 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
 | Robert Johnston (F.R.G.S.) - 1873 - 208 pages
...rectilineal angle. 2. A segment of a circle being given, describe the circle of which it is the segment. 8. Give Euclid's definition of proportion and of similar...extracting the cube root of an algebraical expression. Q~.4 [ 143.3 I Ov. 1 9 5. Reduce to its lowest terms the expression „ — T » . . 1 2x* + 9a" +... | |
 | Euclides - 1874 - 342 pages
...first, to a similar and similarly described triangle upon the second. PROPOSITION 20. — Theorem. Similar polygons may be divided into the same number...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.... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...9.) the parallelograms are therefore about the same diagonal. PROP. XVII.— THEOREM. (Euc. VI. 20.) Similar polygons may be divided into the same number of similar triangles; and the polygons are to one another in the duplicate ratio of their homologous sides. M Let ABODE and... | |
 | Richard Wormell - 1876 - 268 pages
...of Theorem LXXXIV proved on page 214 may now be enunciated in the words of Euclid as follows : — Similar polygons may be divided into the same number...triangles having the same ratio to one another that the polygtnis have, and the polygons have to one another the duplicate ratio of that winch their homologous... | |
 | Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...the figure A is similar to the figure B. VI. Def. 1. y. ED PROPOSITION XXI. THEOREM. (Eucl. vi. 20.) Similar polygons may be divided into the same number...similar triangles, having the same ratio to one another, which the polygons have ; and the polygons are to one another in the duplicate ratio of their homologous... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...second couplets of (1) and (2) are equal ; hence, ACD : AFD :: AFD : EFD, PROPOSITION XII. THEOREM. Two similar polygons may be divided into the same number of similar triangles, similarly placed. Let ACDEF and PQRST be similar polygons, the equal angles in both being taken in... | |
 | J. G - 1878 - 408 pages
...TRIGONOMETRY, CONICS. Afternoon Paper. 1. Similar polygons may be divided into the same number of siml triangles, having the same ratio to one another that the polygons have. 2. From a fixed point a series of straight lines are drawn to cut two para straight lines. Prove that... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...first two terms of this proportion are proportional to ABC and DEF. Proposition 20. Theorem.—Similar polygons may be divided into the same number of similar...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 similar... | |
 | James Russell Soley - Naval education - 1880 - 346 pages
...the equal angles are homologous sides; that is, are the antecedents or the consequents of the ratios. Similar polygons may be divided into the same number...the same ratio to one another that the polygons have ; and the polygons are to on^ another in the duplicate ratio of their homologous sides. TRIGONOMETRY.... | |
 | Education, Higher - 1884 - 538 pages
...fall more than two equal lines to the circumference, that point is the centre of the circle. . 15. 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. . / 16. "From... | |
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