Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
< >
page |< < (45) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div281" type="section" level="1" n="94">
          <p>
            <s xml:id="echoid-s5041" xml:space="preserve">
              <pb o="45" file="0201" n="201" rhead="DE CENTRO GRAVIT. SOLID."/>
            ad punctum ω. </s>
            <s xml:id="echoid-s5042" xml:space="preserve">Sed quoniam π circum ſcripta itidem alia
              <lb/>
            figura æquali interuallo ad portionis centrum accedit, ubi
              <lb/>
            primum φ applieuerit ſe ad ω, & </s>
            <s xml:id="echoid-s5043" xml:space="preserve">π ad punctũ ψ, hoc eſt ad
              <lb/>
            portionis centrum ſe applicabit. </s>
            <s xml:id="echoid-s5044" xml:space="preserve">quod fieri nullo modo
              <lb/>
            poſſe perſpicuum eſt. </s>
            <s xml:id="echoid-s5045" xml:space="preserve">non aliter idem abſurdum ſequetur,
              <lb/>
            ſi ponamus centrum portionis recedere à medio ad par-
              <lb/>
            tes ω; </s>
            <s xml:id="echoid-s5046" xml:space="preserve">eſſet enim aliquando centrum figuræ inſcriptæ idem
              <lb/>
            quod portionis centrũ. </s>
            <s xml:id="echoid-s5047" xml:space="preserve">ergo punctum e centrum erit gra
              <lb/>
            uitatis portionis a b c. </s>
            <s xml:id="echoid-s5048" xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s5049" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5050" xml:space="preserve">Quod autem ſupra demõſtratum eſt in portione conoi-
              <lb/>
            dis recta per figuras, quæ ex cylindris æqualem altitudi-
              <lb/>
            dinem habentibus conſtant, idem ſimiliter demonſtrabi-
              <lb/>
            mus per figuras ex cylindri portionibus conſtantes in ea
              <lb/>
            portione, quæ plano non ad axem recto abſcinditur. </s>
            <s xml:id="echoid-s5051" xml:space="preserve">ut
              <lb/>
            enim tradidimus in commentariis in undecimam propoſi
              <lb/>
            tionem libri Archimedis de conoidibus & </s>
            <s xml:id="echoid-s5052" xml:space="preserve">ſphæroidibus.
              <lb/>
            </s>
            <s xml:id="echoid-s5053" xml:space="preserve">portiones cylindri, quæ æquali ſunt altitudine eam inter ſe
              <lb/>
            ſe proportionem habent, quam ipſarum baſes; </s>
            <s xml:id="echoid-s5054" xml:space="preserve">baſes autẽ
              <lb/>
            quæ ſunt ellipſes ſimiles eandem proportionem habere,
              <lb/>
              <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">corol. 15
                <lb/>
              deconoi-
                <lb/>
              dibus &
                <lb/>
              ſphæroi-
                <lb/>
              dibus.</note>
            quam quadrata diametrorum eiuſdem rationis, ex corol-
              <lb/>
            lario ſeptimæ propoſitionis libri de conoidibus, & </s>
            <s xml:id="echoid-s5055" xml:space="preserve">ſphæ-
              <lb/>
            roidibus, manifeſte apparet.</s>
            <s xml:id="echoid-s5056" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div284" type="section" level="1" n="95">
          <head xml:id="echoid-head102" xml:space="preserve">THEOREMA XXIIII. PROPOSITIO XXX.</head>
          <p>
            <s xml:id="echoid-s5057" xml:space="preserve">SI à portione conoidis rectanguli alia portio
              <lb/>
            abſcindatur, plano baſi æquidiſtante; </s>
            <s xml:id="echoid-s5058" xml:space="preserve">habebit
              <lb/>
            portio tota ad eam, quæ abſciſſa eſt, duplam pro
              <lb/>
            portio nem eius, quæ eſt baſis maioris portionis
              <lb/>
            ad baſi m minoris, uel quæ axis maioris ad axem
              <lb/>
            minoris.</s>
            <s xml:id="echoid-s5059" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum