Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Books 3-9 - Page 234by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| Joseph Denison - 1840
...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
...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
...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
...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... | |
| 1868
...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... | |
| EDWARD RAVENSCROFT - 1871
...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
...(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
...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... | |
| Sandhurst roy. military coll - 1880
...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,... | |
| ...of ratios. Show from this definition that the ratio 3 : 4 is different from that of 4 : 5. 5. Prove **that similar triangles are to one another in the duplicate ratio of** their homologous sides. 6. Divide a given finite straight line into any required number of equal parts.... | |
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