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

Table of figures

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[151] Fig. 32.* 17. Iun.
[152] Fig. 33.* 19. Oct.
[153] Fig. 34.* 21. Oct.
[154] Fig. 35.* 9. Nov.
[155] Fig. 36.* 27. Nov.
[156] Fig. 37.* 16. Dec.
[157] Fig. 38.* 18. Ian. 1657.
[158] Fig. 39.* 29. Mart.
[159] Fig. 40.* 30. Mart.
[160] Fig. 41.* 18. Maii.
[161] Fig. 42.* 19. Maii.
[162] Fig. 43.* 17. Dec.
[163] Fig. 44.* 18. Dec.
[164] Fig. 45.* 27. Dec.
[165] Fig. 46.* 11. Mart 1658.
[166] Fig. 47.* 16. Mart.
[167] Fig. 48.* 23. Mart.
[168] Fig. 49.* 3. Apr.
[169] Fig. 50.* 10. Nov.
[170] Fig. 51.* 16. Ian. 1659.
[171] Fig. 52.12. Febr. *
[172] Fig. 53.* 24. Febr.
[173] Fig. 54.25. Febr. *
[174] Fig. 55.14. Mart. *
[175] Fig. 56.16. Mart. *
[176] Fig. 57.* 21. Mart.
[177] Fig. 58.* 22. Mart.
[178] Fig. 59.26. Mart. *
[179] Pag. 574.TAB. XLIX.Fig. 2.
[180] Fig. 1.C K O B H N G M S * F D A L E
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            <s xml:id="echoid-s3132" xml:space="preserve">
              <pb o="428" file="0146" n="155" rhead="VERA CIRCULI"/>
            ſequentes Vqab, {aa.</s>
            <s xml:id="echoid-s3133" xml:space="preserve">/Vqab} ſumma terminorum convergentium
              <emph style="super">a + b</emph>
              <lb/>
            multiplicata in terminum convergentem primum
              <emph style="sub">a</emph>
            efficit
              <lb/>
            aa + ab: </s>
            <s xml:id="echoid-s3134" xml:space="preserve">& </s>
            <s xml:id="echoid-s3135" xml:space="preserve">ſumma terminorum convergentium immediate ſe-
              <lb/>
            quentium nempe Vqab + {aa/Vqab} multiplicata in primum terminum
              <lb/>
            convergentem
              <emph style="super">Vqab</emph>
            efficit etiam aa + ab; </s>
            <s xml:id="echoid-s3136" xml:space="preserve">ex his invenienda ſit ſe-
              <lb/>
            riei propoſitæ terminatio. </s>
            <s xml:id="echoid-s3137" xml:space="preserve">manifeſtum eſt quantitatem aa + ab
              <lb/>
            eodem modo fieri à terminis convergentibus
              <emph style="super">a, b,</emph>
            quo à termi-
              <lb/>
            nis convergentibus immediatè ſequentibus Vqab, {aa/Vqab:</s>
            <s xml:id="echoid-s3138" xml:space="preserve">} & </s>
            <s xml:id="echoid-s3139" xml:space="preserve">quo-
              <lb/>
            niam quantitates
              <emph style="super">a, b,</emph>
            indefinitæ ponuntur pro quibuslibet to-
              <lb/>
            tius ſeriei terminis convergentibus, evidens eſt ſummam quo-
              <lb/>
            rumcunque terminorum convergentium propoſitæ ſeriei mul-
              <lb/>
            tiplicatam in primum terminum convergentem efficere quan-
              <lb/>
            titatem æqualem illi, quæ fit à ſumma terminorum conver-
              <lb/>
            gentium immediatè ſequentium multiplicata etiam in primum
              <lb/>
            ſuum terminum convergentem; </s>
            <s xml:id="echoid-s3140" xml:space="preserve">cumque duo termini conver-
              <lb/>
            gentes duos terminos convergentes ſemper immediatè ſe-
              <lb/>
            quuntur, manifeſtum eſt ſummam duorum quorumlibet ter-
              <lb/>
            minorum convergentium multiplicatam in primum ſemper
              <lb/>
            efficere eandem quantitatem nempe aa + ab, atque ultimi ter-
              <lb/>
            mini convergentes ſunt æquales, & </s>
            <s xml:id="echoid-s3141" xml:space="preserve">proinde ſit ultimus ille
              <lb/>
            terminus ſeu ſeriei terminatio
              <emph style="super">z</emph>
            , quæ ſibi addita & </s>
            <s xml:id="echoid-s3142" xml:space="preserve">in ſum-
              <lb/>
            mam multiplicata efficit
              <emph style="super">2 zz</emph>
            , quæ quantitas debet eſſe æqua-
              <lb/>
            lis quantitati aa + ab, & </s>
            <s xml:id="echoid-s3143" xml:space="preserve">æquatione reſoluta dabitur
              <emph style="super">z</emph>
            ſeu ſeriei
              <lb/>
            terminatio {Vq aa + ab,/2} quam invenire oportuit.</s>
            <s xml:id="echoid-s3144" xml:space="preserve"/>
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            <s xml:id="echoid-s3145" xml:space="preserve">Et proinde ad inveniendam cujuscunque ſeriei convergen-
              <lb/>
            tis terminationem; </s>
            <s xml:id="echoid-s3146" xml:space="preserve">opus eſt ſolummodo invenire quantitatem
              <lb/>
            eodem modo compoſitam ex terminis convergentibus primis,
              <lb/>
            quo componitur eadem quantitas ex terminis convergentibus
              <lb/>
            ſecundis.</s>
            <s xml:id="echoid-s3147" xml:space="preserve"/>
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        <div xml:id="echoid-div165" type="section" level="1" n="77">
          <head xml:id="echoid-head113" xml:space="preserve">CONSECTARIUM.</head>
          <p>
            <s xml:id="echoid-s3148" xml:space="preserve">Quoniam non refert in problemate ſive termini conver-
              <lb/>
            gentes a, b, ſint primi, ſecundi, vel tertii &</s>
            <s xml:id="echoid-s3149" xml:space="preserve">c; </s>
            <s xml:id="echoid-s3150" xml:space="preserve">manifeſtum </s>
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