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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DEIIS QVAE VEH. IN AQVA.
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              <pb o="43" file="0101" n="101" rhead="DEIIS QVAE VEH. IN AQVA."/>
            ad quadratum bd: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam habet portio ad humidum in
              <lb/>
            grauitate, eandem quadratum nt habet ad bd quadratũ,
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            ex iis, quæ dicta ſunt: </s>
            <s xml:space="preserve">conſtat n t lineæ ψ æqualem eſſe,
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            quare & </s>
            <s xml:space="preserve">portio-
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              <anchor type="figure" xlink:label="fig-0101-01a" xlink:href="fig-0101-01"/>
            nes a n z, a g q
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            ſunt æquales. </s>
            <s xml:space="preserve">Et
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            quoniam in por
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            tionibus æquali
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            bus, & </s>
            <s xml:space="preserve">ſimilibus
              <lb/>
            a g q l, a n z l, ab
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            extremitatibus
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            baſiũ ductæ ſunt
              <lb/>
            a q, a z, quæ æ-
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            quales portiões
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            abſcindunt: </s>
            <s xml:space="preserve">per
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            ſpicuum eſt an-
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            gulos facere æ-
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            quales cum por
              <lb/>
            tionum diame-
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            tris: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangu-
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            lorum n fs, g ω c, angulos, qui ad f ω æquales eſſe: </s>
            <s xml:space="preserve">itemque
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            æquales inter ſe, s b, c b; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">s r, c r, quare & </s>
            <s xml:space="preserve">n χ, g y æquales:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">χ t y i. </s>
            <s xml:space="preserve">cũq; </s>
            <s xml:space="preserve">g h dupla ſit ipſius h i, erit n χ minor, quàm
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            duplaipſius χ t. </s>
            <s xml:space="preserve">Sit igitur n m ipſius m t dupla: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta
              <lb/>
            m K protrahatur ad e. </s>
            <s xml:space="preserve">Itaque centrum grauitatis totius
              <lb/>
            erit punctum K: </s>
            <s xml:space="preserve">partis eius, quæ eſt in humido, punctũ m: </s>
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              <lb/>
            eius autem, quæ extra humidum in linea protracta, quod
              <lb/>
            ſit e. </s>
            <s xml:space="preserve">ergo ex proxime demonſtratis patet, nõ manere por
              <lb/>
            tionem, ſed inclinari adeo, ut baſis nullo modo ſuperficiẽ
              <lb/>
            humidi contingat. </s>
            <s xml:space="preserve">At uero portionem conſiſtere ita, uta-
              <lb/>
            xis cum ſuperficie humidi faciat angulum angulo φ mino-
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            rem, ſic demonſtrabitur. </s>
            <s xml:space="preserve">conſiſtat enim, ſi fieri poteſt, ut
              <lb/>
            non faciat angulum minorem angulo φ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia eadem diſ-
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            ponantur; </s>
            <s xml:space="preserve">ut in ſubiecta figura. </s>
            <s xml:space="preserve">eodem modo demonſtra</s>
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