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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ARCHIMEDIS
midum demiſſa adeo, ut baſis ipſius tota ſit in hu
mido, &
poſita inclinata, nec conuertetur ita, ut
axis ipſius ſecũdum perpendicularem ſit, nec ma
nebit inclinata, niſi quãdo axis cum ſuperficie hu
midi angulum fecerit æqualem angulo ſimiliter
ut prius, aſſumpto.
SIT portio, qualis dicta eſt: ponaturq; d b æ qualis axi
portionis:
& b _k_ quidem ſit dupla ipſius _k_ d; k r autem
æqualis ei, quæ uſque ad axem:
& c b ſeſquialtera b r.
Quam uero proportionem habet portio ad humidum in
grauitate, eam habeat exceſſus, quo quadratum b d exce-
dit quadratum f q, ad ipſum b d quadratum:
& ſit f ipſius
q dupla.
conſtat igitur exceſſum, quo quadratum b d ex-
cedit quadratum
Figure: /permanent/library/4E7V2WGH/figures/0064-01 not scanned
[Figure 41]
b c ad quadratum
b d, minorem ha-
bere proportio-
nem, quàm exceſ-
ſus, quo quadratũ
b d excedit qua-
dratum f q ad b d
quadratum.
eſt e-
nim b c exceſſus
quo axis portiõis
maior eſt, quã ſeſ-
quialter eius, quæ
uſque ad axem.
quare quadr atum
Ab d magis excedit
quadratum f q, quàm b c quadratum:
& idcirco linea f q
minor eſt, quàm b c itemq;
f minor, quàm br. Sit ipſi ſ

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