Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[11. PROPOSITIO IIII.]
[12. PROPOSITIO V.]
[13. PROPOSITIO VI.]
[14. PROPOSITIO VII.]
[15. POSITIO II.]
[16. COMMENTARIVS.]
[17. PROPOSITIO VIII.]
[18. COMMENTARIVS.]
[19. PROPOSITIO IX.]
[20. COMMENTARIVS.]
[21. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.]
[22. PROPOSITIO II.]
[23. COMMENTARIVS.]
[24. PROPOSITIO III.]
[25. PROPOSITIO IIII.]
[26. COMMENTARIVS.]
[27. PROPOSITIO V.]
[28. COMMENTARIVS.]
[29. PROPOSITIO VI.]
[30. COMMENTARIVS.]
[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.]
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FED. COMMANDINI
triangulum m k φ triangulo n k φ. ergo anguli l z k, o z k,
m φ k, n φ k æquales ſunt, ac recti.
quòd cum etiam recti
ſint, qui ad k;
æquidiſtabunt lineæ l o, m n axi b d. & ita.
28. primi.demonſtrabuntur l m, o n ipſi a c æquidiſtare. Rurſus ſi
iungantur a l, l b, b m, m c, c n, n d, d o, o a:
& bifariam di
uidantur:
à centro autem k ad diuiſiones ductæ lineæ pro-
trahantur uſque ad ſectionem in puncta p q r s t u x y:
& po
ſtremo p y, q x, r u, s t, q r, p s, y t, x u coniungantur.
Simili-
ter oſtendemus lineas
Figure: /permanent/library/4E7V2WGH/figures/0120-01 not scanned
[Figure 75]
p y, q x, r u, s t axi b d æ-
quidiſtantes eſſe:
& q r,
p s, y t, x u æquidiſtan-
tesipſi a c.
Itaque dico
harum figurarum in el-
lipſi deſcriptarum cen-
trum grauitatis eſſe pũ-
ctum k, idem quod &
el
lipſis centrum.
quadri-
lateri enim a b c d cen-
trum eſt k, ex decima e-
iuſdem libri Archime-
dis, quippe cũ in eo om
nes diametri cõueniãt.
Sed in figura alb m c n
13. Archi
medis.
d o, quoniam trianguli
alb centrum grauitatis
Vltima.eſt in linea l e:
trapezijq́; a b m o centrum in linea e k: trape
zij o m c d in k g:
& trianguli c n d in ipſa g n: erit magnitu
dinis ex his omnibus conſtantis, uidelicet totius figuræ cen
trum grauitatis in linea l n:
& o b eandem cauſſam in linea
o m.
eſt enim trianguli a o d centrum in linea o h: trapezij
a l n d in h k:
trapezij l b c n in k f: & trianguli b m c in fm.
cum ergo figuræ a l b m c n d o centrum grauitatis ſit in li-
nea l n, &
in linea o m; erit centrum ipſius punctum k, in

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