Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

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              <pb o="37" file="0185" n="185" rhead="DE CENTRO GRAVIT. SOLID."/>
            ducta fuerìnt, ira ut in unum punctum y coeant, erunt triã
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            gala u y l, x y p, t y _k_ inter ſe ſimilia: </s>
            <s xml:id="echoid-s4630" xml:space="preserve">& </s>
            <s xml:id="echoid-s4631" xml:space="preserve">ſimilia etiam triangu
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            la l y r, p y s, _k_ y q. </s>
            <s xml:id="echoid-s4632" xml:space="preserve">quare ut in 19 huius, demonſtrabitur
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            x p, ad p s: </s>
            <s xml:id="echoid-s4633" xml:space="preserve">itemq; </s>
            <s xml:id="echoid-s4634" xml:space="preserve">t k ad _k_ q èandem habere proportionẽ,
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            quam u l ad l r. </s>
            <s xml:id="echoid-s4635" xml:space="preserve">Sed ut u l ad l r, ita eſt triangulum a b c ad
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            triangulum a c d: </s>
            <s xml:id="echoid-s4636" xml:space="preserve">& </s>
            <s xml:id="echoid-s4637" xml:space="preserve">ut t k ad K q, ita triangulum e f g ad
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            triangulum e g h. </s>
            <s xml:id="echoid-s4638" xml:space="preserve">Vt autem triangulum a b c ad triangu-
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            lum a c d, ita pyramis a b c y ad pyramidem a c d y. </s>
            <s xml:id="echoid-s4639" xml:space="preserve">& </s>
            <s xml:id="echoid-s4640" xml:space="preserve">ut
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            triangulum e f g ad triangulum e g h, ita pyramis e f g y
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            ad pyramidem e g h y; </s>
            <s xml:id="echoid-s4641" xml:space="preserve">ergo ut pyramis a b c y ad pyramidẽ
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            a c d y, ita pyramis e f g y ad pyramidem e g h y. </s>
            <s xml:id="echoid-s4642" xml:space="preserve">reliquum
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              <note position="right" xlink:label="note-0185-01" xlink:href="note-0185-01a" xml:space="preserve">19. quinti</note>
            igitur fruſtũ l f ad reliquum fruſtũ l h eſt ut pyramis a b c y
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            ad pyramidem a c d y, hoc eſt ut u l ad l r, & </s>
            <s xml:id="echoid-s4643" xml:space="preserve">ut x p ad p s.
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            </s>
            <s xml:id="echoid-s4644" xml:space="preserve">Quòd cum fruſti l f centrum grauitatis ſit s: </s>
            <s xml:id="echoid-s4645" xml:space="preserve">& </s>
            <s xml:id="echoid-s4646" xml:space="preserve">fruſti l h ſit
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            centrum x: </s>
            <s xml:id="echoid-s4647" xml:space="preserve">conſtat punctum p totius fruſti a g grauitatis
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              <note position="right" xlink:label="note-0185-02" xlink:href="note-0185-02a" xml:space="preserve">8. Archi-
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              medis.</note>
            eſſe centrum. </s>
            <s xml:id="echoid-s4648" xml:space="preserve">Eodem modo fiet demonſtratio etiam in
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            aliis pyramidibus.</s>
            <s xml:id="echoid-s4649" xml:space="preserve"/>
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            <s xml:id="echoid-s4650" xml:space="preserve">Sit fruſtum a d à cono, uel coni portione abſciſſum, cu-
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            ius maior baſis circulus, uel ellipſis circa diametrum a b;
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            </s>
            <s xml:id="echoid-s4651" xml:space="preserve">minor circa diametrum c d: </s>
            <s xml:id="echoid-s4652" xml:space="preserve">& </s>
            <s xml:id="echoid-s4653" xml:space="preserve">axis e f. </s>
            <s xml:id="echoid-s4654" xml:space="preserve">diuidatur autẽ e f
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            in g, ita ut e g ad g f eandem proportionem habeat, quam
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            duplum diametri a b unà cum diametro c d ad duplum c d
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            unà cum a b. </s>
            <s xml:id="echoid-s4655" xml:space="preserve">Sitq; </s>
            <s xml:id="echoid-s4656" xml:space="preserve">g h quarta pars lineæ g e: </s>
            <s xml:id="echoid-s4657" xml:space="preserve">& </s>
            <s xml:id="echoid-s4658" xml:space="preserve">ſit ſ K item
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            quarta pars totius f e axis. </s>
            <s xml:id="echoid-s4659" xml:space="preserve">Rurfus quam proportionem
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            habet fruſtum a d ad conum, uel coni portionem, in eadẽ
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            baſi, & </s>
            <s xml:id="echoid-s4660" xml:space="preserve">æquali altitudine, habeat linea _k_ h ad h l. </s>
            <s xml:id="echoid-s4661" xml:space="preserve">Dico pun-
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            ctum l fruſti a d grauitatis centrum eſſe. </s>
            <s xml:id="echoid-s4662" xml:space="preserve">Si enim fieri po-
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            teſt, ſit m centrum: </s>
            <s xml:id="echoid-s4663" xml:space="preserve">producaturq; </s>
            <s xml:id="echoid-s4664" xml:space="preserve">l m extra fruſtum in n: </s>
            <s xml:id="echoid-s4665" xml:space="preserve">
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            & </s>
            <s xml:id="echoid-s4666" xml:space="preserve">ut n l ad l m, ita fiat circulus, uel ellipſis circa diametrũ
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            a b ad aliud ſpacium, in quo ſit o. </s>
            <s xml:id="echoid-s4667" xml:space="preserve">Itaque in circulo, uel
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            ellipſi circa diametrum a b rectilinea figura plane deſcri-
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            batur, ita ut quæ relinquuntur portiones ſint o ſpacio mi-
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            nores: </s>
            <s xml:id="echoid-s4668" xml:space="preserve">& </s>
            <s xml:id="echoid-s4669" xml:space="preserve">inteiligatur pyramis a p b, baſim habens rectili-
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            neam figuram in circulo, uel ellipſi a b deſcriptam: </s>
            <s xml:id="echoid-s4670" xml:space="preserve">à </s>
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