 | sir Thomas Dyke Acland (11th bart.) - 1858 - Liczba stron: 270
...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 equal... | |
 | Anthony Nesbit - 1859 - Liczba stron: 494
...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 of... | |
 | Thomas Lund - 1859 - Liczba stron: 390
...JP -# a, 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... | |
 | Sandhurst roy. military coll - 1859 - Liczba stron: 672
...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 from... | |
 | EDUCATION SOCIETY'S PRESS, CULLA - 1860 - Liczba stron: 612
...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. Give... | |
 | Euclides - 1860 - Liczba stron: 288
...rectilineal figure may be described upon a given straight line, similar to one of six or more sides. Similar triangles are to one another in the duplicate ratio of their homologous sides. Given that ABC and DEF are similar triangles, having the angle B equal to the angle E, and AB to BC... | |
 | Eucleides - 1860 - Liczba stron: 396
...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 - 1860 - Liczba stron: 380
...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... | |
 | Euclides - 1861 - Liczba stron: 464
...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... | |
 | War office - 1861 - Liczba stron: 714
...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... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
