Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div192" type="section" level="1" n="64">
          <p>
            <s xml:id="echoid-s2960" xml:space="preserve">
              <pb file="0118" n="118" rhead="FED. COMMANDINI"/>
            do in reliquis figuris æquilateris, & </s>
            <s xml:id="echoid-s2961" xml:space="preserve">æquiangulis, quæ in cir-
              <lb/>
            culo deſcribuntur, probabimus cẽtrum grauitatis earum,
              <lb/>
            & </s>
            <s xml:id="echoid-s2962" xml:space="preserve">centrum circuli idem eſſe. </s>
            <s xml:id="echoid-s2963" xml:space="preserve">quod quidem demonſtrare
              <lb/>
            oportebat.</s>
            <s xml:id="echoid-s2964" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2965" xml:space="preserve">Ex quibus apparet cuiuslibet figuræ rectilineæ
              <lb/>
            in circulo plane deſcriptæ centrum grauitatis idẽ
              <lb/>
            eſſe, quod & </s>
            <s xml:id="echoid-s2966" xml:space="preserve">circuli centrum.</s>
            <s xml:id="echoid-s2967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2968" xml:space="preserve">Figuram in circulo plane deſcriptam appella-
              <lb/>
              <note position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">γνωρ@ μω@</note>
            mus, cuiuſmodi eſt ea, quæ in duodecimo elemen
              <lb/>
            torum libro, propoſitione ſecunda deſcribitur.
              <lb/>
            </s>
            <s xml:id="echoid-s2969" xml:space="preserve">ex æqualibus enim lateribus, & </s>
            <s xml:id="echoid-s2970" xml:space="preserve">angulis conſtare
              <lb/>
            perſpicuum eſt.</s>
            <s xml:id="echoid-s2971" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div199" type="section" level="1" n="65">
          <head xml:id="echoid-head72" xml:space="preserve">THEOREMA II. PROPOSITIO II.</head>
          <p>
            <s xml:id="echoid-s2972" xml:space="preserve">Omnis figuræ rectilineæ in ellipſi plane deſcri-
              <lb/>
            ptæ centrum grauitatis eſt idem, quod ellipſis
              <lb/>
            centrum.</s>
            <s xml:id="echoid-s2973" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2974" xml:space="preserve">Quo modo figura rectilinea in ellipſi plane deſcribatur,
              <lb/>
            docuimus in commentarijs in quintam propoſitionem li-
              <lb/>
            bri Archimedis de conoidibus, & </s>
            <s xml:id="echoid-s2975" xml:space="preserve">ſphæroidibus.</s>
            <s xml:id="echoid-s2976" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2977" xml:space="preserve">Sit ellipſis a b c d, cuius maior axis a c, minor b d: </s>
            <s xml:id="echoid-s2978" xml:space="preserve">iun-
              <lb/>
            ganturq́; </s>
            <s xml:id="echoid-s2979" xml:space="preserve">a b, b c, c d, d a: </s>
            <s xml:id="echoid-s2980" xml:space="preserve">& </s>
            <s xml:id="echoid-s2981" xml:space="preserve">bifariam diuidantur in pun-
              <lb/>
            ctis e f g h. </s>
            <s xml:id="echoid-s2982" xml:space="preserve">à centro autem, quod ſit k ductæ lineæ k e, k f,
              <lb/>
            k g, k h uſque ad ſectionem in puncta l m n o protrahan-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s2983" xml:space="preserve">& </s>
            <s xml:id="echoid-s2984" xml:space="preserve">iungantur l m, m n, n o, o l, ita ut a c ſecet li-
              <lb/>
            neas l o, m n, in z φ punctis, & </s>
            <s xml:id="echoid-s2985" xml:space="preserve">b d ſecet l m, o n in χ ψ.
              <lb/>
            </s>
            <s xml:id="echoid-s2986" xml:space="preserve">erunt l k, k n linea una, itemq́ue linea unaipſæ m k, k o: </s>
            <s xml:id="echoid-s2987" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s2988" xml:space="preserve">lineæ b a, c d æquidiſtabunt lineæ m o: </s>
            <s xml:id="echoid-s2989" xml:space="preserve">& </s>
            <s xml:id="echoid-s2990" xml:space="preserve">b c, a d ipſi
              <lb/>
            l n. </s>
            <s xml:id="echoid-s2991" xml:space="preserve">rurſus l o, m n axi b d æquidiſtabunt: </s>
            <s xml:id="echoid-s2992" xml:space="preserve">& </s>
            <s xml:id="echoid-s2993" xml:space="preserve">l </s>
          </p>
        </div>
      </text>
    </echo>
Impressum