You are here: BP HOME > BPG > Euclid: Elementa > record
Euclid: Elementa

Choose languages

Choose images, etc.

Choose languages
Choose display
    Enter number of multiples in view:
  • Enable images
  • Enable footnotes
    • Show all footnotes
    • Minimize footnotes
Search-help
Choose specific texts..
Click to Expand/Collapse OptionTitle
Click to Expand/Collapse OptionPreface
Click to Expand/Collapse OptionBook I
Click to Expand/Collapse OptionBook ΙI
Click to Expand/Collapse OptionBook IΙΙ
Click to Expand/Collapse OptionBook IV
Click to Expand/Collapse OptionBook V
Click to Expand/Collapse OptionBook VI
Click to Expand/Collapse OptionBook VII
Click to Expand/Collapse OptionBook VIII
Click to Expand/Collapse OptionBook ΙΧ
Click to Expand/Collapse OptionBook Χ
Click to Expand/Collapse OptionBook ΧI
Click to Expand/Collapse OptionBook ΧIΙ
Click to Expand/Collapse OptionBook ΧIΙΙ
gre V,0
ιζ᾽ Δι᾽ ἴσου λόγος ἐστὶ πλειόνων ὄντων μεγεθῶν καὶ ἄλλων αὐτοῖς ἴσων τὸ πλῆθος σύνδυο λαμβανομένων καὶ ἐν τῷ αὐτῷ λόγῳ, ὅταν ᾖ ὡς ἐν τοῖς πρώτοις μεγέθεσι τὸ πρῶτον πρὸς τὸ ἔσχατον, οὕτως ἐν τοῖς δευτέροις μεγέθεσι τὸ πρῶτον πρὸς τὸ ἔσχατον: ἢ ἄλλως: Λῆψις τῶν ἄκρων καθ᾽ ὑπεξαίρεσιν τῶν μέσων.
eng
17. A ratio ex aequali arises when, there being several magnitudes and another set equal to them in multitude which taken two and two are in the same proportion, as the first is to the last among the first magnitudes, so is the first to the last among the second magnitudes;
Or, in other words, it means taking the extreme terms by virtue of the removal of the intermediate terms.
lat Sic
Per equale proportio est pluribus quantitatibus existentibus et aliis ipsis equalibus multitudine binis sumptis et in eadem proportione quando fuerit ut in primis quantitatibus primum ad extremum ita in secundis quantitatibus primum ad extremum.
lat Gerard
No Latin
lat Adelard
No Latin
lat Hermann
No Latin
ara Uppsala
No Arabic
ara Tuṣi
No Arabic
ara Nairizi
No Arabic
san
No Sanskrit
lat Clavius
No Latin
kin 幾何原本 p. 228-229
第十七界
有平理。彼此幾何。各自三以上。相為同理之連比例。則此之第一與三。若彼之第一與三。又曰。去其中。取其首尾。
甲、乙、丙、三幾何。丁、戊、己、三幾何。等數。相為同理之連比例者。甲與乙、若丁與戊。乙與丙、若戊與己也。今平推首甲、與尾丙。若首丁、與尾己。(p. 二二九)
平理之分。又有二種。如後二界。
http://www2.hf.uio.no/common/apps/permlink/permlink.php?app=polyglotta&context=record&uid=6ae84d0a-3ed4-11e1-aecb-00215aecadea
Go to Wiki Documentation
Enhet: Det humanistiske fakultet   Utviklet av: IT-seksjonen ved HF
Login