...triangle FIK similar to AD E. The polygon FGHIK will be similar to ABCDE, as required. For these two polygons are composed of the same number of triangles, similar each to each, and similarly situated (Prop. XXX. Cor., Bk. IV.). PROBLEM XXXVI. 341. Two similar polygons being' given, to construct a similar...

...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 be divided...

...triangle FIK similar to AD E. The polygon FGHIK will be similar to ABCDE, as required. For these two polygons are composed of the same number of triangles, similar each to each, and similarly situated (Prop. XXX. Cor., Bk. IV.). PROBLEM XXXVI. 341. Two similar polygons being given, to construct a similar...

...triangle FIK similar to AD E. The polygon FGHIK will be similar to ABCDE, as required. For these two polygons are composed of the same number of triangles, similar each to each, and similarly situated (Prop. XXX. Cor., Bk. IV.). PBOBLEM XXXVI. 341. Two similar polygons being given, to construct a similar...

...the first proportion, we have, ABC:ADE::AB*:AD\ THEOREM XVII. Similar polygons may be divided into the same number of triangles, similar each to each, and similarly situated. ~LetABCDE and FGHIK\}& two similar polygons, having the angle A equal to the angle F, B to G, CtoH,...

...THEOREM. ELEMENTS OF GEOMETRY. K 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 being similar,...

...passes through O. In the same way, Dd is shown to pass through O. PROPOSITION X.— THEOREM. 38. If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon AB CD, etc., be composed of the triangles ABC, A...

...ac But, from the hypothesis [1J, we have by (12), AB AC ab ac PROPOSITION X.—THEOREM. 38. If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon ABCD, etc., be composed of the triangles ABC, ACD,...

...triangle FIK similar to AD E. The polygon FG HIK will be similar to ABCDE, as required. For these two polygons are composed of the same number of triangles, similar each to each, and similarly situated (Theo. XX. Cor., Bk. IV.). PROBLEM VII. To inscribe a square in a given circle. Draw two diameters,...

...each to each, to the remaining triangles of the polygon A' B' C' D' E' F' G' H' ; that is, the two polygons are composed of the same number of triangles similar each to each and similarly placed : therefore they are similar to each other [42], WWTBD THEOREM 44. Two parallelograms about...