Ghetaldi, Marino, Marini Ghetaldi Promotvs Archimedis sev de varijs corporum generibus grauitate & magnitudine comparatis

Page concordance

< >
Scan Original
11
12
13 1
14 2
15 3
16 4
17 5
18 6
19 7
20 8
21 9
22 10
23 11
24 12
25 13
26 14
27 15
28 16
29 17
30 18
31 19
32 20
33 21
34 22
35 23
36 24
37 25
38 26
39 27
40 28
< >
page |< < (4) of 89 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div10" type="section" level="1" n="8">
          <p>
            <s xml:id="echoid-s173" xml:space="preserve">
              <pb o="4" file="0016" n="16" rhead="PROMOTVS"/>
            quam A, primus terminus in ſerie ſecunda ad BC, ſecundum, ergo, & </s>
            <s xml:id="echoid-s174" xml:space="preserve">
              <lb/>
            D, tertius terminus in ſerie prima ad EI, quartum, minorem habebit
              <lb/>
            rationem quam D, tertius terminus in ſerie ſecunda ad EG, quartum.
              <lb/>
            </s>
            <s xml:id="echoid-s175" xml:space="preserve">Quoniam igitur D, minorem habet rationem ad EI, quam ad EG,
              <lb/>
            erit EI, maior quam EG, quod eſt abſurdum. </s>
            <s xml:id="echoid-s176" xml:space="preserve">Non igitur eſt vt
              <note position="left" xlink:label="note-0016-01" xlink:href="note-0016-01a" xml:space="preserve">10. 5.
                <lb/>
              Elem.</note>
            ad BC, ita D, ad maiorem quam EF, oſtenſum autem eſt neque ad mi-
              <lb/>
            norem; </s>
            <s xml:id="echoid-s177" xml:space="preserve">quare vt A, ad BC, ita erit D, ad EF. </s>
            <s xml:id="echoid-s178" xml:space="preserve">& </s>
            <s xml:id="echoid-s179" xml:space="preserve">incommenſurabilia igi-
              <lb/>
            tur corpora eiuſdem generis eandem in grauitate rationem habent,
              <lb/>
            quam in magnitudine, quod erat demonſtrandum.</s>
            <s xml:id="echoid-s180" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s181" xml:space="preserve">ID QVOD nos duobus præcedentibus Theorematis de-
              <lb/>
            monſtrauimus, nõnulli, vt per ſe notum, & </s>
            <s xml:id="echoid-s182" xml:space="preserve">vt commune quod-
              <lb/>
            dam axioma ſupponunt, quam bene & </s>
            <s xml:id="echoid-s183" xml:space="preserve">rationabiliter ipſi vide-
              <lb/>
            rint; </s>
            <s xml:id="echoid-s184" xml:space="preserve">melius enim Euclides propoſitionem 20. </s>
            <s xml:id="echoid-s185" xml:space="preserve">primi libri Ele-
              <lb/>
            mentorum ſuppoſuiſſet vt pronunciatum; </s>
            <s xml:id="echoid-s186" xml:space="preserve">vnicuique enim no-
              <lb/>
            tius eſt duo trianguli latera reliquo eſſe maiora (cum & </s>
            <s xml:id="echoid-s187" xml:space="preserve">Aſino
              <lb/>
            illud ſit notum) quam corpora grauia eiuſdem generis eandem
              <lb/>
            in grauitate rationem habere, quam in magnitudine, & </s>
            <s xml:id="echoid-s188" xml:space="preserve">tamen
              <lb/>
            illam propoſitionem demonſtrat Euclides, non ſupponit, non
              <lb/>
            igitur hæc, quæ minus ad principij rationem accedit, ſuppo-
              <lb/>
            nenda fuit, ſed demonſtranda.</s>
            <s xml:id="echoid-s189" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div13" type="section" level="1" n="9">
          <head xml:id="echoid-head12" xml:space="preserve">THEOREMA IV. PROPOS. IV.</head>
          <p>
            <s xml:id="echoid-s190" xml:space="preserve">SI quatuor corporum grauium primum ad ſecundũ
              <lb/>
            eandem in magnitudine rationem habeat, quam
              <lb/>
            tertium ad quartum, primum autem, & </s>
            <s xml:id="echoid-s191" xml:space="preserve">ſecundum ſint
              <lb/>
            eiuſdem generis, itidem tertium, & </s>
            <s xml:id="echoid-s192" xml:space="preserve">quartum; </s>
            <s xml:id="echoid-s193" xml:space="preserve">& </s>
            <s xml:id="echoid-s194" xml:space="preserve">in gra-
              <lb/>
            uitate primum ad ſecundum eandem rationem habebit,
              <lb/>
            quam tertium ad quartum.</s>
            <s xml:id="echoid-s195" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s196" xml:space="preserve">PRIMVM enim A, ad ſecundum B, eandem in magnitudine ra-
              <lb/>
            tionem habeat, quam tertium C, ad quartum D, ſint autem A, B,
              <lb/>
            eiuſdem generis, itidem C, D. </s>
            <s xml:id="echoid-s197" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s198" xml:space="preserve">in grauitate primum A, ad
              <lb/>
            ſecundum B, eandem rationem habere, quam tertium C, ad D, quar-
              <lb/>
            tum. </s>
            <s xml:id="echoid-s199" xml:space="preserve">Sint enim earum grauitates E, ipſius A, & </s>
            <s xml:id="echoid-s200" xml:space="preserve">F, ipſius B, ipſius
              <lb/>
            vero C, ſit grauitas G, & </s>
            <s xml:id="echoid-s201" xml:space="preserve">ipſius D, grauitas H, quoniam igitur </s>
          </p>
        </div>
      </text>
    </echo>
Impressum