| London City Mission - 1840 - 620 Seiten
...argument nor testimony would suit the determination of such a case. If I want to determine whether similar **triangles are to one another in the duplicate ratio of their homologous** sides; the proper evidence will be to examine, by the powers of the mind, into the proofs which are... | |
| Euclides - 1841 - 378 Seiten
...rectilineal figure of six, or any number of sides. Which was to be done. PROP. XIX. THEOR. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to... | |
| Joseph Denison - 1841 - 210 Seiten
...to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar **triangles are to one another in the duplicate ratio of their homologous** sides, therefore, (5 Euclid, 11.) the simi-lar triangles are to one another as the squares of their... | |
| Joseph Denison - 1841 - 210 Seiten
...to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar **triangles are to one another in the duplicate ratio of their homologous** sides, therefore, (5 Euclid, 11.) the similar triangles are to one another as the squares of their... | |
| Euclides - 1842 - 320 Seiten
...described upon a given straight line similar to one given, and so on. QEF PROP. XIX. THEOR. SIMILAR **triangles are to one another in the duplicate ratio of their homologous** sides. ABC has to the triangle DEF the duplicate ratio of that which вc has to EF. Take BG a third... | |
| 1844 - 456 Seiten
...common chord will be bisected at right angles by a straight line joining their centres. 4. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. 5. About the centre of a given circle describe another circle, equal in area to half the former.... | |
| 1844 - 688 Seiten
...the distance of A" from K. FRIDAY, Jan. 5. 9. ..ll£ SENIOR MODERATOR AND JUNIOR EXAMINER. 1. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. 2. Every solid angle is contained by plane angles which are together less than four right angles.... | |
| Euclid - 1845 - 218 Seiten
...straight line similar to one given, and so on. Which was to be done. PROPOSITION XIX. THEOR. — Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to... | |
| Euclides - 1845 - 546 Seiten
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to... | |
| Euclid, James Thomson - 1845 - 380 Seiten
...methods, however, of performing this and many other problems, the student PROP. XIX. THEOR. — Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Let ABC, DEF be similar triangles, having the angles B and E equal, and AB : BC : : DE : EF,... | |
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