 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.  The Cambridge Examiner - Сторінка 1211884Повний перегляд - Докладніше про цю книгу
 | Euclid - 1845 - 218 стор.
...EF. Therefore, similar triangles, &c. QED PROPOSITION* XX. THEOR. — Similar polygons may be dirided into the same number of similar triangles, having...one another that the polygons have; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
 | Scottish school-book assoc - 1845 - 444 стор.
...are the doubles of equiangular triangles. PROPOSITION LXXI THEOREM. Similar polygons ABODE, FGHIK, may be divided „ into the same number of similar triangles, having the same ratio that the polygons have ; and the polygons are to one another as the squares of their corresponding... | |
 | Euclid, James Thomson - 1845 - 382 стор.
...triangle upon the first to a similar triangle, similarly described on the second. PROP. XX. THEOR. — Similar polygons may be divided into the same number of similar triangles : (2) these triangles have the same ratio to one another that the polygons have : and (3) the polygons... | |
 | Euclid, John Playfair - 1846 - 334 стор.
...triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. PROP. XX. THEOR. Similar polygons may be divided into the same number...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABGDE, FGHKL,... | |
 | Euclides - 1846 - 292 стор.
...triangle upon the first to a similar and similarly described triangle upon the second. PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles, having the same ratio to otie another that the polygons have; and the polygons are to one another in the duplicate ratio of... | |
 | Euclides - 1846 - 272 стор.
...polygons (FGIKL and AEDCB) may be divided into similar triangles, equal in number, and homologous to all. And the polygons are to one another in the duplicate ratio of their homologous sides. PART 1. — Because in the triangles FGI and AED, the angles G and E are G ( equal, and the sides about... | |
 | Dennis M'Curdy - 1846 - 168 стор.
...to a similar triangle upon the second. The same is true of similar parallelograms, p. 41, 1. 20 Th. Similar polygons may be divided into the same number of similar triangles, having to each other the ratio of the polygons; which is the duplicate ratio of their homologous sides. Let... | |
 | Joseph Denison - 1846 - 106 стор.
...similar, and consequently the approximating sides homologous, and (6 Euclid 19) because similar triangles are to one another in the duplicate ratio of their homologous sides; the evanescent triangles are in the duplicate ratio of the homologous sides; and this seems the proper... | |
 | Dennis M'Curdy - 1846 - 166 стор.
...(b) p. 32, 1 ; (c) p. 4, 6 ; ( d) p. 22, 5 ; (c) def. 1, 6 and def. 35, 1. 19 Th. Similar triangles are to one another in the duplicate ratio of their homologous sides. Given the similar triangles ABC, DEF; having the angles at B, E, equal, and AB to BC as DE to EF: then... | |
 | Anthony Nesbit - 1847 - 492 стор.
...Quantity of Land, by a Line parallel to any one of its Sides. RULE. — The areas of similar triangles are to one another in the duplicate ratio of their homologous sides : hence, as the area of the triangle ABC is to the square of the side AC, or BC, so is the area of... | |
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