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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          <p>
            <s xml:space="preserve">
              <pb file="0120" n="120" rhead="FED. COMMANDINI"/>
            triangulum m k φ triangulo n k φ. </s>
            <s xml:space="preserve">ergo anguli l z k, o z k,
              <lb/>
            m φ k, n φ k æquales ſunt, ac recti. </s>
            <s xml:space="preserve">quòd cum etiam recti
              <lb/>
            ſint, qui ad k; </s>
            <s xml:space="preserve">æquidiſtabunt lineæ l o, m n axi b d. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita.
              <lb/>
            </s>
            <s xml:space="preserve">
              <anchor type="note" xlink:label="note-0120-01a" xlink:href="note-0120-01"/>
            demonſtrabuntur l m, o n ipſi a c æquidiſtare. </s>
            <s xml:space="preserve">Rurſus ſi
              <lb/>
            iungantur a l, l b, b m, m c, c n, n d, d o, o a: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam di
              <lb/>
            uidantur: </s>
            <s xml:space="preserve">à centro autem k ad diuiſiones ductæ lineæ pro-
              <lb/>
            trahantur uſque ad ſectionem in puncta p q r s t u x y: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">po
              <lb/>
            ſtremo p y, q x, r u, s t, q r, p s, y t, x u coniungantur. </s>
            <s xml:space="preserve">Simili-
              <lb/>
            ter oſtendemus lineas
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              <anchor type="figure" xlink:label="fig-0120-01a" xlink:href="fig-0120-01"/>
            p y, q x, r u, s t axi b d æ-
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            quidiſtantes eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">q r,
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            p s, y t, x u æquidiſtan-
              <lb/>
            tesipſi a c. </s>
            <s xml:space="preserve">Itaque dico
              <lb/>
            harum figurarum in el-
              <lb/>
            lipſi deſcriptarum cen-
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            trum grauitatis eſſe pũ-
              <lb/>
            ctum k, idem quod & </s>
            <s xml:space="preserve">el
              <lb/>
            lipſis centrum. </s>
            <s xml:space="preserve">quadri-
              <lb/>
            lateri enim a b c d cen-
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            trum eſt k, ex decima e-
              <lb/>
            iuſdem libri Archime-
              <lb/>
            dis, quippe cũ in eo om
              <lb/>
            nes diametri cõueniãt.
              <lb/>
            </s>
            <s xml:space="preserve">Sed in figura alb m c n
              <lb/>
              <anchor type="note" xlink:label="note-0120-02a" xlink:href="note-0120-02"/>
            d o, quoniam trianguli
              <lb/>
            alb centrum grauitatis
              <lb/>
              <anchor type="note" xlink:label="note-0120-03a" xlink:href="note-0120-03"/>
            eſt in linea l e: </s>
            <s xml:space="preserve">trapezijq́; </s>
            <s xml:space="preserve">a b m o centrum in linea e k: </s>
            <s xml:space="preserve">trape
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            zij o m c d in k g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">trianguli c n d in ipſa g n: </s>
            <s xml:space="preserve">erit magnitu
              <lb/>
            dinis ex his omnibus conſtantis, uidelicet totius figuræ cen
              <lb/>
            trum grauitatis in linea l n: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">o b eandem cauſſam in linea
              <lb/>
            o m. </s>
            <s xml:space="preserve">eſt enim trianguli a o d centrum in linea o h: </s>
            <s xml:space="preserve">trapezij
              <lb/>
            a l n d in h k: </s>
            <s xml:space="preserve">trapezij l b c n in k f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">trianguli b m c in fm.
              <lb/>
            </s>
            <s xml:space="preserve">cum ergo figuræ a l b m c n d o centrum grauitatis ſit in li-
              <lb/>
            nea l n, & </s>
            <s xml:space="preserve">in linea o m; </s>
            <s xml:space="preserve">erit centrum ipſius punctum k, in</s>
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