 | Education Department - 1879 - 1118 pàgines
...the part of which between two given straight lines shall be divided in a given proportion. 5. Similar triangles are to one another in the duplicate ratio of their homologous sides. Show that they are also in the duplicate ratio of the radii of their circumscribing circles.... | |
 | University of Bombay - 1903 - 1170 pàgines
...points X and T, so that DX and DY may be equal. 9. Give the definition of duplicate ratio. 10 Similar triangles are to one another in the duplicate ratio of their homologous sides. Deduce that the duplicate ratios of equal ratios are equal, and also that similar triangles... | |
 | Wales univ, univ. coll. of Wales - 1878 - 188 pàgines
...two lines and their difference is equal to the difference of their squares. 12. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 13. If two chords of a circle intersect, the rectangles contained by the segments are equal.... | |
 | Manchester univ - 1877 - 544 pàgines
...this. Prove that equal magnitudes have the same ratio to the same magnitude and conversely. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. Bisect a triangle by a line perpendicular to one of the sides. 11. Enunciate and prove the general... | |
 | 1874 - 748 pàgines
...another as their bases. 10. Find a mean proportional between two given straight lines. 1 1 . Similar triangles are to one another in the duplicate ratio of their homologous sides. ALGEBRA. Tuesday, 20th May. 2 PM to 5 PM 1. If x = 4, у = 3, find the numerical value of (at... | |
 | Edinburgh Mathematical Society - 1900 - 410 pàgines
...equal to the square on the mean, the three straight lines are proportional. EUCLID VI. 19. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEFbetwu similar triangles, having the angles at В, С equal to the angles at E, F... | |
 | University of St. Andrews - 1891 - 440 pàgines
...12, and 15 inches respectively, where is the centre and what is the radius of the circle 1 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. Two similar triangles have homologous sides, 3 and 2 inches respectively. The area of the larger... | |
 | Sir Norman Lockyer - 1886 - 688 pàgines
...mention one only— the proof which he judiciously gives of the fundamental proposition that " similar triangles are to one another in the duplicate ratio of their homologous sides " depends directly on the ist Proposition only of the Sixth Book, instead of the chain being... | |
 | 1904 - 1032 pàgines
...the liberty which each of these excellent works takes with Euclid's Prop. 19, Bk. vi. — " similar triangles are to one another in the duplicate ratio of their homologous sides " — mysterious but high-sounding to countless generations of schoolboys. Here it is, in identical... | |
 | Great Britain. Parliament. House of Commons - 1861 - 588 pàgines
...a segment of a circle, which Khali contain an angle equal to a given rectilineal angle. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. Investigate a rule for finding the greatest common measure of two algebraical expressions.... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
