Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
< >
page |< < (25) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div94" type="section" level="1" n="37">
          <p style="it">
            <s xml:id="echoid-s1428" xml:space="preserve">
              <pb o="25" file="0061" n="61" rhead="DE IIS QVAE VEH. IN AQVA."/>
            b ψ dupla ſit ψ d, erit d b ipſius b ψ ſeſquialtera. </s>
            <s xml:id="echoid-s1429" xml:space="preserve">& </s>
            <s xml:id="echoid-s1430" xml:space="preserve">quoniam e b ſeſ
              <lb/>
            quialtera est b r, ſequitur reliquam c d ipſius ψ r, boc est eius, quæ
              <lb/>
              <note position="right" xlink:label="note-0061-01" xlink:href="note-0061-01a" xml:space="preserve">12. quinti</note>
            uſque ad axem ſeſquialteram eſſe. </s>
            <s xml:id="echoid-s1431" xml:space="preserve">quare b c erit exceſſus, quo axis
              <lb/>
            maior est, quàm ſeſquialter eius, quæ uſque ad axem.</s>
            <s xml:id="echoid-s1432" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1433" xml:space="preserve">_Quare f q minor éſtipſa b c.</s>
            <s xml:id="echoid-s1434" xml:space="preserve">]_ Nam cum portio ad bumi-
              <lb/>
              <note position="right" xlink:label="note-0061-02" xlink:href="note-0061-02a" xml:space="preserve">B</note>
            dum in grauitate proportionem habeat eandem, quàm quadratum
              <lb/>
            f q ad quadratum d b: </s>
            <s xml:id="echoid-s1435" xml:space="preserve">habeatq, minorem proportionem, quàm qua
              <lb/>
            dratum factum ab exceſſu, quo axis maior eſt, quàm ſeſquialter eius,
              <lb/>
            quæ uſque ad axem, ad quadratum ab axe; </s>
            <s xml:id="echoid-s1436" xml:space="preserve">boc eſt minorem, quàm
              <lb/>
            quadratum c b ad quadratum b d: </s>
            <s xml:id="echoid-s1437" xml:space="preserve">ponitur enim linea b d æqualis
              <lb/>
            axi: </s>
            <s xml:id="echoid-s1438" xml:space="preserve">quadratum f q ad quadratum d b proportionem minorem ha-
              <lb/>
            bebit, quàm quadratum c b ad idem b d quadratum. </s>
            <s xml:id="echoid-s1439" xml:space="preserve">ergo quadra-
              <lb/>
              <note position="right" xlink:label="note-0061-03" xlink:href="note-0061-03a" xml:space="preserve">8. quinti.</note>
            tum f q minus erit quadrato c b: </s>
            <s xml:id="echoid-s1440" xml:space="preserve">& </s>
            <s xml:id="echoid-s1441" xml:space="preserve">propterea linea f q ipſa b c
              <lb/>
            minor.</s>
            <s xml:id="echoid-s1442" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1443" xml:space="preserve">_Etidcirco f minor ipſa b r.</s>
            <s xml:id="echoid-s1444" xml:space="preserve">]_ Quoniam enim c b ſeſquial-
              <lb/>
              <note position="right" xlink:label="note-0061-04" xlink:href="note-0061-04a" xml:space="preserve">C</note>
            tera eſt b r, & </s>
            <s xml:id="echoid-s1445" xml:space="preserve">f q ipſius f ſeſquialtera: </s>
            <s xml:id="echoid-s1446" xml:space="preserve">estq; </s>
            <s xml:id="echoid-s1447" xml:space="preserve">f q minor b c; </s>
            <s xml:id="echoid-s1448" xml:space="preserve">& </s>
            <s xml:id="echoid-s1449" xml:space="preserve">f
              <lb/>
              <note position="right" xlink:label="note-0061-05" xlink:href="note-0061-05a" xml:space="preserve">14. quin-
                <lb/>
              ti.</note>
            ipſa b r minor erit.</s>
            <s xml:id="echoid-s1450" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1451" xml:space="preserve">_Itaque quoniam ponitur axis portionis cum ſuperficie_
              <lb/>
              <note position="right" xlink:label="note-0061-06" xlink:href="note-0061-06a" xml:space="preserve">D</note>
            _humidi facere angulum maiorem angulo b: </s>
            <s xml:id="echoid-s1452" xml:space="preserve">erit angulus_
              <lb/>
            _p y i angulo b maior.</s>
            <s xml:id="echoid-s1453" xml:space="preserve">]_ Nam cum linea p y ſuperficiei bumidi
              <lb/>
            æ quidistet; </s>
            <s xml:id="echoid-s1454" xml:space="preserve">uidelicet ipſi x s: </s>
            <s xml:id="echoid-s1455" xml:space="preserve">angulus p y i æqualis erit angulo, qui
              <lb/>
              <note position="right" xlink:label="note-0061-07" xlink:href="note-0061-07a" xml:space="preserve">29. primi</note>
            diametro portionis n o, & </s>
            <s xml:id="echoid-s1456" xml:space="preserve">linea x s continetur. </s>
            <s xml:id="echoid-s1457" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s1458" xml:space="preserve">angulo
              <lb/>
            b maior erit.</s>
            <s xml:id="echoid-s1459" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1460" xml:space="preserve">_Maiorem igitur proportionem habet quadratum p i ad_
              <lb/>
              <note position="right" xlink:label="note-0061-08" xlink:href="note-0061-08a" xml:space="preserve">E</note>
            _quadratum i y, quàm quadratum e ψ ad ψ b quadratu.</s>
            <s xml:id="echoid-s1461" xml:space="preserve">]_
              <lb/>
            Deſcribantur ſeorſum triangula p i y, e ψ b. </s>
            <s xml:id="echoid-s1462" xml:space="preserve">& </s>
            <s xml:id="echoid-s1463" xml:space="preserve">cum angulus p y i
              <lb/>
            maior ſit angulo e b ψ, ad lineam i y, atque ad punctum y in ea da-
              <lb/>
            tum fiat angulus u y i æqualis angulo e b ψ. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">est autem angulus ad
              <lb/>
            i rectus æqualis recto ad ψ. </s>
            <s xml:id="echoid-s1465" xml:space="preserve">reliquus igitur y u i reliquo b c ψ est
              <lb/>
            æqualis. </s>
            <s xml:id="echoid-s1466" xml:space="preserve">quare linea u i ad lineam i y eandem proportionem ha-
              <lb/>
              <note position="right" xlink:label="note-0061-09" xlink:href="note-0061-09a" xml:space="preserve">4. ſexti.</note>
            bet, quam linea e ψ ad ψ b. </s>
            <s xml:id="echoid-s1467" xml:space="preserve">Sed linea p i, quæ maior est ipſa u i ad
              <lb/>
              <note position="right" xlink:label="note-0061-10" xlink:href="note-0061-10a" xml:space="preserve">8. quinti.</note>
            lineam in maiorem habet proportionem quam u i ad eandem. </s>
            <s xml:id="echoid-s1468" xml:space="preserve">ergo
              <lb/>
              <note position="right" xlink:label="note-0061-11" xlink:href="note-0061-11a" xml:space="preserve">13. quin-
                <lb/>
              ti.</note>
            p i ad i y maiorem proportionem habebit, quàm e ψ ad ψ b: </s>
            <s xml:id="echoid-s1469" xml:space="preserve">& </s>
            <s xml:id="echoid-s1470" xml:space="preserve">
              <lb/>
            propterea quadratum p i ad quadratum i y maiorem habebit, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum