Quantum redactiones paginae "Aequatio" differant
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Si aequatio noscitur vera esse, in eam operationes hae sequentes faciantur et veram etiam habeas:
# Ullum valorem [[additio|adde]] ambobus lateribus: si a = b, tum a + c = b + c.
# Ullum valorem [[subtractio|subtrahe]] de ambobus lateribus: si a = b, tum a - c = b - c.
# Ambo latera [[multiplicatio|multiplicentur]] ullo valore: si a = b, tum ac = bc.
# Ambo latera [[divisio|dividantur]] ullo valore excluso [[zero]]: si a = b, et c ≠ 0, tum a/c = b/c.
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The algebraic properties (1-4) imply that equality is a [[congruence relation]] for a [[field (mathematics)|field]]; in fact, it is essentially the only one.
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