Commandino, Federico, Liber de centro gravitatis solidorum, 1565

Page concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
page |< < of 101 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000798">
                <pb pagenum="38" xlink:href="023/01/083.jpg"/>
              ad portiones ſolidas maiorem habet
                <expan abbr="proportionẽ">proportionem</expan>
              , quàm
                <lb/>
              nl ad lm: & diuidendo fruſtum pyramidis ad dictas por­
                <lb/>
              tiones maiorem proportionem habet, quàm nm ad ml. </s>
              <lb/>
              <s id="s.000799">fiat igitur ut fruſtum pyramidis ad portiones, ita qm ad
                <lb/>
              m l. </s>
              <s id="s.000800">Itaque quoniam à fruſto coni, uel coni portionis ad,
                <lb/>
              cuius grauitatis centrum eſt m, aufertur fruſtum pyrami­
                <lb/>
              dis habens centrum l; erit reliquæ magnitudinis, quæ ex
                <lb/>
              portionibus ſolidis conſtat; grauitatis
                <expan abbr="cẽtrum">centrum</expan>
              in linea lm
                <lb/>
              producta, atque in puncto q, extra figuram poſito: quod
                <lb/>
              fieri nullo modo poteſt. </s>
              <s id="s.000801">relinquitur ergo, ut punctum l ſit
                <lb/>
              fruſti ad grauitatis centrum. </s>
              <s id="s.000802">quz omnia demonſtranda
                <lb/>
              proponebantur.</s>
            </p>
            <p type="margin">
              <s id="s.000803">
                <margin.target id="marg95"/>
              22. huius</s>
            </p>
            <p type="margin">
              <s id="s.000804">
                <margin.target id="marg96"/>
              19. quínti</s>
            </p>
            <p type="head">
              <s id="s.000805">THEOREMA XXII. PROPOSITIO XXVII.</s>
            </p>
            <p type="main">
              <s id="s.000806">OMNIVM ſolidorum in ſphæra deſcripto­
                <lb/>
              rum, quæ æqualibus, & ſimilibus baſibus conti­
                <lb/>
              nentur, centrum grauitatis eſt idem, quod ſphæ­
                <lb/>
              ræ centrum.</s>
            </p>
            <p type="main">
              <s id="s.000807">Solida eiuſmodi corpora regularia appellare ſolent, de
                <lb/>
              quibus agitur in tribus ultimis libris elementorum: ſunt
                <lb/>
              autem numero quinque, tetrahedrum, uel pyramis, hexa­
                <lb/>
              hedrum, uel cubus, octahedrum, dodecahedrum, & icoſa­
                <lb/>
              hedrum.</s>
            </p>
            <p type="main">
              <s id="s.000808">Sit primo abcd pyramis
                <expan abbr="ĩ">im</expan>
              ſphæra deſcripta, cuius ſphæ
                <lb/>
              ræ centrum ſit e. </s>
              <s id="s.000809">Dico e pyramidis abcd grauitatis eſſe
                <lb/>
              centrum. </s>
              <s id="s.000810">Si enim iuncta dc producatur ad baſim abc in
                <lb/>
              f; ex iis, quæ demonſtrauit Campanus in quartodecimo li
                <lb/>
              bro elementorum, propoſitione decima quinta, & decima
                <lb/>
              ſeptima, erit f centrum circuli circa triangulum abc de­
                <lb/>
              ſcripti: atque erit ef ſexta pars ipſius ſphæræ axis. </s>
              <s id="s.000811">quare
                <lb/>
              ex prima huius conſtat trianguli abc grauitatis centrum
                <lb/>
              eſſe punctum f: & idcirco lineam df eſſe pyramidis axem. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum