Glossary entry (derived from question below)
Italian term or phrase:
Postulati d\'ordine
English translation:
Axioms/postulates of order
Italian term
Italy
Native in: Italian 
Works in: English to Italian, Spanish to Italian, Italian to English
Postulati d'ordine
Geometria nel piano euclideo
Concetti primitivi, postulati di appartenenza, postulati d'ordine.
I postulati di appartenenza, se non ho capito male (data la mia ignoranza in geometria) dovrebbero corrispondere ai postulati di Euclide (pertanto il tentativo di traduzione è "Euclid's postulates). Tuttavia, non trovo un'idea di traduzione per i "postulati d'ordine". Qualcuno ha un suggerimento?
Grazie in anticipo
| 5 +1 | Axioms/postulates of order |
texjax DDS PhD
|
Mar 4, 2022 18:45: Ivana UK changed "Level" from "Non-PRO" to "PRO"
PRO (3): texjax DDS PhD, philgoddard, Ivana UK
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Proposed translations
Degree + PhD in Dentistry, ATA-Certified
Native in: Italian 
Works in: English to Italian, Italian to English, Italian
Axioms/postulates of order
Postulati dell'ordine
Danno il concetto di ordine sulla retta e nel piano:
Data una retta e su di essa due punti distinti si puo' scegliere sulla retta un verso per cui il primo punto preceda il secondo ed il secondo segua il primo
Data una retta e su di essa due punti distinti esiste sempre un terzo punto che si trovi compreso fra il primo ed il secondo (in pratica significa che i punti su qualunque segmento di retta sono infiniti)
http://www.ripmat.it/mate/f/fb/fbbd.html
Axioms of Order
When B is between A and C then, A, B and C are distinct points lying on a line and B is between C and A.
Given a pair of points A and B there is a point C so that B is between A and C.
If B lies between A and C then A does not lie between B and C.
https://www.imsc.res.in/~kapil/geometry/euclid/node3.html
This assumption is based on geometrical intuition, and indeed, it cannot
be deduced from Euclid's postulates; to make it strictly demonstrable and independent of any reference to intuition, a special group of postulates has been
added to those of Euclids, they are the postulates of order. One of these-to give
an example asserts that if A, B, C are points on a straight line 1, and if B lies
between A and C, then B also lies between C and A
https://www.princeton.edu/~hhalvors/teaching/phi520_s2015/he...
Discussion
I don't believe that "postulati di appartenenza" are "Euclid's postulates", and I suggest posting a separate question for that. These are pro terms.