Postulate - Postulate

Japanese: 公準 - こうじゅん

A translation of the word "postulate." Also called "requirement." Of the propositions that are considered completely self-evident in Euclid's "Elementa Geometry," the following five that are specific to geometry are called postulates, and the more general ones are called axioms (common concepts). 1. A straight line can be drawn from any point to any other point. 2. A limited number of straight lines can be extended. 3. A circle can be drawn with any center and radius. 4. All right angles are equal. 5. When one line intersects two other lines and the sum of the interior angles on one side is less than two right angles, the two lines will intersect on that side when extended (parallel axiom). Note that in modern times, there is no distinction between postulates and axioms, and they are both referred to as axioms.
→ Related topic: Euclidean geometry

Source : Heibonsha Encyclopedia About MyPedia Information

Japanese:

postulateの訳語。要請とも。ユークリッドの《幾何学原本》で全く自明と思われる命題のうち，幾何学特有の以下五つを公準と呼び，より一般的なものを公理（共通概念）と呼んだ。1.任意の点から任意の点に直線が引ける。2.限られた直線を延長できる。3.任意の中心と半径で円が書ける。4.直角はすべて相等しい。5.一つの直線が二つの直線に交わり，その一方の側の内角の和が２直角より小さいときは，その２直線を延長するとその側で交わる（平行線公理）。なお，現代では公準と公理を区別しないで公理とよんでいる。
→関連項目ユークリッド幾何学

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