This proof is the converse to proposition number 37. In an introductory book like book i this separation makes it easier to follow the logic, but in later books special cases are often bundled into the general proposition. Euclid could have bundled the two propositions into one. If in a triangle two angles be equal to one another, the sides which subtend the equal angles will. An invitation to read book x of euclids elements core. Sometimes the justification is quoted in full as c. Like those propositions, this one assumes an ambient plane containing all the three lines. Euclids elements, book i department of mathematics and. Propositions 1 to 4 deal with the socalled euclidean algorithm, or anthyphairesis, which has no apparent relevance to the material that follows. The latin translation of euclids elements attributed to. The book v of euclids element contains the most celebrated theory of ancient greek mathematics. This is the first proposition which depends on the parallel postulate. A semicircle is the figure contained by the diameter and the circumference cut off by it. To construct an equilateral triangle on a given finite straight line.
They are not part of euclid s elements, but it is a tradition to include them as a guide to the reader. Stoicheia is a mathematical treatise consisting of books attributed to the ancient greek mathematician euclid in alexandria, ptolemaic egypt c. To place at a given point as an extremity a straight line equal to a given straight line. A diameter of the circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle. Proposition 1, constructing equilateral triangles duration. If in a triangle two angles equal one another, then the sides opposite the equal angles also equal. Some of these indicate little more than certain concepts will be discussed, such as def. Isbaqthabit version primarily between books v and x and by the end of. Proposition 32, the sum of the angles in a triangle duration. This is the thirty ninth proposition in euclids first book of the elements. The statement of this proposition includes three parts, one the converse of i. Given two unequal straight lines, to cut off from the greater a straight line equal to the. The four books contain 115 propositions which are logically developed from five postulates and five common notions.
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