Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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              <pb o="509" file="0233" n="245" rhead="GEOMET. VARIA."/>
            dicularibus ad F D E, unam ex Aſymptotis, & </s>
            <s xml:id="echoid-s4973" xml:space="preserve">quæ ſunt in-
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            ter ſe in ratione A D ad D P, ſi Hyperbola A V ſit æquila-
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            tera & </s>
            <s xml:id="echoid-s4974" xml:space="preserve">quadratum ejus ad angulum Aſymptῶtωn ſit A D F H;
              <lb/>
            </s>
            <s xml:id="echoid-s4975" xml:space="preserve">unde reciproce patet, quomodo queant & </s>
            <s xml:id="echoid-s4976" xml:space="preserve">inveniri puncta hu-
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            jus curvæ poſitâ quadraturâ Hyperboles.</s>
            <s xml:id="echoid-s4977" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4978" xml:space="preserve">Habet illa adhuc alias notabiles affectiones, quales ſunt,
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            quod ſpatium infinitum, inter curvam, Aſymptoton, & </s>
            <s xml:id="echoid-s4979" xml:space="preserve">rectam
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            A D, ſit æquale {1/4} circuli cujus radius eſt A D: </s>
            <s xml:id="echoid-s4980" xml:space="preserve">quod ſoli-
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            dum infinitum, quod producit hoc ſpatium rotando cir-
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            ca Aſymptoton, ſit æquale {1/4} ſphæræ ejuſdem radii; </s>
            <s xml:id="echoid-s4981" xml:space="preserve">quod
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            ſuperficies ejus ſolidi infiniti, ſine baſi, ſit æqualis circulo, cujus
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            radius eſt diagonalis quadrati ex A D.</s>
            <s xml:id="echoid-s4982" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4983" xml:space="preserve">Non autem propter ea qua huc uſque propoſui de hac cur-
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            va hic egi, ſed quia ſimplici Machinâ deſcribi poteſt, quo
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            reducitur Hyperbola ad quadratum, quod mihi viſum eſt Geo-
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            metrarum conſideratione dignum.</s>
            <s xml:id="echoid-s4984" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4985" xml:space="preserve">Conſtructio Machinæ nititur in dictâ Tangentis proprieta-
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            te & </s>
            <s xml:id="echoid-s4986" xml:space="preserve">principio vel lege motus; </s>
            <s xml:id="echoid-s4987" xml:space="preserve">ſcilicet, ſi in plano horizon-
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            tali detur punctum, quod ſuo pondere vel alio modo ali-
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            quantulum reſiſtit, junctum extremitati fili vel vectis inflexi-
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            lis, cujus altera extremitas movetur, punctum illud deſcri-
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            bet curvam, cujus Tangens ſemper erit filum vel vectis. </s>
            <s xml:id="echoid-s4988" xml:space="preserve">In
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            inſtrumento vel machinâ, de qua dixi, movenda eſt extremitas
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            D fili vel vectis D A juxta lineam rectam D N, & </s>
            <s xml:id="echoid-s4989" xml:space="preserve">cavendum ut
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            cuſpis in extremitate altera A hærens erecta maneat dum in-
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            terim premetur in planum horizontale, potius elaterio quam
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            pondere, quoniam ſic curva A K deſcribitur ſine errore ſen-
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            ſibili, licet planum non ſit exacte horizontale; </s>
            <s xml:id="echoid-s4990" xml:space="preserve">Et detegi-
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            tur, an habeat veram figuram reducendo extremitatem vectis
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            N per eandem rectam N D; </s>
            <s xml:id="echoid-s4991" xml:space="preserve">quoniam requiritur, ut cuſpis
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            regrediatur ex K in A, per eandem viam.</s>
            <s xml:id="echoid-s4992" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4993" xml:space="preserve">Si hæc deſcriptio, quæ per leges Mechanicæ eſt
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            acurata poſſet haberi pro Geometricâ, eodem modo ut </s>
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