| Euclides - 1865
...a given straight line similar to one given, and so on. QEF PROP. XIX.— THEOBEM. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** (References— Prop. v. 11, 16, def. 12; vi. 1, 11, 15.) Let ABC, DEF be similar triangles, having... | |
| McGill University - 1865
...that it agrees with Euclid's. 9. Find a third proportional to two given lines. 10. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 11. If 3 men can mow 7 acres of grass in 5 days of 9 hours each, in how many days of 8 hours each will... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for **triangles ; therefore universally, similar rectilineal...in the duplicate ratio of their homologous sides.** COROLLARY 2. If to AB and FG, two of the homologous sides, a third proportional M be taken, [VI. 11.... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for **triangles ; therefore universally, similar rectilineal...in the duplicate ratio of their homologous sides.** COROLLARY 2. If to AB and FG, two of the homologous sides, a third proportional M be taken, [VI. 11.... | |
| Robert Potts - 1868 - 410 sider
...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.** AB has to Jf the duplicate ratio of that which AB has to FG: (v. def. 10.) but the four-sided figure... | |
| Edward Morris Reynolds - 1868 - 136 sider
...triangle in the second. The proof we leave as an exercise for the learner. The proposition that " Similar **figures are to one another in the duplicate ratio of their homologous sides** " is true of curvilinear figures as well as of rectilinear. Thus two circles are to one another as... | |
| How - 1868
...Greek tongues, and understood (what few lads of my age then understood) , that ' similar triangles **are to one another in the duplicate ratio of their homologous sides."** In a word, then, I was something of a scholar, and I may well be forgiven if I were a little proud... | |
| Schools inquiry commission - 1868
...equal to the interior and opposite. 7. Describe a circle about a given square. 8. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** XIX. (Two hours.) Maximum. 1. Translate into French : — Two worthy peasants went together to find... | |
| John A. Smith - 1869
...Perpendiculars. 10 22384 to be deducted. Donble areas. 1500 1500 19520 21020 map. As the areas of similar **figures are to one another in the duplicate ratio of their homologous sides,** we have A : a; IS J : s*. From this proportion we obtain— , jlx«* jo /-4V *= , and S=s I — ] .... | |
| Sir Norman Lockyer - 1904
...which each of these excellent works takes with Euclid's Prop, ig, 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... | |
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