Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo
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              <pb file="0190" n="190" rhead="FED. COMMANDINI"/>
            ctiones circuli ex prima propofitione ſphæricorum Theo
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            doſii: </s>
            <s xml:id="echoid-s4764" xml:space="preserve">unus quidem circa triangulum a b c deſcriptus: </s>
            <s xml:id="echoid-s4765" xml:space="preserve">al-
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            ter uero circa d e f: </s>
            <s xml:id="echoid-s4766" xml:space="preserve">& </s>
            <s xml:id="echoid-s4767" xml:space="preserve">quoniam triangula a b c, d e f æqua-
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            lia ſunt, & </s>
            <s xml:id="echoid-s4768" xml:space="preserve">ſimilia; </s>
            <s xml:id="echoid-s4769" xml:space="preserve">erunt ex prima, & </s>
            <s xml:id="echoid-s4770" xml:space="preserve">ſecunda propoſitione
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            duodecimi libri elementorum, circuli quoque inter ſe ſe
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            æquales. </s>
            <s xml:id="echoid-s4771" xml:space="preserve">poſtremo a centro g ad circulum a b c perpendi
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            cularis ducatur g h; </s>
            <s xml:id="echoid-s4772" xml:space="preserve">& </s>
            <s xml:id="echoid-s4773" xml:space="preserve">alia perpendicularis ducatur ad cir
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            culum d e f, quæ ſit g _k_; </s>
            <s xml:id="echoid-s4774" xml:space="preserve">& </s>
            <s xml:id="echoid-s4775" xml:space="preserve">iungantur a h, d k. </s>
            <s xml:id="echoid-s4776" xml:space="preserve">perſpicuum
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            eſt ex corollario primæ ſphæricorum Theodoſii, punctum
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            h centrum eſſe circuli a b c, & </s>
            <s xml:id="echoid-s4777" xml:space="preserve">k centrum circuli d e f. </s>
            <s xml:id="echoid-s4778" xml:space="preserve">Quo
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            niam igitur triangulorum g a h, g d K latus a g eſt æquale la
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            teri g d; </s>
            <s xml:id="echoid-s4779" xml:space="preserve">ſunt enim à centro ſphæræ ad ſuperficiem: </s>
            <s xml:id="echoid-s4780" xml:space="preserve">atque
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            eſt a h æquale d k: </s>
            <s xml:id="echoid-s4781" xml:space="preserve">& </s>
            <s xml:id="echoid-s4782" xml:space="preserve">ex ſexta propoſitione libri primi ſphæ
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            ricorum Theodoſii g h ipſi g K: </s>
            <s xml:id="echoid-s4783" xml:space="preserve">triangulum g a h æquale
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            erit, & </s>
            <s xml:id="echoid-s4784" xml:space="preserve">ſimile g d k triangulo: </s>
            <s xml:id="echoid-s4785" xml:space="preserve">& </s>
            <s xml:id="echoid-s4786" xml:space="preserve">angulus a g h æqualis an-
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            gulo d g _K_. </s>
            <s xml:id="echoid-s4787" xml:space="preserve">ſed anguli a g h, h g d ſunt æquales duobus re-
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              <note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">13. primi</note>
            ctis. </s>
            <s xml:id="echoid-s4788" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s4789" xml:space="preserve">ipſi h g d, d g k duobus rectis æquales erunt.
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            </s>
            <s xml:id="echoid-s4790" xml:space="preserve">& </s>
            <s xml:id="echoid-s4791" xml:space="preserve">idcirco h g, g _K_ una, atque eadem erit linea. </s>
            <s xml:id="echoid-s4792" xml:space="preserve">cum autem
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              <note position="left" xlink:label="note-0190-02" xlink:href="note-0190-02a" xml:space="preserve">14. primi</note>
            h ſit centrũ circuli, & </s>
            <s xml:id="echoid-s4793" xml:space="preserve">tri-
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              <figure xlink:label="fig-0190-01" xlink:href="fig-0190-01a" number="141">
                <image file="0190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0190-01"/>
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            anguli a b c grauitatis cen
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            trũ probabitur ex iis, quæ
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            in prima propoſitione hu
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            ius tradita funt. </s>
            <s xml:id="echoid-s4794" xml:space="preserve">quare g h
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            erit pyramidis a b c g axis.
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            </s>
            <s xml:id="echoid-s4795" xml:space="preserve">& </s>
            <s xml:id="echoid-s4796" xml:space="preserve">ob eandem cauſſam g k
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            axis pyramidis d e f g. </s>
            <s xml:id="echoid-s4797" xml:space="preserve">Ita-
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            que centrum grauitatis py
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            ramidis a b c g ſit púctum
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            l, & </s>
            <s xml:id="echoid-s4798" xml:space="preserve">pyramidis d e f g ſit m. </s>
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            Similiter ut ſupra demon-
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            ſtrabimus m g, g linter ſe æquales eſſe, & </s>
            <s xml:id="echoid-s4800" xml:space="preserve">punctum g graui
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            tatis centrum magnitudinis, quæ ex utriſque pyramidibus
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            conſtat. </s>
            <s xml:id="echoid-s4801" xml:space="preserve">eodem modo demonſtrabitur, quarumcunque
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            duarum pyramidum, quæ opponuntur, grauitatis </s>
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