| Anthony Nesbit - 1859 - 494 páginas
...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... | |
| Thomas Lund - 1859 - 362 páginas
...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... | |
| Euclides - 1860 - 288 páginas
...AB has to the homologous side FG. COR. 1. — In like manner it may be proved that similar foursided **figures, or of any number of sides, are one to another...duplicate ratio of their homologous sides. COR. 2.** — If to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (V. Def. 18)... | |
| Eucleides - 1860 - 396 páginas
...another in the duplicate ratio of their homologous sides, as has already been proved in the case of **triangles. Therefore, universally, similar rectilineal...in the duplicate ratio of their homologous sides.** COROLLARY 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has... | |
| Robert Potts - 1860 - 361 páginas
...duplicate ratio of their homologous sides : and it has already been proved in triangles : (vI. 19.) **therefore, universally, similar rectilineal figures...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
...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... | |
| War office - 1861 - 12 páginas
...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
...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... | |
| Euclides - 1863
...rectilineal figure of six sides; and so on. QEF PEop. XIX. (THEOHEM.)—Similar triangles (ABC, DEF) **are to one another in the duplicate ratio of their homologous sides.** Let the angle ABC be equal to the angle DEF, and let AB be to BC as DE to EF, so that the side BC is... | |
| 1863
...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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