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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page |< < (37) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
Cum ergo tres portiones ſint a p o i, a ei, atd, con-
Mtentæ rectis lineis, &
rectãgulorum conorum ſectionibus;
rectæq; , ſimiles, & inæquales, quæ contingunt ſe ſe ſuper
unam quamque baſim.
] _Poſt ea uerba, ſuper unamquanque_
_baſim, in trans latione aliqua deſiderari uidentur.
Ad borum autem_
_demonſtrationem non nulla præmittere oportet, quæ etiam ad alia,_
_quæ ſequuntur, neceſſaria erunt._

LEMMA I.

Sit recta linea a b, quam ſecent duæ lineæ inter ſeſe
æquidiſtantes a c, d e, ita ut quam proportionem ba-
bet a b ad b d, eandern haheat a c ad de.
Dico li-
neam, quæ c b puncta coniungit, etiam per ipſum e
tr anſire.
SI enim fieri poteſt, non tranſeat pere, ſed nel ſupra, uel infra.
tranſeat primum infra, ut per f. erunt triangula a b c, d b f inter ſe
ſimilia.
quare ut a b ad b d, ita a c ad d f. ſed ut a b ad bd, ita
4. ſexti.erat a c ad d e.
ergo d f ipſi d e æqualis erit, uidelicet pars to-
9. quinti.ti, quod eſt
Figure: /permanent/library/4E7V2WGH/figures/0073-01 not scanned
[Figure 45]
cbſurdum.
Idem ab-
ſurdum ſe
quetur, ſi
linea c b
ſupra e pú
ctum tran
ſire pona-
tur.
quare
c b etiam
per e ne-
ceſſario tranſibit.
quod oportebat demonſtrare.

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