 | London city mission - 1840 - 620 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 316 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 382 σελίδες
...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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
