Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of figures

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[141] Fig. 3.a B c A C
[142] Fig. 7.D A C B E G
[143] Fig. 6.D A G B
[Figure 144]
[145] Pag. 262.TAB.XXIX.Fig. 1.P E O D C Q H M G N B S R T F
[146] Fig. 4.C A H N E P B L K I
[147] Fig. 3.N Q O P T
[148] Fig. 2.F D I C A B H K E R S G
[149] Fig. 5.L M C M E H O D P I
[150] Pag. 268.TAB. XXX.a a I L K M g N l O c k P Q T S Q V T S R f f e n l d h g b
[151] Pag. 276.TAB.XXXI.Fig. 2.a a m f k b e @ b a g a f b b h
[152] Fig. 1.h g k h d a b c f e l
[153] Pag. 286.TAB.XXXII.Fig. 1.A E C E E D B G
[154] Fig. 2.H N K M
[155] Fig. 4.B A D C
[156] Fig. 5.A E E C H D G B
[157] Fig. 6.A C C C C H G K E F D D D D
[158] Fig. 3.G F F B D D C D A F A E E H
[159] Fig. 7.K L R Z Y H V N S P A C E B X T M G Q O
[160] Pag. 308.TAB.XXXIII.Fig. 1.P F Q K H L R G B E C N O 3 A 2
[161] Fig. 8.R G M K N D B V C A
[162] Fig. 7.R d D G g B h H E V C u A c
[163] Fig. 2.B F G C H A K D E
[164] Fig. 4.A B G F E C D
[165] Fig. 6.T G D H B E M L N C K I S P F V R Q O A
[166] Fig. 3.A E G B D F C
[167] Fig. 5.N K F E C B A H L V W R G
[168] Fig. 9.Z R A X H C B D M K S Q G
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          <pb o="135" file="0195" n="213" rhead="HOROLOG. OSCILLATOR."/>
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        <div xml:id="echoid-div265" type="section" level="1" n="99">
          <head xml:id="echoid-head125" xml:space="preserve">PROPOSITIO IX.</head>
          <note position="right" xml:space="preserve">
            <emph style="sc">De centro-</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS.</emph>
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          <p style="it">
            <s xml:id="echoid-s3047" xml:space="preserve">DAtâ figurâ planâ & </s>
            <s xml:id="echoid-s3048" xml:space="preserve">in eodem plano lineâ re-
              <lb/>
            ctâ, quæ vel ſecet figuram vel non, ad quam
              <lb/>
            perpendiculares cadant à particulis ſingulis minimis
              <lb/>
            & </s>
            <s xml:id="echoid-s3049" xml:space="preserve">æqualibus, in quas figura diviſa intelligitur;
              <lb/>
            </s>
            <s xml:id="echoid-s3050" xml:space="preserve">invenire ſummam quadratorum ab omnibus iſtis per-
              <lb/>
            pendicularibus; </s>
            <s xml:id="echoid-s3051" xml:space="preserve">ſive planum, cujus multiplex, ſe-
              <lb/>
            cundum particularum numerum, dictæ quadrato-
              <lb/>
            rum ſummæ æquale ſit.</s>
            <s xml:id="echoid-s3052" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3053" xml:space="preserve">Sit data figura plana A B C, & </s>
            <s xml:id="echoid-s3054" xml:space="preserve">in eodem plano recta
              <lb/>
              <note position="right" xlink:label="note-0195-02" xlink:href="note-0195-02a" xml:space="preserve">TAB. XIX.
                <lb/>
              Fig. 5. 6.</note>
            E D; </s>
            <s xml:id="echoid-s3055" xml:space="preserve">divisâque figurâ cogitatu in particulas minimas æqua-
              <lb/>
            les, intelligantur ab unaquaque earum perpendiculares du-
              <lb/>
            ctæ in rectam E D, ſicut à particula F ducta eſt F K. </s>
            <s xml:id="echoid-s3056" xml:space="preserve">O-
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            porteatque invenire ſummam quadratorum ab omnibus iſtis
              <lb/>
            perpendicularibus.</s>
            <s xml:id="echoid-s3057" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3058" xml:space="preserve">Sit datæ E D parallela recta A L, quæ figuram tangat,
              <lb/>
            ac tota extra eam poſita ſit. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">Poteſt autem figuram vel ab ea-
              <lb/>
            dem parte ex qua eſt E D, vel à parte oppoſita contingere.
              <lb/>
            </s>
            <s xml:id="echoid-s3060" xml:space="preserve">Diſtantia vero centri gravitatis figuræ ab recta A L ſit recta
              <lb/>
            G A, ſecans E D in E; </s>
            <s xml:id="echoid-s3061" xml:space="preserve">& </s>
            <s xml:id="echoid-s3062" xml:space="preserve">ſubcentrica cunei, ſuper figura
              <lb/>
            abſciſſi plano per rectam A L, ſit H A. </s>
            <s xml:id="echoid-s3063" xml:space="preserve">Dico ſummam qua-
              <lb/>
            dratorum quæſitam æquari rectangulo A G H una cum qua-
              <lb/>
            drato E G, multiplicibus ſecundum particularum numerum,
              <lb/>
            in quas figura diviſa intelligitur.</s>
            <s xml:id="echoid-s3064" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3065" xml:space="preserve">Occurrat enim F K, ſi opus eſt producta, tangenti A L
              <lb/>
            in L puncto. </s>
            <s xml:id="echoid-s3066" xml:space="preserve">Itaque primum, eo caſu quo recta E D à ſi-
              <lb/>
            gura diſtat, & </s>
            <s xml:id="echoid-s3067" xml:space="preserve">tangens A L ad eandem figuræ partem ducta
              <lb/>
            eſt, ſic propoſitum oſtendetur. </s>
            <s xml:id="echoid-s3068" xml:space="preserve">Summa omnium quadrato-
              <lb/>
            rum F K æquatur totidem quadratis K L, una cum bis to-
              <lb/>
            tidem rectangulis K L F, & </s>
            <s xml:id="echoid-s3069" xml:space="preserve">totidem inſuper quadratis L F.
              <lb/>
            </s>
            <s xml:id="echoid-s3070" xml:space="preserve">Sed quadrata K L æquantur totidem quadratis E A. </s>
            <s xml:id="echoid-s3071" xml:space="preserve">Et re-
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            ctangula K L F æqualia eſſe conſtat totidem </s>
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