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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FED. COMMANDINI
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            qr, eodem, quo ſupra, modo oſtendemns f g ad p q, ut f h
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            ad p r. </s>
            <s xml:space="preserve">ſed priſma a e ad ipſum k o eſt, ut f h ad p r. </s>
            <s xml:space="preserve">ergo
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            & </s>
            <s xml:space="preserve">ut f g axis ad axem p q. </s>
            <s xml:space="preserve">ex quibus fit, ut pyramis a b c d f
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            ad pyrami-
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            dẽ k l m n p
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            eandem-ha
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            beat pro-
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            portionẽ,
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            quãaxis ad
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            axẽ. </s>
            <s xml:space="preserve">quod
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            demonſtrã
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            dũ fuerat.</s>
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            <s xml:space="preserve">Simili ra
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            tione in a-
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            liis priſma-
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            tibus & </s>
            <s xml:space="preserve">py
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            ramidibus eadem demonſtrabuntur.</s>
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        <div type="section" level="1" n="86">
          <head xml:space="preserve">THEOREMA XVII. PROPOSITIO XXI.</head>
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            <s xml:space="preserve">Priſmata omnia, & </s>
            <s xml:space="preserve">pyramides inter ſe propor
              <lb/>
            tionem habent compoſitam ex proportione ba-
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            ſium, & </s>
            <s xml:space="preserve">proportione altitudinum.</s>
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          </p>
          <p>
            <s xml:space="preserve">Sint duo priſmata a e, g m: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">priſmatis a e baſis qua
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            drilaterum a b c d, & </s>
            <s xml:space="preserve">altitudo e f: </s>
            <s xml:space="preserve">priſmatis uero g m ba-
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            fis quadrilaterum g h K l, & </s>
            <s xml:space="preserve">altitudo m n. </s>
            <s xml:space="preserve">Dico priſma a e
              <lb/>
            ad priſma g m proportionem habere compoſitam ex pro
              <lb/>
            portione baſis a b c d ad baſim g h k l, & </s>
            <s xml:space="preserve">ex proportione
              <lb/>
            altitudinis e f, ad altitudinem m n.</s>
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          <p>
            <s xml:space="preserve">Sint enim primum e f, m n æquales: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut baſis a b c d
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            ad baſim g h k l, ita fiat linea, in qua o ad lineam, in qua p:
              <lb/>
            </s>
            <s xml:space="preserve">ut autem e f ad m n, ita linea p ad lineam q. </s>
            <s xml:space="preserve">erunt lineæ
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            p q inter ſe æquales. </s>
            <s xml:space="preserve">Itaque priſma a e ad priſma g m eã</s>
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