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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Elements of Geometry and Trigonometry - Page 124
by Adrien Marie Legendre - 1863 - 455 pages

## Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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 number...

## Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 246 pages
...equal to those of the triangle DEF (Prop. X.), that is, the triangles are similar. PROPOSITION XIX. THEOREM. Similar polygons may be divided into the...of triangles, similar each to each, and similarly situated ; and, conversely, polygons which are composed of the same number of triangles, similar each...

## Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...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...

## Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...ratio ; hence, ABC : DEF : : AL : DN. THEOREM XX. Two similar polygons may be divided into an equal number of triangles, similar each to each, and similarly...placed. Let ABCDE and FGHIK be two similar polygons. From the angle A draw the diagonals AC, AD ; and from the homologous angle F, draw FH, FL Now, since...

## Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 pages
...: AL : DX. FH : DEF ABK DE; DME, N D THEOREM XX. Two similar polygons may be divided into an equal number of triangles, similar each to each, and similarly...placed. Let ABCDE and FGHIK be two similar polygons From the angle A draw the diagonals AC, AD: and from the homologous angle F, draw FH, FI. Now, since...

## Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 340 pages
...ABC : DEF : : AL : DN Two similar polygons may be divided into an equal number of triangles, s1milar each to each, and similarly placed. Let ABCDE and FGHIK be two similar polygons. From the angle A draw the diagonals AC, AD : •1ngle, Jf, draw FH, r/, . .'Now, since die polygons...

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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...

## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...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...