Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[61. ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[62. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.]
[63. PETITIONES.]
[64. THEOREMA I. PROPOSITIO I.]
[65. THEOREMA II. PROPOSITIO II.]
[66. THE OREMA III. PROPOSITIO III.]
[67. THE OREMA IIII. PROPOSITIO IIII.]
[68. ALITER.]
[69. THEOREMA V. PROPOSITIO V.]
[70. COROLLARIVM.]
[71. THEOREMA VI. PROPOSITIO VI.]
[72. THE OREMA VII. PROPOSITIO VII.]
[73. THE OREMA VIII. PROPOSITIO VIII.]
[74. THE OREMA IX. PROPOSITIO IX.]
[75. PROBLEMA I. PROPOSITIO X.]
[76. PROBLEMA II. PROPOSITIO XI.]
[77. PROBLEMA III. PROPOSITIO XII.]
[78. PROBLEMA IIII. PROPOSITIO XIII.]
[79. THEOREMA X. PROPOSITIO XIIII.]
[80. THE OREMA XI. PROPOSITIO XV.]
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FED. COMMANDINI
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            <s xml:space="preserve">Itaque quoniam duæ lineæ K l, l m ſe ſe tangentes, duabus
              <lb/>
            lineis ſe ſe tangentibus a b, b c æquidiſtant; </s>
            <s xml:space="preserve">nec ſunt in eo-
              <lb/>
            dem plano: </s>
            <s xml:space="preserve">angulus
              <emph style="sc">K</emph>
            l m æqualis eſt angulo a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita an
              <lb/>
              <anchor type="note" xlink:label="note-0126-01a" xlink:href="note-0126-01"/>
            gulus l m
              <emph style="sc">K</emph>
            , angulo b c a, & </s>
            <s xml:space="preserve">m
              <emph style="sc">K</emph>
            lipſi c a b æqualis prob abi
              <lb/>
            tur. </s>
            <s xml:space="preserve">triangulum ergo
              <emph style="sc">K</emph>
            l m eſt æquale, & </s>
            <s xml:space="preserve">ſimile triang ulo
              <lb/>
            a b c. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">triangulo d e f. </s>
            <s xml:space="preserve">Ducatur linea c g o, & </s>
            <s xml:space="preserve">per ip
              <lb/>
            ſam, & </s>
            <s xml:space="preserve">per c f ducatur planum ſecans priſma, cuius & </s>
            <s xml:space="preserve">paral
              <lb/>
            lelogrammi a e communis ſectio ſit o p q. </s>
            <s xml:space="preserve">tranſibit linea
              <lb/>
            f q per h, & </s>
            <s xml:space="preserve">m p per n. </s>
            <s xml:space="preserve">nam cum plana æquidiſtantia ſecen
              <lb/>
            tur à plano c q, communes eorum ſectiones c g o, m p, f q
              <lb/>
            ſibi ipſis æquidiſtabunt. </s>
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">æquidiſtant a b,
              <emph style="sc">K</emph>
            l, d e. </s>
            <s xml:space="preserve">an-
              <lb/>
            guli ergo a o c,
              <emph style="sc">K</emph>
            p m, d q f inter ſe æquales ſunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſunt
              <lb/>
              <anchor type="note" xlink:label="note-0126-02a" xlink:href="note-0126-02"/>
            æquales qui ad puncta a k d conſtituuntur. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">reliqui
              <lb/>
            reliquis æquales; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangula a c o, _K_ m p, d f q inter ſe ſimi
              <lb/>
            lia erunt. </s>
            <s xml:space="preserve">Vtigitur ca ad a o, ita fd ad d q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando
              <lb/>
              <anchor type="note" xlink:label="note-0126-03a" xlink:href="note-0126-03"/>
            ut c a ad fd, ita a o ad d q. </s>
            <s xml:space="preserve">eſt autem c a æqualis fd. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">
              <lb/>
            a o ipſi d q. </s>
            <s xml:space="preserve">eadem quoque ratione & </s>
            <s xml:space="preserve">a o ipſi _K_ p æqualis
              <lb/>
            demonſtrabitur. </s>
            <s xml:space="preserve">Itaque ſi triangula, a b c, d e f æqualia & </s>
            <s xml:space="preserve">
              <lb/>
            ſimilia inter ſe aptétur,
              <lb/>
              <anchor type="figure" xlink:label="fig-0126-01a" xlink:href="fig-0126-01"/>
            cadet linea f q in lineam
              <lb/>
            c g o. </s>
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">centrũ gra
              <lb/>
              <anchor type="note" xlink:label="note-0126-04a" xlink:href="note-0126-04"/>
            uitatis h in g centrũ ca-
              <lb/>
            det. </s>
            <s xml:space="preserve">trãſibit igitur linea
              <lb/>
            f q per h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">planum per
              <lb/>
            c o & </s>
            <s xml:space="preserve">c f ductũ per axẽ
              <lb/>
            g h ducetur: </s>
            <s xml:space="preserve">idcircoq; </s>
            <s xml:space="preserve">li
              <lb/>
            neam m p etiã per n trã
              <lb/>
            ſire neceſſe erit. </s>
            <s xml:space="preserve">Quo-
              <lb/>
            niam ergo ſh, c g æqua-
              <lb/>
            les ſunt, & </s>
            <s xml:space="preserve">æquidiſtãtes:
              <lb/>
            </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">h q, g o; </s>
            <s xml:space="preserve">rectæ li-
              <lb/>
            neæ, quæ ipſas cónectũt
              <lb/>
            c m f, g n h, o p q æqua-
              <lb/>
            les & </s>
            <s xml:space="preserve">æquidiſtãtes erũt.</s>
            <s xml:space="preserve"/>
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