 | Joseph Denison - Euclid's Elements - 1840 - 96 pages
...Elements. By means of that proposition the nineteenth proposition of the sixth book of Euclid, viz. that similar triangles are to one another in the duplicate ratio of their homologous sides becomes turned into the following one, viz. that similar triangles are to one... | |
 | Middle-class education - 1857 - 70 pages
...What is 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... | |
 | sir Thomas Dyke Acland (11th bart.) - 1858 - 270 pages
...What is 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... | |
 | Education - 1863 - 406 pages
...that ^5-^— 9=42 or £ the triangle ABC. I should mention 2 to draw ox parallel to BG. Now we know that similar triangles are to one another in the duplicate ratio of their homologous sides . • . BGC : oxC::BGa : ox', or 47.04 : 42::11.2" : 112 the square root of... | |
 | How - 1868 - 296 pages
...in the English, Latin, and Greek tongues, and understood (what few lads of my age then understood) , that ' similar triangles are to one another in the duplicate ratio of their homologous sides." In a word, then, I was something of a scholar, and I may well be forgiven... | |
 | Edinburgh univ - 1871 - 392 pages
...and the part of it without the circle, is equal to the square of the line which touches it. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Given (b) the base of a triangle, find an expression for the base of a similar... | |
 | 1874 - 682 pages
...(a.) Explain the term duplicate ratio, and illustrate its meaning as you would to a class. (b.) Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Describe a circle which will pass through a given point, and touch a given... | |
 | Samuel H. Winter - 1877 - 452 pages
...which have the same base, are to one another as their altitudes. 7. Define duplicate ratio, and prove that similar triangles are to one another in the duplicate ratio of their homologous sides. On the side AB of a triangle ABC, AD is taken equal to one third of AB ; and... | |
 | Queensland. Department of Public Instruction - Education - 1909 - 144 pages
...arcs and sectors. [In this question the bases and arcs may be considered commensurable. ] 12. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides, and that the same holds for similar polygons. MATHEMATICS-PAPER II. 1. Show... | |
 | Sandhurst roy. military coll - 1880 - 68 pages
...ratio and proportion, and explain the terms triplicate ratio, componendo, and ex sequali. 7. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 8. What is meant by the circular measure of an angle ? How many degrees, minutes,... | |
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Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 
