 | Euclides - 1855 - 230 Seiten
...In like manner it may be proved, that similar four-sided figures, or figures of any number of sides, are to one another in the duplicate ratio of their homologous sides, as has already been proved in the case of triangles. Therefore, universally, similar rectilineal figures... | |
 | Cambridge univ, exam. papers - 1856 - 200 Seiten
...are proportionals. Shew how this proposition may be proved by superposition as in Prop. 4, B. 1. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. What can you infer from this as to the ratio of squares to each other ? 5. Describe a rectilineal figure... | |
 | 1857 - 408 Seiten
...the base, the triangles on each^side of it are similar to the whole triangle and to one another. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both... | |
 | Middle-class education - 1857 - 70 Seiten
...the algebraical 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... | |
 | Henry Latham - 1857 - 390 Seiten
...triangle. 7. Give Dcf. 5, Book V. of Euclid, and shew whether the areas 3, 4, 7, 8 are proportionals. Similar triangles are to one another in the duplicate ratio of their homologous sides. Shew how to inscribe a rectangle DEFG in a triangle ABC, so that the angles D, E may be in the straight... | |
 | sir Thomas Dyke Acland (11th bart.) - 1858 - 270 Seiten
...the algebraical 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... | |
 | Thomas Lund - 1859 - 390 Seiten
...= / a, JP -# a, 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 Seiten
...Extract the square 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 Seiten
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, D.EFbe similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | EDUCATION SOCIETY'S PRESS, CULLA - 1860 - 612 Seiten
...has to the fourth ? 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... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
