Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
31 10
32
33 11
34
35 12
36
37 13
38
39 14
40
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
< >
page |< < (18) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div74" type="section" level="1" n="30">
          <pb o="18" file="0047" n="47" rhead="DE IIS QVAE VEH. IN AQVA."/>
          <p>
            <s xml:id="echoid-s1025" xml:space="preserve">Itaque quoniam no ad f ω maiorem habetproportio-
              <lb/>
              <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">B</note>
            nem, quam ad eam, quæ uſque ad axem.</s>
            <s xml:id="echoid-s1026" xml:space="preserve">] _Habet enim diame-_
              <lb/>
            _ter portioms n o ad f ω proportionem eandem, quam quindeeim ad_
              <lb/>
            _quatuor; </s>
            <s xml:id="echoid-s1027" xml:space="preserve">ad eam uero, quæ uſque ad axem minorem proportionem_
              <lb/>
            _habere ponitur, quàm quindecim ad quatuor. </s>
            <s xml:id="echoid-s1028" xml:space="preserve">quare n o ad f ω ma_
              <lb/>
            _iorem habebit proportionem, quàm ad eam, quæ uſque ad axem: </s>
            <s xml:id="echoid-s1029" xml:space="preserve">&_</s>
            <s xml:id="echoid-s1030" xml:space="preserve">
              <lb/>
            _propterea quæ uſque ad axem ipſa f ω maior erit_.
              <lb/>
            </s>
            <s xml:id="echoid-s1031" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">10. quinti</note>
          <p>
            <s xml:id="echoid-s1032" xml:space="preserve">Quoniam ergo in portione a p o l, quæ continetur re-
              <lb/>
            cta linea, & </s>
            <s xml:id="echoid-s1033" xml:space="preserve">rectanguli coni ſectione, _k_ ω quidem æ quidi-
              <lb/>
            ſtans eſt ipſi a l; </s>
            <s xml:id="echoid-s1034" xml:space="preserve">p i uero diametro æquidiſtat; </s>
            <s xml:id="echoid-s1035" xml:space="preserve">ſecaturq;
              <lb/>
            </s>
            <s xml:id="echoid-s1036" xml:space="preserve">ab ipſa k ω in h: </s>
            <s xml:id="echoid-s1037" xml:space="preserve">& </s>
            <s xml:id="echoid-s1038" xml:space="preserve">a c æquidiſtat contingenti in p neceſ-
              <lb/>
            ſarium eſt ipſam p i ad p h uel eandem proportionem ha
              <lb/>
            bere, quam habet n ω ad ω o, uel maiorem. </s>
            <s xml:id="echoid-s1039" xml:space="preserve">hoc enim iam
              <lb/>
            demonſtratum eſt] _Vbi hoc demonſtratum ſit uel ab ipſo Ar-_
              <lb/>
            _chimede, uel ab alio, numdum apparet, quocircanos demonstra-_
              <lb/>
            _tionem afferemus, poſteaquam non nulla, quæ ad eam pertinent ex-_
              <lb/>
            _plicauerimus_.</s>
            <s xml:id="echoid-s1040" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div77" type="section" level="1" n="31">
          <head xml:id="echoid-head36" xml:space="preserve">LEMMAI.</head>
          <p style="it">
            <s xml:id="echoid-s1041" xml:space="preserve">Sint lineæ a b, a c angulum b a c continentes: </s>
            <s xml:id="echoid-s1042" xml:space="preserve">& </s>
            <s xml:id="echoid-s1043" xml:space="preserve">à
              <lb/>
            puncto d, quod in linea a c ſumptum ſit, ducantur d e,
              <lb/>
            d f utcunque ad ipſam a b. </s>
            <s xml:id="echoid-s1044" xml:space="preserve">Sumptis uero in eadem li.
              <lb/>
            </s>
            <s xml:id="echoid-s1045" xml:space="preserve">nea quotlibet punctis g l, ducantur g h, l m ipſi d e
              <lb/>
            æquidistantes; </s>
            <s xml:id="echoid-s1046" xml:space="preserve">& </s>
            <s xml:id="echoid-s1047" xml:space="preserve">g k, l n æquidiſtantes f d. </s>
            <s xml:id="echoid-s1048" xml:space="preserve">deinde à
              <lb/>
            punctis d, g uſque ad lineam m l ducantur, d o p qui
              <lb/>
            dem ſecans g h in o; </s>
            <s xml:id="echoid-s1049" xml:space="preserve">& </s>
            <s xml:id="echoid-s1050" xml:space="preserve">g q, quæ æquidistent ipſi b a. </s>
            <s xml:id="echoid-s1051" xml:space="preserve">
              <lb/>
            Dico lineas, quæ inter æquidiſtantes ipſi f d ad eas, quæ
              <lb/>
            inter æquidiſtantes d e interiiciuntur, uidelicet k n ad g q,
              <lb/>
            uel ad o p; </s>
            <s xml:id="echoid-s1052" xml:space="preserve">f k ad d o; </s>
            <s xml:id="echoid-s1053" xml:space="preserve">& </s>
            <s xml:id="echoid-s1054" xml:space="preserve">f n ad d p eandem inter ſe ſe
              <lb/>
            proportionem habere: </s>
            <s xml:id="echoid-s1055" xml:space="preserve">nempe eam, quã habet a f ad a e.</s>
            <s xml:id="echoid-s1056" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum