Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
page |< < (44) 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-s4986" xml:space="preserve">
              <pb o="44" file="0199" n="199" rhead="DE CENTRO GRAVIT. SOLID."/>
            relinquetur p e ipſi n χ æqualis. </s>
            <s xml:id="echoid-s4987" xml:space="preserve">cum autem b e ſit dupla
              <lb/>
            e d, & </s>
            <s xml:id="echoid-s4988" xml:space="preserve">o p dupla p n, hoc eſt ipſius e χ, & </s>
            <s xml:id="echoid-s4989" xml:space="preserve">reliquum, uideli-
              <lb/>
            cet b o unà cum p e ipſius reliqui χ d duplnm erit. </s>
            <s xml:id="echoid-s4990" xml:space="preserve">eſtque
              <lb/>
              <note position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">19. quinti</note>
            b o dupla ζ d. </s>
            <s xml:id="echoid-s4991" xml:space="preserve">ergo p e, hoc eſt n χ ipſius χ ρ dupla. </s>
            <s xml:id="echoid-s4992" xml:space="preserve">ſed d n
              <lb/>
            dupla eſt n ζ. </s>
            <s xml:id="echoid-s4993" xml:space="preserve">reliqua igitur d χ dupla reliquæ χ n. </s>
            <s xml:id="echoid-s4994" xml:space="preserve">ſunt au-
              <lb/>
            tem d χ, p n inter ſe æquales: </s>
            <s xml:id="echoid-s4995" xml:space="preserve">itemq; </s>
            <s xml:id="echoid-s4996" xml:space="preserve">æquales χ n, p e. </s>
            <s xml:id="echoid-s4997" xml:space="preserve">qua-
              <lb/>
            re conſtat n p ipſius p e duplam eſſe. </s>
            <s xml:id="echoid-s4998" xml:space="preserve">& </s>
            <s xml:id="echoid-s4999" xml:space="preserve">idcirco p e ipſi e n
              <lb/>
            æqualem. </s>
            <s xml:id="echoid-s5000" xml:space="preserve">Rurſus cum ſit μ ν dupla o ν, & </s>
            <s xml:id="echoid-s5001" xml:space="preserve">μ σ dupla σ ν; </s>
            <s xml:id="echoid-s5002" xml:space="preserve">erit
              <lb/>
            etiam reliqua ν σ o dupla. </s>
            <s xml:id="echoid-s5003" xml:space="preserve">Eadem quoque ratione
              <lb/>
            cõcludetur π υ dupla υ m. </s>
            <s xml:id="echoid-s5004" xml:space="preserve">ergo ut ν σ ad σ O, ita π υ ad υ m:
              <lb/>
            </s>
            <s xml:id="echoid-s5005" xml:space="preserve">componendoq;</s>
            <s xml:id="echoid-s5006" xml:space="preserve">, & </s>
            <s xml:id="echoid-s5007" xml:space="preserve">permutando, ut υ o ad π m, ita o σ ad
              <lb/>
            m υ & </s>
            <s xml:id="echoid-s5008" xml:space="preserve">ſunt æquales ν o, π m. </s>
            <s xml:id="echoid-s5009" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s5010" xml:space="preserve">o σ, m υ æquales. </s>
            <s xml:id="echoid-s5011" xml:space="preserve">præ
              <lb/>
            terea σ π dupla eſt π τ, & </s>
            <s xml:id="echoid-s5012" xml:space="preserve">ν π ipſius π m. </s>
            <s xml:id="echoid-s5013" xml:space="preserve">reliqua igitur σ ν re
              <lb/>
            liquæ m τ dupla. </s>
            <s xml:id="echoid-s5014" xml:space="preserve">atque erat ν σ dupla σ o. </s>
            <s xml:id="echoid-s5015" xml:space="preserve">ergo m τ, σ o æ-
              <lb/>
            quales ſunt: </s>
