Euclid book 1 prop 17

In any triangle, if one of the sides is produced, then the exterior angle is greater than either of the interior and opposite angles. This is the seventeenth proposition in euclids first book of the elements. Use of proposition 17 this proposition is used in iii. This proof shows that if you add any two angles together within a. Euclids elements, book xii, proposition 17 proposition 17 given two spheres about the same center, to inscribe in the greater sphere a polyhedral solid which does not touch the lesser sphere at its surface.

Euclids elements, book iii, proposition 17 proposition 17 from a given point to draw a straight line touching a given circle. In a triangle two angles taken together in any manner are less than two right angles. On a given finite straight line to construct an equilateral triangle. Proposition 18 from book of euclids elements to set out the sides of the five aforementioned figures, and to compare them with one another. Project euclid presents euclids elements, book 1, proposition 17 in any triangle the sum of any two angles is less than two right angles. Let a be the given point, and bcd the given circle. It focuses on how to construct a line at a given point equal to a given line. Euclids plan and proposition 6 its interesting that although euclid delayed any explicit use of the 5th postulate until proposition 29, some of the earlier propositions tacitly rely on it. Although euclid is fairly careful to prove the results on ratios that he uses later, there are some that he didnt notice he used, for instance, the law of trichotomy for ratios. Euclid book 1 proposition 17 two angles of triangle less than 180. For one thing, the elements ends with constructions of the five regular solids in book xiii, so it is a nice aesthetic touch to begin with the construction of a regular triangle. This is the second proposition in euclid s first book of the elements.