Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[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.]
< >
page |< < of 213 > >|
ARCHIMEDIS
quædam recta linea g i, ſectionibus a g q l, a x d interiecta,
&
ipſi b d æquidiſtans; quæ mediam coni ſectionem in pun
cto h, &
rectam
Figure: /permanent/library/4E7V2WGH/figures/0100-01 not scanned
[Figure 66]
lineam r y in y
ſecet.
demonſtra
bitur g h dupla
h i, quemadmo-
dum demonſtra
ta eſt o g ipſius
g x dupla.
duca-
tur poſtea g ω cõ
tingens a g q l ſe
ctioneming:
&
g c ad b d perpé
dicularis:
iun-
ctaq;
ai produ-
catur ad q.
erit
ergo a i æqualis
i q:
& a q ipſi g ω
æquidiſtans.
Demonſtrandũ eſt portionẽ in humidũ demiſ
fam, inclinatamq;
adeo, ut baſis ipſius non cõtingat humi-
dũ, conſiſtere inclinatã ita, ut axis cum ſuperficie humidi
angulum faciat minorem angulo φ:
& baſis humidi ſuper-
ficiem nullo modo contingat.
Demittatur enim in humi-
dum;
& conſiſtat ita, ut baſis ipſius in uno puncto contin-
gat ſuperficiem humidi.
ſecta autem portione per axem,
plano ad humidi ſuperficiem recto, ſit portionis ſectio a n
z l rectanguli coni ſectio:
ſuperficiei humidi a z: axis autẽ
portionis, &
ſectionis diameter b d: ſeceturq; b d in pun-
ctis _K_ r, ut ſuperius dictum eſt:
& ducatur n f quidem ipſi
a z æquidiſtans, &
contingens coni ſectionem in pũcto n;
n t uero æquidiſtans ipſi b d: & n s ad eandem perpendi-
cularis.
Quoniam igitur portio ad humidum in grauitate,
cam habet proportionem, quam quadratum, quod fit à χ

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index