            <s xml:id="echoid-s5016" xml:space="preserve">& </s>
            <s xml:id="echoid-s5017" xml:space="preserve">ita æquales m υ, n φ. </s>
            <s xml:id="echoid-s5018" xml:space="preserve">at o σ, eſt æqualis
              <lb/>
            m υ. </s>
            <s xml:id="echoid-s5019" xml:space="preserve">Sequitur igitur, ut omnes o σ, m τ, m υ, n φ in-
              <lb/>
            ter ſe ſint æquales. </s>
            <s xml:id="echoid-s5020" xml:space="preserve">Sed ut ρ π ad π τ, hoc eſt ut 3 ad 2, ita n d
              <lb/>
            ad d χ: </s>
            <s xml:id="echoid-s5021" xml:space="preserve">permutãdoq; </s>
            <s xml:id="echoid-s5022" xml:space="preserve">ut ρ π ad n d, ita π τ ad d χ. </s>
            <s xml:id="echoid-s5023" xml:space="preserve">& </s>
            <s xml:id="echoid-s5024" xml:space="preserve">ſũt æqua
              <lb/>
            les ζ π, n d. </s>
            <s xml:id="echoid-s5025" xml:space="preserve">ergo d χ, hoc eſt n p, & </s>
            <s xml:id="echoid-s5026" xml:space="preserve">π τ æquales. </s>
            <s xml:id="echoid-s5027" xml:space="preserve">Sed etiam æ-
              <lb/>
            quales n π, π m. </s>
            <s xml:id="echoid-s5028" xml:space="preserve">reliqua igitur π p reliquæ m τ, hoc eſt ipſi
              <lb/>
            n φ æqualis erit. </s>
            <s xml:id="echoid-s5029" xml:space="preserve">quare dempta p π ex p e, & </s>
            <s xml:id="echoid-s5030" xml:space="preserve">φ n dempta ex
              <lb/>
            n e, relinquitur p e æqualis e φ. </s>
            <s xml:id="echoid-s5031" xml:space="preserve">Itaque π, ρ centra figurarũ
              <lb/>
            ſecundo loco deſcriptarum a primis centris p n æquali in-
              <lb/>
            teruallo recedunt. </s>
            <s xml:id="echoid-s5032" xml:space="preserve">quòd ſi rurſus aliæ figuræ deſcribantur,
              <lb/>
            eodem modo demonſtrabimus earum centra æqualiter ab
              <lb/>
            his recedere, & </s>
            <s xml:id="echoid-s5033" xml:space="preserve">ad portionis conoidis centrum propius ad
              <lb/>
            moueri. </s>
            <s xml:id="echoid-s5034" xml:space="preserve">Ex quibus conſtat lineam π φ à centro grauitatis
              <lb/>
            portionis diuidi in partes æquales. </s>
            <s xml:id="echoid-s5035" xml:space="preserve">Si enim fieri poteſt, non
              <lb/>
            ſit centrum in puncto e, quod eſt lineæ π φ medium: </s>
            <s xml:id="echoid-s5036" xml:space="preserve">ſed in
              <lb/>
            ψ: </s>
            <s xml:id="echoid-s5037" xml:space="preserve">& </s>
            <s xml:id="echoid-s5038" xml:space="preserve">ipſi π ψ æqualis fiat φ ω. </s>
            <s xml:id="echoid-s5039" xml:space="preserve">Cum igitur in portione ſolida
              <lb/>
            quædam figura inſcribi posſit, ita ut linea, quæ inter cen-
              <lb/>
            trum grauitatis portionis, & </s>
            <s xml:id="echoid-s5040" xml:space="preserve">inſcriptæ figuræ interiicitur,
              <lb/>
            qualibet linea propoſita ſit minor, quod proxime demon-
              <lb/>
            ſtrauimus: </s>
            <s xml:id="echoid-s5041" xml:space="preserve">perueniet tandem φ centrum inſcriptæ </s>
          </p>
        </div>
      </text>
    </echo>
Impressum