 Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.  Guide to the Civil service - Page 126by Henry White - 1864Full view - About this book
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...But we have proved above^ Proposition 20. Theorem. — Similar polygons may be divided into the game number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons are to each other as the squares of their homologous sides. Let ABCDE, FGHKL be... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...on the first to a similar and similarly described triangle on the second. PROPOSITION 20. THEOREM. Similar polygons may be divided into the same number...same ratio to one another that the polygons have; and the polygons are to one another in the duplicate ratio of their homologous sides. Let ABODE, FGHKL... | |
 | Euclides - 1884 - 434 pages
...similar which can be divided into the same number of similar and similarly situated triangles. 5. Prove that similar polygons may be divided into the same number of similar triangles having their vertices at points situated within the polygons. (Such points are called homologous points with... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...that AC is a mean proportional between AB, AD. 10. Define similar polygons, and prove that they can be divided into the same number of similar triangles,...same ratio to one another that the polygons have. n. If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...on Y.' Ex. 714.— In the FIR. of VI. 8, BD : DC :: sq. on BA : sq. on AC. PROPOSITION 20. THEOREM. Similar polygons may be divided into the same number of similar triangles which are to one another in the same ratio as the polygons are ; and the polygons are to one another... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...vi., PROP, n.) Conclusion : A and B, being any regular polygons, etc. PROPOSITION XII. 4O3. Theorem : Similar polygons may be divided into the same number of similar triangles similarly placed. Statement : Similar polygons, ABD and GHJ, may be divided into the same number of... | |
 | Euclid - Geometry - 1892 - 460 pages
...DEF; Proved. .'. the A ABC : the A DEF in the duplicate ratio of BC : EF. QED PROPOSITION 20. THEOREM. Similar polygons may be divided into the same number of similar triangles, having the same ratio each to each that the polygons have; and the polygons are to one another in the duplicate ratio of... | |
 | 1899 - 972 pages
...solutions will be accepted. Dr. MORAN, Head Insi>ector. Mr. PEDLOW, District Inspector. SECTION A. 1. Prove that similar polygons may be divided into the same number of similar triangles, and that these triangles have the same ratio to one another that the polygons have. 2. Describe a rectilineal... | |
 | 1900 - 650 pages
...half the difference of the lines. 3. Inscribe a regular hexagon in a given circle. 4. Prove that (1) similar polygons may be divided into the same number of similar triangles ; (2) the corresponding triangles have the same ratio to one another which the polygons have ; (3)... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...and the lines joining their homologous vertices meet in a point. x PROPOSITION XXVI. THEOREM 303. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. Hyp. Polygon ABODE ~ polygon A'B'OD'E'. To prove A ABC ~... | |
| |
