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-s3684" xml:space="preserve">
              <pb o="445" file="0163" n="172" rhead="ET HYPERBOLÆ QUADRATURA."/>
            F D M K, P L M D. </s>
            <s xml:id="echoid-s3685" xml:space="preserve">dico triangulum A F L eſſe medium arith-
              <lb/>
            meticum inter parallelogramma F D M K, P L M D. </s>
            <s xml:id="echoid-s3686" xml:space="preserve">Grego-
              <lb/>
            rius à S. </s>
            <s xml:id="echoid-s3687" xml:space="preserve">Vincentio in Lib. </s>
            <s xml:id="echoid-s3688" xml:space="preserve">de Hyperbola demonſtrat triangu-
              <lb/>
            lum A F L eſſe æquale trapezio D F L M, ſed manifeſtum eſt
              <lb/>
            trapezium D F L M eſſe medium arithmeticum inter paral-
              <lb/>
            lelogramma F D M K, P L M D; </s>
            <s xml:id="echoid-s3689" xml:space="preserve">& </s>
            <s xml:id="echoid-s3690" xml:space="preserve">ideo patet propo-
              <lb/>
            ſitum.</s>
            <s xml:id="echoid-s3691" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div201" type="section" level="1" n="97">
          <head xml:id="echoid-head133" xml:space="preserve">PROP. XXVII. THEOREMA.</head>
          <p>
            <s xml:id="echoid-s3692" xml:space="preserve">Iisdem poſitis: </s>
            <s xml:id="echoid-s3693" xml:space="preserve">ducatur A I rectam F L bifariam dividens in
              <lb/>
              <note position="right" xlink:label="note-0163-01" xlink:href="note-0163-01a" xml:space="preserve">TAB.
                <lb/>
              XLVIII.
                <lb/>
              fig. 4.</note>
            I & </s>
            <s xml:id="echoid-s3694" xml:space="preserve">hyperbolam interſecans in puncto G, fiatque trape-
              <lb/>
            zium ſectori circumſcriptum A F G L, quod dico eſſe me-
              <lb/>
            dium geometricum inter parallellogramma F D M K, P L M D.
              <lb/>
            </s>
            <s xml:id="echoid-s3695" xml:space="preserve">ex demonſtratis Gregorii à S. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">Vincentio evidens eſt trape-
              <lb/>
            zium A F G L æquale eſſe rectilineo D F G L M. </s>
            <s xml:id="echoid-s3697" xml:space="preserve">& </s>
            <s xml:id="echoid-s3698" xml:space="preserve">quoniam
              <lb/>
            A G I recta ſecat rectam F L bifariam in I, ex ejuſdem Gre-
              <lb/>
            gorii à S. </s>
            <s xml:id="echoid-s3699" xml:space="preserve">Vincentio Lib. </s>
            <s xml:id="echoid-s3700" xml:space="preserve">de hyperbola, manifeſtum eſt rectas
              <lb/>
            L M, G H, FD, eſſe continuè proportionales in eadem ratione
              <lb/>
            cum tribus continuè proportionalibus A D, A H, A M. </s>
            <s xml:id="echoid-s3701" xml:space="preserve">aſym-
              <lb/>
            ptoto A O per punctum G ducatur parallela recta R G S
              <lb/>
            rectis F D, M K, occurrens in punctis R, S. </s>
            <s xml:id="echoid-s3702" xml:space="preserve">quoniam rectæ
              <lb/>
            F D, G H, L M, ſunt continuè proportionales, erit dividen-
              <lb/>
            do & </s>
            <s xml:id="echoid-s3703" xml:space="preserve">permutando F R ad S L ut G H ad L M: </s>
            <s xml:id="echoid-s3704" xml:space="preserve">& </s>
            <s xml:id="echoid-s3705" xml:space="preserve">quoniam
              <lb/>
            rectæ M A, H A, D A, ſunt continuè proportionales, erit
              <lb/>
            etiam dividendo & </s>
            <s xml:id="echoid-s3706" xml:space="preserve">permutando M H ad H D hoc eſt S G ad
              <lb/>
            G R ut H A ad D A, vel ut G H ad L M; </s>
            <s xml:id="echoid-s3707" xml:space="preserve">& </s>
            <s xml:id="echoid-s3708" xml:space="preserve">proinde F R
              <lb/>
            eſt ad S L ut S G ad G R, cumque anguli F R G, G S L, ſint
              <lb/>
            æquales ob parallelas F R, S L, erunt triangula F R G, G L S,
              <lb/>
            æqualia; </s>
            <s xml:id="echoid-s3709" xml:space="preserve">& </s>
            <s xml:id="echoid-s3710" xml:space="preserve">proinde parallelogrammum R D M S æquale eſt
              <lb/>
            rectilineo D F G L M ſeu trapezio A F G L; </s>
            <s xml:id="echoid-s3711" xml:space="preserve">ſed parallelo-
              <lb/>
            grammum R D M S eſt medium geometricum inter parale-
              <lb/>
            logramma P D M L, F D M K, quoniam eandem habentia alti-
              <lb/>
            tudinem eorum baſes nempe L M, S M, K M, ſunt continuè
              <lb/>
            proportionales; </s>
            <s xml:id="echoid-s3712" xml:space="preserve">& </s>
            <s xml:id="echoid-s3713" xml:space="preserve">ideo trapezium A F G L eſt medium </s>
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