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Following the list of definitions is a list of postulates. Each
postulate is an axiom—which means a statement which is accepted without
proof— specific to the subject matter, in this case, plane geometry.
Most of them are constructions. For instance,
Post.I.1 says a straight line can be drawn
between two points, and
Post.I.3 says a circle can be drawn given a
specified point to be the center and another point to be on the
circumference. The fourth postulate,
Post.I.4, is not a constuction, but says that
all right angles are equal.
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- Postulat 1. Per dos punts
diferents hi passa una única recta.
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- Postulat 2. Un segment rectilini
pot ser sempre allargat.
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- Postulat 3. Hi ha una única
circumferència amb un centre i un radi donats.
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- Postulat 4. Tots els angles rectes
són iguals.
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- Postulat 5. Si una secant talla a
dues rectes formant a un costat angles interiors la suma dels quals és
menor
- que dos angles rectes; les dues rectes,
suficientement allargades es tallen en el mateix costat.
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