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 |< < (30) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div254" type="section" level="1" n="87">
          <p>
            <s xml:id="echoid-s4278" xml:space="preserve">
              <pb o="30" file="0171" n="171" rhead="DE CENTRO GRAVIT. SOLID."/>
            pra demonſtratum eſt, ita eſſe cylindrum, uel cylindri por-
              <lb/>
              <note position="right" xlink:label="note-0171-01" xlink:href="note-0171-01a" xml:space="preserve">8. huius</note>
            tionem ad priſina, cuius baſis rectilinea figura, & </s>
            <s xml:id="echoid-s4279" xml:space="preserve">æqua-
              <lb/>
            lis altitudo. </s>
            <s xml:id="echoid-s4280" xml:space="preserve">ergo per conuerſionem rationis, ut circulus,
              <lb/>
            uel ellipſis ad portiones, ita conus, uel coni portio ad por-
              <lb/>
            tiones ſolidas. </s>
            <s xml:id="echoid-s4281" xml:space="preserve">quare conus uel coni portio ad portiones
              <lb/>
            ſolidas maiorem habet proportionem, quam g e ad e f: </s>
            <s xml:id="echoid-s4282" xml:space="preserve">& </s>
            <s xml:id="echoid-s4283" xml:space="preserve">
              <lb/>
            diuidendo, pyramis ad portiones ſolidas maiorem pro-
              <lb/>
            portionem habet, quam g f ad f e. </s>
            <s xml:id="echoid-s4284" xml:space="preserve">ſiat igitur q f ad f e
              <lb/>
            ut pyramis ad dictas portiones. </s>
            <s xml:id="echoid-s4285" xml:space="preserve">Itaque quoniam à cono
              <lb/>
            uel coni portione, cuius grauitatis centrum eſt f, aufer-
              <lb/>
            tur pyramis, cuius centrum e; </s>
            <s xml:id="echoid-s4286" xml:space="preserve">reliquæ magnitudinis,
              <lb/>
            quæ ex ſolidis portionibus conſtat, centrum grauitatis
              <lb/>
            erit in linea e f protracta, & </s>
            <s xml:id="echoid-s4287" xml:space="preserve">in puncto q. </s>
            <s xml:id="echoid-s4288" xml:space="preserve">quod fieri
              <lb/>
            non poteft: </s>
            <s xml:id="echoid-s4289" xml:space="preserve">eſt enim centrum grauitatis intra. </s>
            <s xml:id="echoid-s4290" xml:space="preserve">Conſtat
              <lb/>
            igitur coni, uel coni portionis grauitatis centrum eſſe pun
              <lb/>
            ctum e. </s>
            <s xml:id="echoid-s4291" xml:space="preserve">quæ omnia demonſtrare oportebat.</s>
            <s xml:id="echoid-s4292" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div258" type="section" level="1" n="88">
          <head xml:id="echoid-head95" xml:space="preserve">THEOREMA XIX. PROPOSITIO XXIII.</head>
          <p>
            <s xml:id="echoid-s4293" xml:space="preserve">
              <emph style="sc">Qvodlibet</emph>
            fruſtum à pyramide, quæ
              <lb/>
            triangularem baſim habeat, abſciſſum, diuiditur
              <lb/>
            in tres pyramides proportionales, in ea proportio
              <lb/>
            ne, quæ eſt lateris maioris baſis ad latus minoris
              <lb/>
            ipſi reſpondens.</s>
            <s xml:id="echoid-s4294" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4295" xml:space="preserve">Hoc demonſtrauit Leonardus Piſanus in libro, qui de-
              <lb/>
            praxi geometriæ inſcribitur. </s>
            <s xml:id="echoid-s4296" xml:space="preserve">Sed quoniam is adhucim-
              <lb/>
            preſſus non eſt, nos ipſius demonſtrationem breuíter
              <lb/>
            perſtringemus, rem ipſam ſecuti, non uerba. </s>
            <s xml:id="echoid-s4297" xml:space="preserve">Sit fru-
              <lb/>
            ſtum pyramidis a b c d e f, cuíus maior baſis triangulum
              <lb/>
            a b c, minor d e f: </s>
            <s xml:id="echoid-s4298" xml:space="preserve">& </s>
            <s xml:id="echoid-s4299" xml:space="preserve">iunctis a e, e c, c d, per line-
              <lb/>
            as a e, e c ducatur planum ſecans fruſtum: </s>
            <s xml:id="echoid-s4300" xml:space="preserve">itemque per
              <lb/>
            lineas e c, c d; </s>
            <s xml:id="echoid-s4301" xml:space="preserve">& </s>
            <s xml:id="echoid-s4302" xml:space="preserve">per c d, d a alia plana ducantur, quæ,
              <lb/>
            diuident fruſtum in tres pyramides a b c e, a d c e, d e f c.</s>
            <s xml:id="echoid-s4303" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>