 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
 | sir Thomas Dyke Acland (11th bart.) - 1858 - 270 стор.
...expression for the mean proportional between two given quantities ? 19. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is equal... | |
 | Anthony Nesbit - 1859 - 494 стор.
...triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, similar triangles are to one another in the duplicate , ratio of their homologous sides. (Euc. B VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XIV. In any triangle the double of the square of... | |
 | Thomas Lund - 1859 - 390 стор.
...tt/ DX * Sometimes called 'homologous sides'. 'f- Euclid's enunciation of this is: 'Similar triangles are to one another in the duplicate ratio of their homologous sides'. X zB=z&, zC=zc; then AB, ab being any two corresponding, or homologous, sides, the triangle ABC shall... | |
 | Sandhurst roy. military coll - 1859 - 672 стор.
...root of 321489. Voluntary Portion. 1. To describe a circle about a given square. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. One of the two digits of a number is double the other, and if 27 be added to the number the digits... | |
 | Robert Potts - 1860 - 380 стор.
...the first, to a similar and similarly described triangle upon the second. PROPOSITION XX. THEOREM. 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 homo-' logous sides have. Let ABCDE, FGHKL... | |
 | Euclides - 1860 - 288 стор.
...the first to a similar, and similarly described triangle upon the second. PROPOSITION XX. THEOREM. 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. Given that ABCDE... | |
 | Eucleides - 1860 - 396 стор.
...rectangle under the (. means. The lines are proportionals. The lines are proportionals. CONSEQUENCES. They may be divided into the same number of similar triangles,...same ratio to one another that the polygons have. The polygons have to one another the duplicate ratio of that which their homologous sides have. /Their... | |
 | EDUCATION SOCIETY'S PRESS, CULLA - 1860 - 612 стор.
...The sides about the equal angles of equiangular triangles are proportionals. 12. Similar triangles are to one another in the duplicate ratio of their homologous sides. LOGIC. I.—LOWER STANDARD. What ii the use of words ? Explain First and Second Intention. 2. Give... | |
 | John Playfair - 1860 - 334 стор.
...their homologous side* tng r polygons may be divided into the same number of similar triangles, havthe same ratio to one another that the polygons have; and the polygons have. Let ABCDE, FGHKL, be similar polygons, and let AB be the homologous side to FG: the polygons... | |
 | Euclides - 1861 - 464 стор.
...the other; for the Areas are as the squares of the sides; and 2a : Ia = 4 : 1. PROP. 20. — THEOR. Similar Polygons may be divided into the same number...one another that the polygons have, and the polygons have to one another the duplicate ratio of that which their homologous sides have. Similar polygons... | |
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