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

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            <s xml:id="echoid-s5153" xml:space="preserve">
              <pb o="517" file="0241" n="253" rhead="GEOMET. VARIA."/>
            portionales fieri poſſit, ubi ratio tangentis ad abſciſ-
              <lb/>
            ſam eſt ea quæ numeri ad numerum, hinc apparuit curvam
              <lb/>
            quæſitam tunc iis accenſendam quæ geometricæ vocantur,
              <lb/>
            alias eſſe ex heterogeneis; </s>
            <s xml:id="echoid-s5154" xml:space="preserve">ac tamen conſtructionem dari
              <lb/>
            poſita lineæ logarithmicæ deſcriptione, quam quidem hic ad-
              <lb/>
            ducerem, niſi viderem haud difficulter ex ipſa Jacobi Ber-
              <lb/>
            noullii doctiſſima ſimul breviſſimaque ſolutione omnia erui
              <lb/>
            poſſe, ut jam ab aliis occupatam dubitem.</s>
            <s xml:id="echoid-s5155" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5156" xml:space="preserve">Colligitur vero ex his illud animadverſione dignum,
              <lb/>
            nempe quandocunque in inveſtigatione curvarum ex tan-
              <lb/>
            gentibus aut ſubtangentibus ejus, ad ſimiles ei, quam dixi,
              <lb/>
            æquationes pervenietur, aut in quibus habeatur utrinque
              <lb/>
            elementum ſpatii ad trapezium hyperbolicum reductibilis;
              <lb/>
            </s>
            <s xml:id="echoid-s5157" xml:space="preserve">tunc idem hoc, quod mirabile hic accidit, eventurum, ut
              <lb/>
            curvæ geometricæ diverſorum generum graduumque exi-
              <lb/>
            ſtant, ſi hyperbolarum ad quas devenitur rectangula
              <lb/>
            quæ in aſymptotis, ſint commenſurabilia. </s>
            <s xml:id="echoid-s5158" xml:space="preserve">Præterea
              <lb/>
            obſervanda venit in hoc problemate inuſitata ac ſin-
              <lb/>
            gularis analyſis via, quæ ad alia multa in hac Tan-
              <lb/>
            gentium doctrina aditum aperit, ut egregie jam ani-
              <lb/>
            madvertit Vir Celeberrimus calculi differentialis inven-
              <lb/>
            tor, ſine quo vix eſſet, ut ad haſce geometriæ ſubti-
              <lb/>
            litates admitteremur. </s>
            <s xml:id="echoid-s5159" xml:space="preserve">Porro quod ad curvarum, de qui-
              <lb/>
            bus agitur, deſignationem in plano attinet, poſſem, ſi
              <lb/>
            operæ pretium eſſet, alios modos ac fortaſſe com-
              <lb/>
            modiores indicare quam qui a Cl. </s>
            <s xml:id="echoid-s5160" xml:space="preserve">Bernoullio præſcri-
              <lb/>
            bitur, atque etiam docere qua ratione optime peraga-
              <lb/>
            tur deſcriptio noſtræ quadratricis hyperbolæ, quæ in-
              <lb/>
            ter Tractorias (ita enim vocari poſſunt) ſimpliciſſi-
              <lb/>
            ma cenſenda eſt, cum ad eam filis nihil opus ſit,
              <lb/>
            ſed bacillo tantum utrimque cuſpidem lateri infixam
              <lb/>
            habente, quo fit ut & </s>
            <s xml:id="echoid-s5161" xml:space="preserve">regreſſu explorari poſſit quam
              <lb/>
            recte exarata ſit. </s>
            <s xml:id="echoid-s5162" xml:space="preserve">Sed his ſuperſedendum arbitror, do-
              <lb/>
            nec inſignis uſus aliquis harum linearum in lucem
              <lb/>
            proferatur. </s>
            <s xml:id="echoid-s5163" xml:space="preserve">Interim aliam quandam utiliſſimam </s>
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