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

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            <s xml:id="echoid-s2707" xml:space="preserve">
              <pb file="0129" n="138" rhead="AD LECTOREM."/>
            tæ; </s>
            <s xml:id="echoid-s2708" xml:space="preserve">neque quantum ſcio ab ullo alio tractata eſt hæc materia, etiamſi geometriæ ſpeculativæ non ſo- lum utiliſſima ſit, ſed etiam maxime admirabilis;</s>
            <s xml:id="echoid-s2709" xml:space="preserve"> in ipſo enim limine admiranda occurrunt theorema- ta; </s>
            <s xml:id="echoid-s2710" xml:space="preserve">e.</s>
            <s xml:id="echoid-s2711" xml:space="preserve">g. </s>
            <s xml:id="echoid-s2712" xml:space="preserve">Si fuerit progreſſio geometrica cujus unus terminus fuerit propoſitæ quantitati commenſurabi- lis longitudine vel poteſtate quacunque, & </s>
            <s xml:id="echoid-s2713" xml:space="preserve">alius quilibet, binomium, trinomium, &</s>
            <s xml:id="echoid-s2714" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2715" xml:space="preserve">quodcunque, impoſsibile eſt duos totius progreſſionis terminos in infinitum continuatæ eſſe inter ſe commenſurabiles longitudine vel poteſtate quacunque: </s>
            <s xml:id="echoid-s2716" xml:space="preserve">alia multa poſſem afferre, ſed pro commodiore fortaſſis tempo- re hæc reſervo, ſatis exiſtimans pro præſenti hæc analyticè demonſtraſſe; </s>
            <s xml:id="echoid-s2717" xml:space="preserve">etſi enim analyſis aſſenſum adeo violenter non cogat ac geometria, nunquam ta- men reſpuit nec reſpuere poteſt geometria, quodpro- bavit ſemel analyſis geometrica. </s>
            <s xml:id="echoid-s2718" xml:space="preserve">Ex hac inventione deduco quoque novam ſectionem angularium & </s>
            <s xml:id="echoid-s2719" xml:space="preserve">lo- gorithmorum doctrinam, facilem quidem, in praxi expeditiſsimam & </s>
            <s xml:id="echoid-s2720" xml:space="preserve">geometrica demonſtratione muni- tam; </s>
            <s xml:id="echoid-s2721" xml:space="preserve">hactenus enim logorithmorum conſtructio pro- lixiſſima, conjectura potius quam ſcientia videba- tur, & </s>
            <s xml:id="echoid-s2722" xml:space="preserve">diviſio anguli in partes æquales ultra quin- que numero primo numeratas in praxim vix ad- mitti poterat. </s>
            <s xml:id="echoid-s2723" xml:space="preserve">hæc omnia ſumma (qua poſſum) bre- vitate & </s>
            <s xml:id="echoid-s2724" xml:space="preserve">perſpicuitate demonſtro; </s>
            <s xml:id="echoid-s2725" xml:space="preserve">neque ſcrupulo- ſus ſum in citationibus, utpote peregrinus, & </s>
            <s xml:id="echoid-s2726" xml:space="preserve">li- bris ad tale opus deſtitutus, te enim ſuppono in geometricis non mediocriter verſatum, alioquin </s>
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