserve">arcum in duas
              <lb/>
            partes æquales linea B D.</s>
            <s xml:id="echoid-s4270" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4271" xml:space="preserve">Ducta ſubtenſa A B ſumantur ejus {2/3} & </s>
            <s xml:id="echoid-s4272" xml:space="preserve">ponantur ab A ad E
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            in producta lineâ C D; </s>
            <s xml:id="echoid-s4273" xml:space="preserve">tum diminuta D E decimâ parte E F,
              <lb/>
            ducatur F B, & </s>
            <s xml:id="echoid-s4274" xml:space="preserve">tandem ipſi perpendicularis B G. </s>
            <s xml:id="echoid-s4275" xml:space="preserve">Erit linea
              <lb/>
            A G æqualis arcui A B, vel dupla linea æqualis arcui A B C,
              <lb/>
            quæ tam parum excedet, ut tunc etiam, quum arcus erit æ-
              <lb/>
            qualis ſemicircumferentiæ Circuli exceſſus non ſit {1/1400}. </s>
            <s xml:id="echoid-s4276" xml:space="preserve">lon-
              <lb/>
            gitudinis; </s>
            <s xml:id="echoid-s4277" xml:space="preserve">ſed ſi tantum ſit {1/3} circumferentiæ, differentia non erit
              <lb/>
            {1/13000}, ſi autem arcus tantum ſit pars quarta circumferentiæ er-
              <lb/>
            ror non erit {1/90000} longitudinis.</s>
            <s xml:id="echoid-s4278" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4279" xml:space="preserve">Poſſem hic addere approximationem & </s>
            <s xml:id="echoid-s4280" xml:space="preserve">conſtructionem
              <lb/>
            omnino ſimilem pro quadratura Hyperboles, paulo magis
              <lb/>
            accedentem ad veram quam media Arithmetica D
              <emph style="super">ni</emph>
            . </s>
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