Archimedes, Archimedis De insidentibvs aqvae

Table of contents

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[11.] Theorema v. Propoſitio v.
[12.] Theorema vj. Propoſitio vj.
[13.] Theorema vij. Propoſitio vij.
[14.] Suppoſitio ſecunda.
[15.] Theorema viij. Propoſitio viij.
[16.] AR CHIM EDIS DE INSIDENTIBVS AQV AE.
[17.] LIBER SECVNDVS. TROIANO CVRTIO VENETIIS, APVD TROIANVM CVRTIVM. M D L X V
[18.] FABRITIO DENORES FILIO IACOBI COMITIS TRIPOLIS CVRTIVS TROIANVS S. P. D.
[19.] INSIDENTIBVS AQV AE. LIB. II. PRIMVS.
[20.] SECVNDVS.
[21.] TERTIVS.
[22.] QVARTVS.
[23.] QVINTVS.
[24.] SEXTVS.
[25.] SEPTIMVS.
[26.] OCTAVVS.
[27.] NONVS.
[28.] DECIMVS.
[29.] Archimedis de inſidentibus in bumido li-ber ſecundus explicit, ad laudem Dei.
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            copulata autem z, t, inuenietur centrum eius, quòd extra humidum in
              <lb/>
            educta, & </s>
            <s xml:id="echoid-s525" xml:space="preserve">ſit g. </s>
            <s xml:id="echoid-s526" xml:space="preserve">& </s>
            <s xml:id="echoid-s527" xml:space="preserve">ducatur perpendicularis ad ſuperficiem bumidi per
              <lb/>
            z, g, æquediſtanter ipſi n, o, palam igitur, quòd non manet tota portio,
              <lb/>
            ſed reuoluetur ita, ut axis ad ſuperficiem humidi faciat angulum mino-
              <lb/>
            rem, quàm illo, quem nunc facit: </s>
            <s xml:id="echoid-s528" xml:space="preserve">quoniam nec axe faciente ad humidum
              <lb/>
            angulum maiorem, quàm b, conſiſtit portio, neque minorem. </s>
            <s xml:id="echoid-s529" xml:space="preserve">Manifeſtũ
              <lb/>
            quòd tantum angulum faciente conſistet. </s>
            <s xml:id="echoid-s530" xml:space="preserve">Sic enim erit quæ i, o, æqualis
              <lb/>
            ipſi x, b, & </s>
            <s xml:id="echoid-s531" xml:space="preserve">quæ ***, ipſi x, r, & </s>
            <s xml:id="echoid-s532" xml:space="preserve">quæ p h, ipſi f, erit igitur m, h, æmyolia
              <lb/>
            ipſius p, h, quæ autem p, b, ipſi b, ***, dupla quod autem ergo
              <lb/>
            eius, quod in humido centrum grauitatis eſt. </s>
            <s xml:id="echoid-s533" xml:space="preserve">Quare ſecundum eandem
              <lb/>
            perpendicularem ſurſum ferretur, et quod extra deorſum ferretur mane
              <lb/>
            bit ergo contra pellentur enim adinuicem.</s>
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          <head xml:id="echoid-head37" xml:space="preserve">NONVS.</head>
          <p>
            <s xml:id="echoid-s535" xml:space="preserve">Recta portio rectanguli conoydalis, quando axem habue
              <lb/>
            rit maiorem quidem, quàm hemiolium eius quæ uſque ad a-
              <lb/>
            xem, minorem autem ut hanc habeat proportione, quam
              <lb/>
            habent quindecim ad quattuor: </s>
            <s xml:id="echoid-s536" xml:space="preserve">& </s>
            <s xml:id="echoid-s537" xml:space="preserve">in grauitate ad humidũ
              <lb/>
            habeat proportionem maiorem proportione, quam habet
              <lb/>
            exceſſus, quo tetragonum quod ab axe eſt maius tetragono,
              <lb/>
            quod ab exceſſu, quo axis eſt maior, quàm hemiolius eius,
              <lb/>
            quæ uſq; </s>
            <s xml:id="echoid-s538" xml:space="preserve">ad axem ad tetragonum, quod ab axe demiſſa in hu
              <lb/>
            midũ, ita ut baſis ipſius tota, ſit in humido poſita inclinata,
              <lb/>
            nec ut axis ipſius ſecundum perpendicularem ſit, necmane
              <lb/>
            bit inclina ta, niſi quã do axis ipſius ad ſuperficiem humidife
              <lb/>
            cerit angulum
              <unsure/>
            æqu alem accepto ſimiliter, ut prius.</s>
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