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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volum 2
Uten tilgangsbegrensning - 1858
12 Recap 9 Ax 9 Concl 9 Recap Algebra and Arithmetic already alternate angles equal angle contained angle equal angle triangle apply Assum BOOKS OF EUCLID Construction Construction and Demonstration consult the Gradations course Data Definitions describe a parallelogram DIAGRAMS difference double drawn equal angles equal bases established examination four rt GEOMETRICAL REASONING GEOMETRY given in numbers given point given st given triangle half hypotenuse knowledge Learner Let the equal line falling margin meaning mind Natural object opposite parallelogram parallels are equal perp PRACTICAL PRICE Principles printed PROB Progress Prop Quæs recommended rectil rectilineal figure references REMARKS render respecting SCHOL SECOND BOOKS Series side equal side together equal sides simultaneously SKELETON PROPOSITIONS squares be given squares described THEOR third angle truths uniformity vertex vertical write written
Side xxiv - If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other; the angle also contained by the sides of that which has the greater base, shall be greater than the angle contained by the sides equal to them of the other.
Side xx - Therefore any two sides, &c. QED PROP. XXI. THEOR. If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Side xxiv - IF two triangles have two angles of one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal angles, or...
Side xli - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side xliii - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC...
Side xxxviii - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Side xxi - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third (20.
Side xl - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle.