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

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        <div xml:id="echoid-div215" type="section" level="1" n="104">
          <pb o="458" file="0178" n="188" rhead="VERA CIRCULI"/>
          <note position="right" xml:space="preserve">
            <lb/>
          71 # 2016399 factus ex 3, 11, 29, 43 & 49(
            <emph style="super">2</emph>
          )7
            <lb/>
          " # 2016400 factus ex 16(
            <emph style="super">4</emph>
          )2, 25(
            <emph style="super">2</emph>
          )5 & 5041(
            <emph style="super">2</emph>
          )71
            <lb/>
          73 # 5116644 factus ex 4(
            <emph style="super">2</emph>
          )2, 9(
            <emph style="super">2</emph>
          )3, 169(
            <emph style="super">2</emph>
          )13, & 841(
            <emph style="super">2</emph>
          )29
            <lb/>
          " # 5116645 factus ex 7, 17, 19, 31, 73
            <lb/>
          79 # 5997600 factus ex 17, 32(
            <emph style="super">5</emph>
          )2, 9(
            <emph style="super">2</emph>
          )3, 25(
            <emph style="super">2</emph>
          )5 & 49(
            <emph style="super">2</emph>
          )7
            <lb/>
          " # 5997601 factus ex 961(
            <emph style="super">2</emph>
          )31 & 6241(
            <emph style="super">2</emph>
          )79
            <lb/>
          83 # 1164240 factus ex 5, 11, 49(
            <emph style="super">2</emph>
          )7, 16(
            <emph style="super">4</emph>
          )2, 27(
            <emph style="super">3</emph>
          )3
            <lb/>
          " # 1164241 factus ex 169(
            <emph style="super">2</emph>
          )13 & 6889(
            <emph style="super">2</emph>
          )83
            <lb/>
          89 # 2859480 factus ex 5, 47, 8(
            <emph style="super">3</emph>
          )2, 169(
            <emph style="super">2</emph>
          )13 & 9(
            <emph style="super">2</emph>
          )3
            <lb/>
          " # 2859481 factus ex 361(
            <emph style="super">2</emph>
          )19 & 7921(
            <emph style="super">2</emph>
          )89
            <lb/>
          97 # 1138488 factus ex 3, 13, 41, 89, & 8(
            <emph style="super">3</emph>
          )2
            <lb/>
          " # 1138489 factus ex 121(
            <emph style="super">2</emph>
          )11 & 9409(
            <emph style="super">2</emph>
          )97
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3883" xml:space="preserve">Pro numeris primis inter 100 & </s>
            <s xml:id="echoid-s3884" xml:space="preserve">1000 ſit hæc regula: </s>
            <s xml:id="echoid-s3885" xml:space="preserve">ante
              <lb/>
            numerum primum cujus logorithmus quæritur, ſumantur im-
              <lb/>
            mediatè duo numeri proximi, & </s>
            <s xml:id="echoid-s3886" xml:space="preserve">poſt eum numerus imme-
              <lb/>
            diatè ſequens, qui tres numeri cum illo primo ſunt quatuor
              <lb/>
            numeri in ſuo naturali ordine ſe invicem ſequentes; </s>
            <s xml:id="echoid-s3887" xml:space="preserve">deinde
              <lb/>
            multiplicetur primus numerus in cubum tertii & </s>
            <s xml:id="echoid-s3888" xml:space="preserve">quartus in
              <lb/>
            cubum ſecundi, eritque factorum differentia æqualis ſummæ
              <lb/>
            primi & </s>
            <s xml:id="echoid-s3889" xml:space="preserve">quarti vel ſecundi & </s>
            <s xml:id="echoid-s3890" xml:space="preserve">tertii, ut facile demonſtrari po-
              <lb/>
            teſt; </s>
            <s xml:id="echoid-s3891" xml:space="preserve">iſtique numeri facti habent ad minimum ſex notas pri-
              <lb/>
            mas omnino eaſdem, & </s>
            <s xml:id="echoid-s3892" xml:space="preserve">proinde parum inter ſe differunt; </s>
            <s xml:id="echoid-s3893" xml:space="preserve">at-
              <lb/>
            que omnium horum quatuor numerorum (excepto tertii) lo-
              <lb/>
            gorithmi cognoſcuntur ex ipſa progrediendi methodo, & </s>
            <s xml:id="echoid-s3894" xml:space="preserve">
              <lb/>
            ideo ad noſtram abbreviationem ſunt idonei. </s>
            <s xml:id="echoid-s3895" xml:space="preserve">in numeris ul-
              <lb/>
            tra 1000 non opus eſt tanto apparatu, quoniam rectangulum
              <lb/>
            numerorum, inter quos immediatè comprehenditur numerus
              <lb/>
            primus cujus quæritur logorithmus, unitate ſolummodo defi-
              <lb/>
            cit à quadrato numeri primi; </s>
            <s xml:id="echoid-s3896" xml:space="preserve">eorumque ideo primæ ſex no-
              <lb/>
            tæ ad minimum ſunt eædem; </s>
            <s xml:id="echoid-s3897" xml:space="preserve">atque primi & </s>
            <s xml:id="echoid-s3898" xml:space="preserve">tertii dantur lo-
              <lb/>
            gorithmi, & </s>
            <s xml:id="echoid-s3899" xml:space="preserve">ideo ad noſtrum inſtitutum ſunt idonei.</s>
            <s xml:id="echoid-s3900" xml:space="preserve"/>
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