Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s4763" xml:space="preserve">
              <pb file="0190" n="190" rhead="FED. COMMANDINI"/>
            ctiones circuli ex prima propofitione ſphæricorum Theo
              <lb/>
            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-
              <lb/>
            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-
              <lb/>
            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
              <lb/>
            duodecimi libri elementorum, circuli quoque inter ſe ſe
              <lb/>
            æquales. </s>
            <s xml:id="echoid-s4771" xml:space="preserve">poſtremo a centro g ad circulum a b c perpendi
              <lb/>
            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
              <lb/>
            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
              <lb/>
            eſt ex corollario primæ ſphæricorum Theodoſii, punctum
              <lb/>
            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
              <lb/>
            niam igitur triangulorum g a h, g d K latus a g eſt æquale la
              <lb/>
            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
              <lb/>
            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
              <lb/>
            ricorum Theodoſii g h ipſi g K: </s>
            <s xml:id="echoid-s4783" xml:space="preserve">triangulum g a h æquale
              <lb/>
            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-
              <lb/>
            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-
              <lb/>
              <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.
              <lb/>
            </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
              <lb/>
              <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-
              <lb/>
              <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"/>
              </figure>
            anguli a b c grauitatis cen
              <lb/>
            trũ probabitur ex iis, quæ
              <lb/>
            in prima propoſitione hu
              <lb/>
            ius tradita funt. </s>
            <s xml:id="echoid-s4794" xml:space="preserve">quare g h
              <lb/>
            erit pyramidis a b c g axis.
              <lb/>
            </s>
            <s xml:id="echoid-s4795" xml:space="preserve">& </s>
            <s xml:id="echoid-s4796" xml:space="preserve">ob eandem cauſſam g k
              <lb/>
            axis pyramidis d e f g. </s>
            <s xml:id="echoid-s4797" xml:space="preserve">Ita-
              <lb/>
            que centrum grauitatis py
              <lb/>
            ramidis a b c g ſit púctum
              <lb/>
            l, & </s>
            <s xml:id="echoid-s4798" xml:space="preserve">pyramidis d e f g ſit m. </s>
            <s xml:id="echoid-s4799" xml:space="preserve">
              <lb/>
            Similiter ut ſupra demon-
              <lb/>
            ſtrabimus m g, g linter ſe æquales eſſe, & </s>
            <s xml:id="echoid-s4800" xml:space="preserve">punctum g graui
              <lb/>
            tatis centrum magnitudinis, quæ ex utriſque pyramidibus
              <lb/>
            conſtat. </s>
            <s xml:id="echoid-s4801" xml:space="preserve">eodem modo demonſtrabitur, quarumcunque
              <lb/>
            duarum pyramidum, quæ opponuntur, grauitatis </s>
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