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

Table of handwritten notes

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            <s xml:id="echoid-s4019" xml:space="preserve">
              <pb o="465" file="0185" n="195" rhead="IN LIB JAC. GREG."/>
            Propoſitionis non bene ſit ſolutum; </s>
            <s xml:id="echoid-s4020" xml:space="preserve">Non enim ſufficit, ut
              <lb/>
            inveniatur terminatio progreſſionis convergentis, inveniſſe
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            quantitatem compoſitam eodem modo e primis & </s>
            <s xml:id="echoid-s4021" xml:space="preserve">ſecundis
              <lb/>
            terminis; </s>
            <s xml:id="echoid-s4022" xml:space="preserve">nam talis ſolutio tantum locum habet quando
              <lb/>
            quantitas illa detegitur, non inveſtigatâ quantitate quæ di-
              <lb/>
            citur z in 7 Propoſitione; </s>
            <s xml:id="echoid-s4023" xml:space="preserve">vel quum eadem quantitas non
              <lb/>
            componitur ex ulla quantitate quæ datur in terminis progreſ-
              <lb/>
            ſionis, ut in 7
              <emph style="super">a</emph>
            . </s>
            <s xml:id="echoid-s4024" xml:space="preserve">Propoſitione, ubi z = {me/d}; </s>
            <s xml:id="echoid-s4025" xml:space="preserve">nam Autor ſu-
              <lb/>
            mendo z = {mae - mbe/ad - bd} non videtur obſervaſſe, diviſionem poſ-
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            ſe fieri per a-b.</s>
            <s xml:id="echoid-s4026" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4027" xml:space="preserve">In exemplo propoſitionis 10, non quæritur quantitas z,
              <lb/>
            ſed z appellatur ipſa terminatio; </s>
            <s xml:id="echoid-s4028" xml:space="preserve">& </s>
            <s xml:id="echoid-s4029" xml:space="preserve">in tranſitu notandum eſt
              <lb/>
            exemplum illud allatum eſſe citra propoſitum nam progreſ-
              <lb/>
            ſio, cujus primi termini ſunt a, b, & </s>
            <s xml:id="echoid-s4030" xml:space="preserve">ſecundi & </s>
            <s xml:id="echoid-s4031" xml:space="preserve">Vab,
              <lb/>
            {aa/Vab} non eſt progreſſio conyergens, neque habet terminatio-
              <lb/>
            nem, quamvis autor illam inveniat.</s>
            <s xml:id="echoid-s4032" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4033" xml:space="preserve">Quod attinet ad methodum, quam Autor propoſuit ad ap-
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            propinquandum per numeros ad dimenſionem Circuli; </s>
            <s xml:id="echoid-s4034" xml:space="preserve">@
              <emph style="super">us</emph>
              <lb/>
            Hugenius dixit ſibi videri ſe quid magis accuratum dediſſe
              <lb/>
            in libro cui titulus eſt de Circuli magnitudine, edito 1654.
              <lb/>
            </s>
            <s xml:id="echoid-s4035" xml:space="preserve">Addidit illa, quæ Gregorius habet de dimenſione Hy-
              <lb/>
            perbolæ & </s>
            <s xml:id="echoid-s4036" xml:space="preserve">ratione quam habet cum Logarithmis, bona
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            quidem eſſe ſed minime nova membris ſocietatis, cum poſ-
              <lb/>
            ſint recordari, ſe ipſis idem jam propoſuiſſe, regulamque ad in-
              <lb/>
            veniendos logarithmos, jamdudum actis eorum inſertam eſſe. </s>
            <s xml:id="echoid-s4037" xml:space="preserve">
              <lb/>
            Se etiam non credere illud novum videri regiæ ſocietati An-
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            glicanæ, cum qua jam ante plures annos communicavit me-
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            thodum ad invenienda pondera aëris in diverſis altitudini-
              <lb/>
            bus ſupra terram, quæ fundamentum in hac ipsâ Hyperbolæ
              <lb/>
            dimenſione habet.</s>
            <s xml:id="echoid-s4038" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4039" xml:space="preserve">Hæc autem eſt methodus, quam D
              <emph style="super">us</emph>
            Hugenius propoſuit
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            ad inveniendum per logarithmos dimenſionem Spatii Hy-
              <lb/>
            perbolici contenti inter Curvam & </s>
            <s xml:id="echoid-s4040" xml:space="preserve">unam ex Aſymptotis & </s>
            <s xml:id="echoid-s4041" xml:space="preserve">
              <lb/>
            duas lineas paralelas ad alteram Aſymptoton, data ratione </s>
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