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
quia o g ipſius g x eſt dupla. Sit p h dupla h t: & iun-
cta h κ ad ω producatur.
erit totius quidem portionis cen
trum grauitatis k;
partis eius, quæ intra humidum h; eius
uero, quæ extra humidum in linea κ ω, quod ſit ω.
Itaque
demonſtrabitur
Figure: /permanent/library/4E7V2WGH/figures/0092-01 not scanned
[Figure 56]
ſimiliter &
k z ad
humidi ſuperſi-
ciem perpẽdicu-
laris, &
quæ per
puncta h ω æqui-
diſtantes ipſi κ z
ducuntur.
quare
nõ manebit por
tio, ſed inclinabi
tur, donec baſis
ipſius in uno pũ
cto contingat ſu
perficiem humi-
di:
atque ita con
ſiſtet.
nam in por
tionibus æquali-
bus a o q l, a p m l, ductæ erunt ab extremitatibus baſium
a q, a m, quæ æquales portiones abſcindunt:
etenim a o q
ipſi a p m, utin ſuperioribus æqualis demonſtrabitur.
ergo
Eæquales faciunt acutos angulos a q, a m cum diametris ba
ſium:
quòd anguli ad χ & n æquales ſint. quare ſi ducta
h k ad ω producatur, erit totius portionis grauitatis cen-
trum k;
partis eius, quæ in humido h; at eius, quæ extra
humidum in linea h κ;
quod ſit ω: & h k ad humidi ſuper-
ficiem perpendicularis.
per eaſdem igitur rectas lineas,
quod quidem in humido eſt, ſurſum, &
quod extra humi-
dum deorſum feretur.
quare manebit portio, cuius baſis
humidi ſuperficiem in uno puncto continget:
& axis cum
ipſa angulum faciet æqualem angulo χ.
Similiter demon-
F

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