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 IIS QVAE VEH. IN AQVA.
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            ſectione e f c diuiditur: </s>
            <s xml:space="preserve">pars uero lineæ c a, quæ eſt in-
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            ter duas ſectiones proportione reſpondebit parti lineæ
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            ductæ, quæ itidem inter eaſdem ſectiones interiicitur; </s>
            <s xml:space="preserve">hoc
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            est ut in propoſita figura, ſi producatur d b uſque ad c h
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            in l, ut ſectioni e f c in puncto m occurrat; </s>
            <s xml:space="preserve">lineam l
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            b ad b m eãdem proportionem habere, quàm c e ad e a.</s>
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            <s xml:space="preserve">Produc. </s>
            <s xml:space="preserve">itur enim
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            q f ad eandem lineá
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            c h in n, ſecás a b c
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            ſectionem in o: </s>
            <s xml:space="preserve">& </s>
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            iuncta b c, quæ tran
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            ſibit per f, ut oſten-
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            ſum eſt, erunt trian-
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            gula c g f, c d b ſi-
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            milia: </s>
            <s xml:space="preserve">itémq; </s>
            <s xml:space="preserve">ſimi-
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            lia íter ſe, c f n, c b l.
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            </s>
            <s xml:space="preserve">quare ut g f ad d b,
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              <anchor type="note" xlink:label="note-0079-01a" xlink:href="note-0079-01"/>
            ita erit c f ad c b:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut c f ad c b, ita
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            f n ad b l. </s>
            <s xml:space="preserve">ergo g f
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              <anchor type="note" xlink:label="note-0079-02a" xlink:href="note-0079-02"/>
            ad d b, ut f n ad b l:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando g f
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            ad f n, ut d b ad b l. </s>
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            eſt autem d b æqua
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            lis ipſi b l ex trigeſi
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            maquinta primi li-
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              <anchor type="note" xlink:label="note-0079-03a" xlink:href="note-0079-03"/>
            bri conicorum. </s>
            <s xml:space="preserve">ergo
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            & </s>
            <s xml:space="preserve">g f ipſi p i æqua
              <lb/>
            lis erit: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex trige
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            ſimatertia eiuſdem
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            linea c h ſectionem
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            e f c in eodem pun-</s>
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