In parallelograms, the opposite sides are equal, and the opposite angles are equal. This is the thirty fourth proposition in euclids first book of the elements. To draw a straight line through a given point parallel to a given straight line. New technologies for the study of euclids elements citeseerx. It is required to draw a straight line through the point a parallel to the straight line bc. Triangles which are on the same base and in the same parallels equal one another. 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. Let a be the given point, and bc the given straight line. 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. Propositions 1 and 2 in book 7 of elements are exactly the famous eu. On a given straight line to construct an equilateral triangle. In isosceles triangles the angles at the base are equal to one another, and, if the equal straight. In parallelogrammic areas the opposite sides and angles equal one another, and the diameter bisects the areas.
490 1320 510 46 33 1024 1074 339 1147 715 237 1326 924 143 988 772 666 1499 661 1128 1331 642 487 167 904 525 891 526 503 548 1024 513 369 511 435 359 98 854 1218 1369 1050 1217