| Henry Latham - 1857 - 390 Seiten
...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... | |
| sir Thomas Dyke Acland (11th bart.) - 1858 - 270 Seiten
...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... | |
| Anthony Nesbit - 1859 - 494 Seiten
...the 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... | |
| Sandhurst roy. military coll - 1859 - 672 Seiten
...speed does each man walk \ Voluntary Portion. 1. Define in Euclid's manner duplicate ratio. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. 2. Define parallel straight lines. If two straight lines be parallel, the straight line drawn... | |
| 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... | |
| EDUCATION SOCIETY'S PRESS, CULLA - 1860 - 608 Seiten
...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.... | |
| Euclides - 1861 - 464 Seiten
...Plans, Maps, and Geometrical Drawings of every kind. PROP. 19. — THEOR. (Very important.) Similar **triangles are to one another in the duplicate ratio of their homologous** sides ; ie, as the squares of their like sides. CON. 11, VI. DEM. Def. 12, V.— 16, V. If four Ms... | |
| War office - 1861 - 714 Seiten
...than a semicircle is greater than a right angle. 10 DIRECT COMMISSIONS. VOLUNTAKY PORTION. 1. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. 2. Describe a rectilineal figure which shall be similar to one given rectilineal figure and... | |
| 1863 - 302 Seiten
...equal parts how a rule of three sum may be solved geometrically. 9. Proposition 19. Theorem. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. J 0. If the superficial content of a triangle which has a base of 40 feet is 800 feet, what... | |
| 1863 - 406 Seiten
...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 which is 10.583+=ox,... | |
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