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
partes d. in pyramide igitur inſcripta erit quædam figura,
ex priſinatibus æqualem altitudinem habentibus cóſtans,
ad partes e:
& altera circumſcripta ad partes d. Sed unum-
quodque eorum priſmatum, quæ in figura inſcripta conti-
nentur, æquale eſt priſmati, quod ab eodem fit triangulo in
figura circumſcripta:
nam priſma p q priſmati p o eſt æ-
quale;
priſma s t æquale priſmati s r; priſma x y priſmati
x u;
priſma η θ priſinati η z; priſina μ ν priſmati μ λ; priſ-
ma ρ σ priſmati ρ π;
& priſma φ χ priſinati φ τ æquale. re-
linquitur ergo, ut circumſcripta figura exuperet inſcriptã
priſmate, quod baſim habet a b c triangulum, &
axem e f.
Illud uero minus eſt ſolida magnitudine propoſita. Eadȩ
ratione inſcribetur, &
circumſcribetur ſolida figura in py-
ramide, quæ quadrilateram, uel plurilaterã baſim habeat.

PROBLEMA II. PROPOSITIO XI.

Dato cono, fieri poteſt, ut figura ſolida in-
ſcribatur, &
altera circumſcribatur ex cylindris
æqualem habentibus altitudinem, ita ut circum-
ſcripta ſuperet inſcriptam, magnitudine, quæ ſo-
lida magnitudine propoſita ſit minor.
SIT conus, cuius axis b d: & ſecetur plano per axem
ducto, ut ſectio ſit triangulum a b c:
intelligaturq; cylin-
drus, qui baſim eandem, &
eundem axem habeat. Hoc igi-
tur cylindro continenter bifariam ſecto, relinquetur cylin
drus minor ſolida magnitudine propoſita.
Sit autem is cy
lindrus, qui baſim habet circulum circa diametrum a c, &

axem d e.
Itaque diuidatur b d in partes æquales ipſi d e
in punctis f g h _K_lm:
& per ea ducantur plana conum ſe-
cantia;
quæ baſi æquidiſtent. erunt ſectiones circuli, cen-
tra in axi habentes, ut in primo libro conicorum, propoſi-

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