 | War office - 1861 - 714 pages
...less 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 equal to... | |
 | Euclides - 1861 - 464 pages
...— to 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 of of... | |
 | Architecture - 1863 - 300 pages
...scale of 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 is the... | |
 | Education - 1863 - 406 pages
...^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 which is 10.583+=ox, or... | |
 | Euclides - 1863 - 122 pages
...and this has been proved of triangles (VI. 19); therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Cor. 2.-—If to AB and FG, two of the homologous sides of the polygon, a third proportional M bo taken... | |
 | Henry White - 1864 - 156 pages
...it is the segment. 3. Give Euclid's definition of proportion and of similar figures, and show that similar polygons may be divided into the same number...same ratio to one another that the polygons have. 4. Investigate a rule for extracting the cube root of an algebraical expression. 5. Reduce to its lowest... | |
 | Euclides - 1864 - 448 pages
...described upon a given straight line similar to one given, and so on. QE r. PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Woolwich roy. military acad - 1864 - 588 pages
...angle at the vertex is the side of a regular decagon inscribed in the same circle. 11. Assuming that similar polygons may be divided into the same number of similar triangles, show that the polygons have to one another the duplicate ratio of their homologous sides. ABOD is a... | |
 | Thomas Baker (Civil engineer) - 1865 - 278 pages
...then, the triangle ABC is to the triangle AED as the square of AB is to I lie. square of AE : that is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their homologous,... | |
| |
Similar triangles are to one another in the duplicate ratio of their homologous sides. 
