Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[31. LEMMAI.]
[32. LEMMA II.]
[33. LEMMA III.]
[34. LEMMA IIII.]
[35. PROPOSITIO VII.]
[36. PROPOSITIO VIII.]
[37. COMMENTARIVS.]
[38. PROPOSITIO IX.]
[39. COMMENTARIVS.]
[40. PROPOSITIO X.]
[41. COMMENTARIVS.]
[42. LEMMA I.]
[43. LEMMA II.]
[44. LEMMA III.]
[45. LEMMA IIII.]
[46. LEMMA V.]
[47. LEMMA VI.]
[48. II.]
[49. III.]
[50. IIII.]
[51. V.]
[52. DEMONSTRATIO SECVNDAE PARTIS.]
[53. COMMENTARIVS.]
[54. DEMONSTRATIO TERTIAE PARTIS.]
[55. COMMENTARIVS.]
[56. DEMONSTRATIO QVARTAE PARTIS.]
[57. DEMONSTRATIO QVINT AE PARTIS.]
[58. FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.]
[59. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.]
[60. CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.]
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DE CENTRO GRA VIT. SOLID.
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              <pb o="11" file="0133" n="133" rhead="DE CENTRO GRA VIT. SOLID."/>
            & </s>
            <s xml:space="preserve">per o ducatur o p ad k m ipſi h g æquidiſtans. </s>
            <s xml:space="preserve">Itaque li
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            nea h m bifariã uſque eò diuidatur, quoad reliqua ſit pars
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            quædam q m, minor o p. </s>
            <s xml:space="preserve">deinde h m, m g diuidantur in
              <lb/>
            partes æ quales ipſi m q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per diuiſiones lineæ ipſi m K
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            æ quidiſtantes ducantur. </s>
            <s xml:space="preserve">puncta uero, in quibus hæ trian-
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            gulorum latera ſecant, coniungantur ductis lineis r s, t u,
              <lb/>
              <anchor type="figure" xlink:label="fig-0133-01a" xlink:href="fig-0133-01"/>
            x y; </s>
            <s xml:space="preserve">quæ baſi g h æquidiſtabunt. </s>
            <s xml:space="preserve">Quoniam enim lineæ g z,
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            h α ſunt æ quales: </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">æquales g m, m h: </s>
            <s xml:space="preserve">ut m g ad g z,
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            ita erit m h, ad h α: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidendo, ut m z ad z g, ita m α ad
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            α h. </s>
            <s xml:space="preserve">Sed ut m z ad z g, ita k r ad r g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut m α ad α h, ita k s
              <lb/>
              <anchor type="note" xlink:label="note-0133-01a" xlink:href="note-0133-01"/>
            ad s h. </s>
            <s xml:space="preserve">quare ut κ r ad r g, ita k s ad s h. </s>
            <s xml:space="preserve">æ quidiſtant igitur
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              <anchor type="note" xlink:label="note-0133-02a" xlink:href="note-0133-02"/>
            inter ſe ſe r s, g h. </s>
            <s xml:space="preserve">eadem quoque ratione demonſtrabimus
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