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

Table of contents

< >
[81.] VIII.
Page: 192 (120)
[82.] IX.
Page: 192 (120)
[83.] X.
Page: 192 (120)
[84.] XI.
Page: 192 (120)
[85.] XII.
Page: 193 (121)
[86.] XIII.
Page: 193 (121)
[87.] HYPOTHESES. I.
Page: 193 (121)
[88.] II.
Page: 198 (123)
[89.] PROPOSITIO I.
Page: 198 (123)
[90.] PROPOSITIO II.
Page: 200 (125)
[91.] PROPOSITIO III.
Page: 200 (125)
[92.] PROPOSITIO IV.
Page: 201 (126)
[93.] PROPOSITIO V.
Page: 202 (127)
[94.] PROPOSITIO VI.
Page: 208 (130)
[95.] DEFINITIO XIV.
Page: 210 (132)
[96.] DEFINITIO XV.
Page: 210 (132)
[97.] PROPOSITIO VII.
Page: 210 (132)
[98.] PROPOSITIO VIII.
Page: 211 (133)
[99.] PROPOSITIO IX.
Page: 213 (135)
[100.] PROPOSITIO X.
Page: 214 (136)
[101.] PROPOSITIO XI.
Page: 218 (137)
[102.] PROPOSITIO XII.
Page: 218 (137)
[103.] PROPOSITIO XIII.
Page: 221 (140)
[104.] PROPOSITIO XIV.
Page: 223 (142)
[105.] PROPOSITIO XV.
Page: 228 (144)
[106.] PROPOSITIO XVI.
Page: 232 (148)
[107.] PROPOSITIO XVII.
Page: 233 (149)
[108.] PROPOSITIO XVIII.
Page: 234 (150)
[109.] PROPOSITIO XIX.
Page: 237 (153)
[110.] PROPOSITIO XX.
Page: 238 (154)
< >
page |< < (54) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div51" type="section" level="1" n="24">
          <p>
            <s xml:id="echoid-s1148" xml:space="preserve">
              <pb o="54" file="0086" n="90" rhead="CHRISTIANI HUGENII"/>
            Atque ita ſpatia quotlibet deinceps conſiderata, quæ æqua-
              <lb/>
              <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            libus temporibus peracta fuerint, æquali exceſſu, qui ipſi
              <lb/>
            B D æqualis ſit, creſcere manifeſtum eſt; </s>
            <s xml:id="echoid-s1149" xml:space="preserve">ſimulque etiam
              <lb/>
            velocitates per æqualia tempora æqualiter augeri.</s>
            <s xml:id="echoid-s1150" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div54" type="section" level="1" n="25">
          <head xml:id="echoid-head47" xml:space="preserve">PROPOSITIO II.</head>
          <p style="it">
            <s xml:id="echoid-s1151" xml:space="preserve">SPatium peractum certo tempore à gravi, è quie-
              <lb/>
            te caſum inchoante, dimidium eſt ejus ſpatii
              <lb/>
            quod pari tempore transiret motu æquabili, cum
              <lb/>
            velocitate quam acquiſivit ultimo caſus momento.</s>
            <s xml:id="echoid-s1152" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1153" xml:space="preserve">Ponantur quæ in propoſitione præcedenti, ubi quidem
              <lb/>
              <note position="left" xlink:label="note-0086-02" xlink:href="note-0086-02a" xml:space="preserve">TAB. V.
                <lb/>
              Fig. 1.</note>
            A B erat ſpatium certo tempore, à gravi cadente ex A, per-
              <lb/>
            actum. </s>
            <s xml:id="echoid-s1154" xml:space="preserve">B D vero ſpatium quod pari tempore transiri intel-
              <lb/>
            ligebatur celeritate æquabili, quanta acquiſita erat in fine
              <lb/>
            primi temporis, ſeu in fine ſpatii A B. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">Dico itaque ſpatium
              <lb/>
            B D duplum eſſe ad A B.</s>
            <s xml:id="echoid-s1156" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1157" xml:space="preserve">Quum enim ſpatia primis quatuor æqualibus temporibus
              <lb/>
            à cadente transmiſſa ſint A B, B E, E G, G H, quorum
              <lb/>
            inter ſe certa quædam eſt proportio: </s>
            <s xml:id="echoid-s1158" xml:space="preserve">ſi eorum temporum du-
              <lb/>
            pla tempora ſumamus, ut nempe pro primo tempore jam
              <lb/>
            accipiantur duo illa quibus ſpatia A B, B E, peracta fue-
              <lb/>
            re; </s>
            <s xml:id="echoid-s1159" xml:space="preserve">pro ſecundo vero tempore duo reliqua quibus peracta
              <lb/>
            fuere ſpatia E G, G K, oportet jam ſpatia A E, E K,
              <lb/>
            quæ ſunt æqualibus temporibus à quiete peracta, inter ſe
              <lb/>
            eſſe ſicut ſpatia A B, B E, quæ æqualibus item tempori-
              <lb/>
            bus à quiete percurrebantur.</s>
            <s xml:id="echoid-s1160" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1161" xml:space="preserve">Quum igitur ſit ut A B ad B E, ita A E ad E K; </s>
            <s xml:id="echoid-s1162" xml:space="preserve">& </s>
            <s xml:id="echoid-s1163" xml:space="preserve">
              <lb/>
            convertendo, ut E B ſive D A ad A B ita K E ad E A:
              <lb/>
            </s>
            <s xml:id="echoid-s1164" xml:space="preserve">erit quoque, dividendo, D B ad B A ut exceſſus K E ſu-
              <lb/>
            pra E A ad E A. </s>
            <s xml:id="echoid-s1165" xml:space="preserve">Quum ſit autem, ex oſtenſis propoſitione
              <lb/>
            præcedenti, K E æqualis tum duplæ A B, tum quintuplæ
              <lb/>
            B D: </s>
            <s xml:id="echoid-s1166" xml:space="preserve">E A vero æqualis tum duplæ A B, tum ſimplici B D; </s>
            <s xml:id="echoid-s1167" xml:space="preserve">
              <lb/>
            apparet dictum exceſſum K E ſupra E A æquari </s>
          </p>
        </div>
      </text>
    </echo>
Impressum