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

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          <pb o="359" file="0067" n="71" rhead="DE CIRCULI MAGNIT. INVENTA."/>
          <p>
            <s xml:id="echoid-s1197" xml:space="preserve">Eſto Circuli portio, ſemicirculo minor, cui maximum ſit in-
              <lb/>
              <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">TAB. XXXVIII.
                <lb/>
              Fig. 3.</note>
            ſcriptum triangulum A B C. </s>
            <s xml:id="echoid-s1198" xml:space="preserve">Dico portionem ad dictum tri-
              <lb/>
            angulum majorem rationem habere quam quatuor ad tria. </s>
            <s xml:id="echoid-s1199" xml:space="preserve">In-
              <lb/>
            ſcribantur enim & </s>
            <s xml:id="echoid-s1200" xml:space="preserve">reliquis portionibus duabus maxima triangu-
              <lb/>
            la A D B, B E C. </s>
            <s xml:id="echoid-s1201" xml:space="preserve">Itaque minus eſt triangulum A B C quam illo
              <lb/>
            rum ſimul quadruplum : </s>
            <s xml:id="echoid-s1202" xml:space="preserve">ac proinde ſpatium aliquod
              <note symbol="*" position="right" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">per. 1. huj.</note>
            poteſt triangulo A B C, quod una cum ipſo minus etiam ſit
              <lb/>
            quam quadruplum dictorum ſimul triangulorum A D B, B E C.
              <lb/>
            </s>
            <s xml:id="echoid-s1203" xml:space="preserve">Eſto itaque eâ ratione adjectum triangulum A F C, ut to-
              <lb/>
            tum ſpatium A B C F minus ſit quam quadruplum triangu-
              <lb/>
            lorum A D B, B E C. </s>
            <s xml:id="echoid-s1204" xml:space="preserve">Et porro in reſiduis portionibus ma-
              <lb/>
            xima triangula inſcribi intelligantur; </s>
            <s xml:id="echoid-s1205" xml:space="preserve">itemque in reſiduis ſem-
              <lb/>
            per, donec portiones quibus poſtremùm inſcribentur ſimul
              <lb/>
            minores ſint triangulo A C F, hoc enim fieri poteſt. </s>
            <s xml:id="echoid-s1206" xml:space="preserve">Ita-
              <lb/>
            que & </s>
            <s xml:id="echoid-s1207" xml:space="preserve">triangula poſtremùm inſcripta ſimul triangulo A C F
              <lb/>
            minora erunt. </s>
            <s xml:id="echoid-s1208" xml:space="preserve">Quia autem ſpatii A B C F quarta parte ma-
              <lb/>
            jora ſunt duo ſimul triangula A D B, B E C. </s>
            <s xml:id="echoid-s1209" xml:space="preserve">Rurſuſque
              <lb/>
            quarta horum parte majora triangula quatuor, quæ portio-
              <lb/>
            nibus reliquis inſcribuntur. </s>
            <s xml:id="echoid-s1210" xml:space="preserve">Et horum quartâ majora ſimili-
              <lb/>
            ter, quæ deinceps: </s>
            <s xml:id="echoid-s1211" xml:space="preserve">atque ita continue, ſi plura fuerint de-
              <lb/>
            ſcripta. </s>
            <s xml:id="echoid-s1212" xml:space="preserve">Erit propterea ſpatium ex quadrilatero A B C F & </s>
            <s xml:id="echoid-s1213" xml:space="preserve">
              <lb/>
            cæteris inſcriptis triangulis, & </s>
            <s xml:id="echoid-s1214" xml:space="preserve">triente eorum, quæ poſtremò
              <lb/>
            inſcripta erunt, compoſitum, majus quam ſeſquitertium i-
              <lb/>
            pſius quadrilateri A B C F. </s>
            <s xml:id="echoid-s1215" xml:space="preserve">Hoc enim ab Archimede demon-
              <lb/>
            ſtratum eſt, quod ſi fuerint ſpatia quotcunque in ratione qua-
              <lb/>
            drupla, ea omnia ſimul cum triente minimi ad maximum ra-
              <lb/>
            tionem habebunt ſeſquitertiam. </s>
            <s xml:id="echoid-s1216" xml:space="preserve">Dividendo itaque, triangula
              <lb/>
            omnia intra portiones A D B, B E C deſcripta cum trien-
              <lb/>
            te poſtremo diſcriptorum majora erunt tertia parte ſpatii
              <lb/>
            A B C F. </s>
            <s xml:id="echoid-s1217" xml:space="preserve">Sed triens dictus minor eſt triente trianguli A C F. </s>
            <s xml:id="echoid-s1218" xml:space="preserve">
              <lb/>
            Igitur dempto illinc triente poſtremò inſcriptorum; </s>
            <s xml:id="echoid-s1219" xml:space="preserve">à ſpatio
              <lb/>
            autem A B C F ablato triangulo A F C, erunt triangula
              <lb/>
            omnia intra portiones A D B, B E C deſcripta, majora
              <lb/>
            triente trianguli A B C . </s>
            <s xml:id="echoid-s1220" xml:space="preserve">Quare componendo, tota
              <note symbol="*" position="right" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">33. 5. Elem.</note>
            rectilinea portioni A B C inſcripta major quam ſeſquitertia
              <lb/>
            trianguli A B C, multoque magis portio ipſa. </s>
            <s xml:id="echoid-s1221" xml:space="preserve">Quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s1222" xml:space="preserve"/>
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