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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 2
Volledige weergave - 1858
9 Concl 9 Recap adjacent already alternate angles equal angle contained angle equal angle triangle apply Assum BOOKS OF EUCLID circle Construction and Demonstration consult the Gradations course Data difference drawn equal angles equal bases equal sides EXERCISES Exposition GEOMETRICAL REASONING GEOMETRY given rectilineal angle given st Gradations greater greater angle half knowledge Learner Let the equal line falling margin method mind opposite parallels are equal PEN-AND-INK EXAMINATIONS perp PRACTICAL PRICE Principles printed PROB proceed produced Progress Prop Quśs recommended rectil rectilineal figure references respecting SCHOL SECOND BOOKS segments Series side equal side together equal sides similar SKELETON PROPOSITIONS squares be given squares described Student THEOR third angle triangle Triangles upon equal truths uniformity vertex vertical write written Нур
Pagina 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.
Pagina 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.
Pagina 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...
Pagina 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.
Pagina 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...
Pagina xxxviii - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Pagina 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.
Pagina 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.