...similarly placed. For, it has already been shewn, that the surfaces of two polyedrons may be divided into the same number of triangles similar each to each, and similarly placed. Consider all the triangles of the one polyedron, except those which form the solid angle A, as the...

...similar, and so on in every pair of corresponding triangles ; hence, similar polygons may be divided into the same number of triangles, similar each to each, and similarly situated. Conversely. Let the polygons be composed of the Same number of similar triangles similarly...

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

...described on any other two homologous sides. PROPOSITION XXVI. THEOEEM. Two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. Let AEDCB, FKIHG, be two similar polygons. From any angle A, in the polygon AEDCB, draw diagonals,...

...described on any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons may be div1ded into the same number of triangles, similar each to each, and similarly placed. Let AEDCB, FKIHG, be two similar polygons. From the vertex of any angle A, in the poly• C gon AEDCB,...

...similarly situated. ELEMENTS OF GEOMETRY. Let ABCDE, FGHIK be two similar polygons ; they may be divided into the same number of triangles similar each to each, and similarly situated. From the homologous angles A and F, draw the diagonals AC, AD and FH, F I. The two polygons...

...any other two homologous sides. PROPOSITION XXX. — THEOREM. 275. Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. A 0 .' D? ; т d I Oi¡ Let ABODE, FG IJ I К be two ^^f\ . H similar polygons ; they may...

...P. IV.), we have, ABC : DEF : : AC2 : DF\ PROPOSITION XXVI. THEOREM. Similar polygons may be divided into the same number of triangles, similar, each to each, and similarly placed. Let ABCDE and FGHIK be two similar polygons, the angle A being equal to the angle F, B to Gr, C to...

...— THEOREM. LLEMfcNTS OF UEOMETRY. H Let ABCDE, FGHIK be two similar polygons; they may be divided into the same number of triangles similar each to each, and similarly situated. From the homologous angles A and F, draw the diagonals AC, AD and FH, F I. The two polygons...

...shown that the corresponding triangles ADE, FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. of the same number of similar triangles, and similarly situated, the two polygons are similar....