Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div242" type="section" level="1" n="84">
          <p>
            <s xml:id="echoid-s3973" xml:space="preserve">
              <pb file="0160" n="160" rhead="FED. COMMANDINI"/>
            æqualibus baſibus, quorum axes cum baſibus æquales an
              <lb/>
            gulos faciant. </s>
            <s xml:id="echoid-s3974" xml:space="preserve">Dico ſolidum a b adſolidũ c d ita eſſe, ut axis
              <lb/>
            e f ad axem g h: </s>
            <s xml:id="echoid-s3975" xml:space="preserve">nam ſi axes ad planum baſis recti ſint, il-
              <lb/>
            lud perſpicue conſtat: </s>
            <s xml:id="echoid-s3976" xml:space="preserve">quoniam eadem linea, & </s>
            <s xml:id="echoid-s3977" xml:space="preserve">axem & </s>
            <s xml:id="echoid-s3978" xml:space="preserve">ſoli
              <lb/>
            di altitudinem determinabit. </s>
            <s xml:id="echoid-s3979" xml:space="preserve">Si uero ſintinclinati, à pun-
              <lb/>
            ctis e g ad ſubiectum planum perpendiculares ducantur
              <lb/>
            e k, g l: </s>
            <s xml:id="echoid-s3980" xml:space="preserve">& </s>
            <s xml:id="echoid-s3981" xml:space="preserve">iungantur f_k_, h l. </s>
            <s xml:id="echoid-s3982" xml:space="preserve">rurſus quoniam axes cum ba
              <lb/>
            ſibus æquales faciunt angulos, eodem modo demonſtrabi
              <lb/>
            tur, triangulum e f K triangulo g h l ſimile eſſe: </s>
            <s xml:id="echoid-s3983" xml:space="preserve">& </s>
            <s xml:id="echoid-s3984" xml:space="preserve">e k ad g l,
              <lb/>
            ut e f ad g h. </s>
            <s xml:id="echoid-s3985" xml:space="preserve">Solidum autem a b ad ſolidum c d eſt, ut
              <lb/>
            e K ad g l. </s>
            <s xml:id="echoid-s3986" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s3987" xml:space="preserve">ut axis e f ad axem g h. </s>
            <s xml:id="echoid-s3988" xml:space="preserve">quæ omnia de
              <lb/>
            monſtrare oportebat.</s>
            <s xml:id="echoid-s3989" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3990" xml:space="preserve">Ex iis quæ demonſtrata ſunt, facile conſtare
              <lb/>
            poteſt, priſmata omnia & </s>
            <s xml:id="echoid-s3991" xml:space="preserve">pyramides, quæ trian-
              <lb/>
            gulares baſes habent, ſiue in eiſdem, ſiue in æqua
              <lb/>
            libus baſibus conſtituantur, eandem proportio-
              <lb/>
              <note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">15. quinti</note>
            nem habere, quam altitudines: </s>
            <s xml:id="echoid-s3992" xml:space="preserve">& </s>
            <s xml:id="echoid-s3993" xml:space="preserve">ſi axes cum ba
              <lb/>
            ſibus æquales angulos contineant, ſimiliter ean-
              <lb/>
            dem, quam axes, habere proportionem: </s>
            <s xml:id="echoid-s3994" xml:space="preserve">ſunt
              <lb/>
              <note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">28. unde-
                <lb/>
              cimi.</note>
            enim ſolida parallelepipeda priſmatum triangula
              <lb/>
            res baſes habentiũ dupla; </s>
            <s xml:id="echoid-s3995" xml:space="preserve">& </s>
            <s xml:id="echoid-s3996" xml:space="preserve">pyramidum ſextupla.</s>
            <s xml:id="echoid-s3997" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">7. duode-
            <lb/>
          cimi.</note>
        </div>
        <div xml:id="echoid-div247" type="section" level="1" n="85">
          <head xml:id="echoid-head92" xml:space="preserve">THE OREMA XVI. PROPOSITIO XX.</head>
          <p>
            <s xml:id="echoid-s3998" xml:space="preserve">Priſmata omnia & </s>
            <s xml:id="echoid-s3999" xml:space="preserve">pyramides, quæ in eiſdem,
              <lb/>
            uel æqualibus baſibus conſtituuntur, eam inter
              <lb/>
            ſe proportionem habent, quam altitudines: </s>
            <s xml:id="echoid-s4000" xml:space="preserve">& </s>
            <s xml:id="echoid-s4001" xml:space="preserve">ſi
              <lb/>
            axes cum baſibus faciant angulos æquales, eam
              <lb/>
            etiam, quam axes habent proportionem.</s>
            <s xml:id="echoid-s4002" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum