Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

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            t u, x y ipſi g h æquidiſtare. </s>
            <s xml:id="echoid-s3403" xml:space="preserve">Et quoniam triangula, quæ
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            fiunt à lineis K y, y u, u s, s h æqualia ſuntinter ſe, & </s>
            <s xml:id="echoid-s3404" xml:space="preserve">ſimilia
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            triangulo K m h: </s>
            <s xml:id="echoid-s3405" xml:space="preserve">habebit triangulum K m h ad triangulũ
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              <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">19. ſexti</note>
            K δ y duplam proportionem eius, quæ eſt lineæ k h ad K y.
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            <s xml:id="echoid-s3406" xml:space="preserve">ſed _K_ h poſita eſt quadrupla ipſius k y. </s>
            <s xml:id="echoid-s3407" xml:space="preserve">ergo triangulum
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            κ m h ad triangulum _K_ δ y eãdem proportionem habebit,
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            quam ſexdecim ad unũ & </s>
            <s xml:id="echoid-s3408" xml:space="preserve">ad quatuor triangula k δ y, y u,
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            u s, s α h habebit eandem, quam fexdecim ad quatuor, hoc
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            eſt quam h K ad κ y: </s>
            <s xml:id="echoid-s3409" xml:space="preserve">& </s>
            <s xml:id="echoid-s3410" xml:space="preserve">ſimiliter eandem habere demonſtra
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            bitur trian-
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            gulum κ m g
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            ad quatuor
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            triãgula K δ
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            x, x γ t, t β r,
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            r z g. </s>
            <s xml:id="echoid-s3411" xml:space="preserve">quare
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              <note position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">2. uel 121
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              quinti.</note>
            totum trian
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            gulum K g h
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            ad omnia tri
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            angula g z r,
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            r β t, t γ x, x δ
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            _K_, K δ y, y u,
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            u s, s α h ita
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            erit, ut h κ a d
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            k y, hoc eſt
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            ut h m ad m
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            q. </s>
            <s xml:id="echoid-s3412" xml:space="preserve">Si igitur in
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            triangulis a b c, d e f deſcribantur figuræ ſimiles ei, quæ de-
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            ſcripta eſt in g h K triangulo: </s>
            <s xml:id="echoid-s3413" xml:space="preserve">& </s>
            <s xml:id="echoid-s3414" xml:space="preserve">per lineas ſibi reſp onden-
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            tes plana ducantur: </s>
            <s xml:id="echoid-s3415" xml:space="preserve">totum priſma a f diuiſum eritin tria
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            ſolida parallelepipeda y γ, u β, s z, quorum baſes ſunt æ qua
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            les & </s>
            <s xml:id="echoid-s3416" xml:space="preserve">ſimiles ipſis parallelogrammis y γ, u β, s z: </s>
            <s xml:id="echoid-s3417" xml:space="preserve">& </s>
            <s xml:id="echoid-s3418" xml:space="preserve">in octo
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            priſmata g z r, r β t, t γ x, x δ K, κ δ y, y u, u s, s α h: </s>
            <s xml:id="echoid-s3419" xml:space="preserve">quorum
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            item baſes æquales, & </s>
            <s xml:id="echoid-s3420" xml:space="preserve">ſimiles ſunt dictis triangulis; </s>
            <s xml:id="echoid-s3421" xml:space="preserve">altitu-
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            do autem in omnibus, totius priſmatis altitudini æ qualis.</s>
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