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

Table of figures

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[91] Fig. 4.D L C E A X V G H L D B
[92] Fig. 5.T F K A V Q Z D E O B X P C Y f I G M L R N S H
[93] Fig. 6.K E A H C L D F G B
[94] Pag. 154.TAB. XXI.Fig. 1.G E G O A K L Q Q M M H F R R N N B D L K C P S V X Z Y X V T
[95] Fig. 3.F A D E B C G H
[96] Fig. 2.G E Ω O Ω S A S Q Q M M R R N X F N V P Φ Δ V B C K D Z
[97] Pag. 156.Fig. 2.S F Z V O V L A Q Q M M I R R N N X T X K E K Y H G P B C D
[98] Fig. 1.F H A E G B C
[99] Fig. 3.C B A E D
[100] Fig. 4.E F E D D D V O B A N C K H
[101] Fig. 5.D D D E F E B A C H K
[102] Pag. 160.Fig. 1.F D D @ N A L C H K M
[103] Fig. 2.D D D F B A L C H K
[104] Fig. 3.C A B
[105] Fig. 4.B A K C E D G
[106] G D E C A K B
[107] G D K C A B
[108] Fig. 5.K B K A C E D F
[109] Fig. 6.Q B Q O N A C E D R P F
[110] Pag. 164.Fig. 1.G B O N C R P F
[111] Fig. 2.G B R F
[112] Fig. 3.A E C F B
[113] Fig. 4.A C E D F B
[114] Fig. 6.A B C G D L
[115] Fig. 5.H A O M R L N
[116] Pag. 166.TAB.XXV.Fig. 1.A O C G D L N
[117] Fig. 2.A B C G D L N
[118] Fig. 3.O C D A K B N E F C D L M
[119] Fig. 4.O A C D F E K B N C L D M
[120] Fig. 5.E A G F H K B D C
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            <s xml:id="echoid-s1167" xml:space="preserve">
              <pb o="55" file="0087" n="91" rhead="HOROLOG. OSCILLATOR."/>
            B D. </s>
            <s xml:id="echoid-s1168" xml:space="preserve">Sicut igitur D B ad B A ita erit quadrupla D B ad
              <lb/>
              <note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            E A: </s>
            <s xml:id="echoid-s1169" xml:space="preserve">unde E A quadrupla erit ipſius B A: </s>
            <s xml:id="echoid-s1170" xml:space="preserve">eadem vero E A
              <lb/>
            æquatur, uti diximus, & </s>
            <s xml:id="echoid-s1171" xml:space="preserve">duplæ A B & </s>
            <s xml:id="echoid-s1172" xml:space="preserve">ſimplici B D. </s>
            <s xml:id="echoid-s1173" xml:space="preserve">er-
              <lb/>
            go B D duplæ A B æqualis erit; </s>
            <s xml:id="echoid-s1174" xml:space="preserve">quod erat demonſtran-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s1175" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div57" type="section" level="1" n="26">
          <head xml:id="echoid-head48" xml:space="preserve">PROPOSITIO III.</head>
          <p style="it">
            <s xml:id="echoid-s1176" xml:space="preserve">SPatia duo, à gravi cadente quibuslibet tempo-
              <lb/>
            ribus transmiſſa, quorum utrumque ab initio
              <lb/>
            deſcenſus accipiatur, ſunt inter ſe in ratione du-
              <lb/>
            plicata eorundem temporum, ſive ut temporum qua-
              <lb/>
            drata, ſive etiam ut quadrata celeritatum in fine
              <lb/>
            cujusque temporis acquiſitarum.</s>
            <s xml:id="echoid-s1177" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1178" xml:space="preserve">Quum enim oſtenſum ſit propoſitione antecedenti ſpa-
              <lb/>
              <note position="right" xlink:label="note-0087-02" xlink:href="note-0087-02a" xml:space="preserve">TAB. V.
                <lb/>
              Fig. 1.</note>
            tia A B, B E, E G, G K, quotcunque fuerint, æqualibus
              <lb/>
            temporibus à cadente, peracta, creſcere æquali exceſſu, qui
              <lb/>
            exceſſus ſit ipſi B D æqualis: </s>
            <s xml:id="echoid-s1179" xml:space="preserve">Patet nunc, quoniam B D eſt
              <lb/>
            dupla A B, ſpatium B E fore triplum A B; </s>
            <s xml:id="echoid-s1180" xml:space="preserve">E G quintu-
              <lb/>
            plum ejuſdem A B; </s>
            <s xml:id="echoid-s1181" xml:space="preserve">G K ſeptuplum; </s>
            <s xml:id="echoid-s1182" xml:space="preserve">aliaque deinceps au-
              <lb/>
            ctum iri ſecundum progreſſionem numerorum imparium ab
              <lb/>
            unitate, 1, 3, 5, 7, 9, &</s>
            <s xml:id="echoid-s1183" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1184" xml:space="preserve">cumque quotlibet horum nu-
              <lb/>
            merorum, ſeſe conſequentium, ſumma faciat quadratum,
              <lb/>
            cujus latus eſt ipſa adſumptorum numerorum multitudo (ve-
              <lb/>
            lut ſi tres primi addantur, facient novem, ſi quatuor ſexde-
              <lb/>
            cim) ſequitur hinc ſpatia, à gravi cadente tranſmiſſa, quo-
              <lb/>
            rum utrumque à principio caſus inchoetur, eſſe inter ſe in
              <lb/>
            ratione duplicata temporum quibus caſus duravit, ſi nempe
              <lb/>
            tempora commenſurabilia ſumantur.</s>
            <s xml:id="echoid-s1185" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1186" xml:space="preserve">Facile autem & </s>
            <s xml:id="echoid-s1187" xml:space="preserve">ad tempora incommenſurabilia demonſtra-
              <lb/>
              <note position="right" xlink:label="note-0087-03" xlink:href="note-0087-03a" xml:space="preserve">TAB. V.
                <lb/>
              Fig. 2.</note>
            tio extendetur. </s>
            <s xml:id="echoid-s1188" xml:space="preserve">Sint enim tempora hujuſmodi, quorum inter
              <lb/>
            ſe ratio ea quæ linearum A B, C D. </s>
            <s xml:id="echoid-s1189" xml:space="preserve">ſpatiaque temporibus
              <lb/>
            his tranſmiſſa ſint E, & </s>
            <s xml:id="echoid-s1190" xml:space="preserve">F, utraque nimirum ab initio de-
              <lb/>
            ſcenſus adſumpta. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">Dico eſſe, ut quadratum A B ad quadra-
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            tum C D, ita ſpatium E ad F.</s>
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