...similar, when they have two angles in each respectivety equal. Second. Two polygons are similar, when both may be divided into the same number of triangles, similar each to each, and similarly placed. But to prevent this latter definition itself from including any superfluous conditions, ftie...

...lines be cut by parallel lines, they are cut in the same ratio. 2. If, on two bases, there be placed the same number of triangles, similar each to each, and similarly situated, the polygons formed by joining the vertices of the triangles will be similar. 3. A straight line, drawn...

...those of the triangle DEF (Prop. X.), that is, the triangles are similar. PROPOSITION XIX. THEOREM. Similar polygons may be divided into the same number...triangles, similar each to each, and similarly situated ; and, conversely, polygons which are composed of the same number of triangles, similar each to each,...

...triangles, similar each to each, and similarly situated ; and, conversely, polygons which are composed of the same number of triangles, similar each to each, and similarly situated, are themselves similar. Let the polygons in the margin be similar, the angle A being equal to the angle...

...of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons tire composed of the same number of triangles, similar each to each,...situated. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in ' the polygon ABCDE, draw diagonals AC, AD to the other angles. From the homologous...

...of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. 92 GEOMETRY. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in the polygon ABCDE, draw...

...similar triangles, &c. PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the same numba of triangles, similar each to each, and similarly...polygons; they may be divided into the same number of similar triangles. Join AC, AD, FH, FI. Because the polygon ABCDE is similar to the E polygon FGHIK,...

...of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated.' From any angle A, in c Let ABCDE, FGHIK. be two similar polygons. the polygon ABCDE, B^--^\ ., ^-A...

...two-thirds of this line from the vertex. PROPOSITION XIX. THEOREM. Two similar polygons are composed of the same number of triangles similar each to each, and similarly situated. Let ABCDF, GHKLM be two similar polygons. From any angle A in the polygon ABCDF, draw the diagonals AC,...

...remaining triangles are similar, whatever be the number of sides in the polygons proposed: therefore, two similar polygons may be divided ,into the same number of triangles, similar, and similarly placed. Scholium. The converse of the proposition is equally true: If two. polygons are...