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

Table of Notes

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            (qui exempli gratia ſint G H, E F) in hyperbola aſymptoto
              <lb/>
            O A paralleli; </s>
            <s xml:id="echoid-s3849" xml:space="preserve">& </s>
            <s xml:id="echoid-s3850" xml:space="preserve">inveniatur ſpatium hyperbolicum EGHF
              <lb/>
            per hujus 32, quod breviter, fit quoniam G H, E F, parum
              <lb/>
            inter ſe differunt. </s>
            <s xml:id="echoid-s3851" xml:space="preserve">ex ſuppoſitione, unius numeri, exempli
              <lb/>
            gratia G H, datur logorithmus, & </s>
            <s xml:id="echoid-s3852" xml:space="preserve">proinde datur ejus logo-
              <lb/>
            rithmi ratio ad logorithmum denarii arbitrarium, quæ ea-
              <lb/>
            dem eſt (ex hactenus demonſtratis) cum ratione ſpatii hyper-
              <lb/>
            bolici G I K H ad ſpatium hyperbolicum L I K M, datur au-
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            tem ex hujus 32 ſpatium L I K M; </s>
            <s xml:id="echoid-s3853" xml:space="preserve">& </s>
            <s xml:id="echoid-s3854" xml:space="preserve">ideo innoteſcit quoque
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            ſpatium I K H G, cumque detur ſpatium E G H F, innote-
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            ſcit quoque E I K F; </s>
            <s xml:id="echoid-s3855" xml:space="preserve">& </s>
            <s xml:id="echoid-s3856" xml:space="preserve">proinde datur logorithmus numeri
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            compoſiti E F; </s>
            <s xml:id="echoid-s3857" xml:space="preserve">cumque ex ſuppoſitione dentur logorithmi
              <lb/>
            omnium numerorum numerum E F componentium, exce-
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            pto numero illo primo cujus logorithmus deſideratur, dabi-
              <lb/>
            tur quoque illius numeri primi logorithmus, quem invenire
              <lb/>
            oportuit. </s>
            <s xml:id="echoid-s3858" xml:space="preserve">Exempli gratia, propoſitum ſit invenire logorith-
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            mum numeri binarii, ſuppoſito arbitrario numeri denariilo-
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            gorithmo, unitate cum 25 cyphris. </s>
            <s xml:id="echoid-s3859" xml:space="preserve">duo numeri compoſiti
              <lb/>
            parum inter ſe differentes ſunt 1000 & </s>
            <s xml:id="echoid-s3860" xml:space="preserve">1024; </s>
            <s xml:id="echoid-s3861" xml:space="preserve">numeri 1000
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            datur logorithmus, nempe triplum ſpatii 23025850929940-
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            456240178700 in antecedente inventi, poſito ſcilicet illo
              <lb/>
            ſpatio numeri denarii logorithmo arbitrario; </s>
            <s xml:id="echoid-s3862" xml:space="preserve">numeri 1024
              <lb/>
            ignoratur logorithmus, eſt enim compoſitus ex ſolo numero
              <lb/>
            primo 2, nempe ejus decies multiplicatus eſt. </s>
            <s xml:id="echoid-s3863" xml:space="preserve">applicentur hi
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            numeri compoſiti in hyperbola, ut dictum eſt; </s>
            <s xml:id="echoid-s3864" xml:space="preserve">ſitque G H
              <lb/>
            1000, E F 1024: </s>
            <s xml:id="echoid-s3865" xml:space="preserve">ſed quoniam I K unitas eſt 1000000000000,
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            erit G H 1000000000000000 & </s>
            <s xml:id="echoid-s3866" xml:space="preserve">E F 1024000000000000,
              <lb/>
            & </s>
            <s xml:id="echoid-s3867" xml:space="preserve">per hujus 32 inveniatur ſpatium E G H F 237165266173-
              <lb/>
            160421183067 (ſeriem convergentem hic appono,</s>
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