 | sir Thomas Dyke Acland (11th bart.) - 1858 - 270 pages
...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... | |
 | Anthony Nesbit - Measurement - 1859 - 494 pages
...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 of... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...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... | |
 | Thomas Lund - Geometry - 1859 - 390 pages
...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... | |
 | Eucleides - 1860 - 396 pages
...homologous sides are parallel. PROPOSITION XIX. THEOREM. — If triangles (ABC, DEF) are similar, they are to one another in the duplicate ratio of their homologous sides (BC, EF). CONSMHTCTION. Take BG a third proportional to BC, EF (a), so that BC is to EF, as EF f* to... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...has already been proved in triangles : (vI. 19.) therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. CoB. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vI. 11.) AB... | |
 | EDUCATION SOCIETY'S PRESS, CULLA - 1860 - 612 pages
...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... | |
 | Euclides - 1861 - 464 pages
...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... | |
 | War office - 1861 - 714 pages
...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... | |
 | Education - 1863 - 406 pages
...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... | |
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... are to one another in the duplicate ratio of their homologous sides. 
