 | Evan Wilhelm Evans - 1862 - 116 pagina’s
...: hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM V. Two triangles having an angle of the one equal to an angle of the other, and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the angle... | |
 | Euclides - 1865 - 402 pagina’s
...the three sides of a triangle to the opposite angles meet in the same point. 14. If two trapezinms have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
 | Robert Potts - 1865 - 528 pagina’s
...reciprocally proportional: and conversely, parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let AB, BC\>& equal parallelograms, which have the angles at B equal. The... | |
 | Euclid, Isaac Todhunter - 1867 - 426 pagina’s
...equal angles reciprocally proportional; and parallelograms which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms, which have the angle FBD equal to the... | |
 | Benjamin Greenleaf - 1868 - 340 pagina’s
...include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, PEF have the... | |
 | Trinity College (Hartford, Conn.) - 1870 - 1008 pagina’s
...parallelograms which have equal bases and equal altitudes are equal. G. Prove that two triangles which have an angle of the one equal to an angle of the other are to each other as the rectangles of the including sides. ENGLISH. I. Correct, criticize, and recast... | |
 | Henry William Watson - 1871 - 320 pagina’s
...triangle AGH, therefore the triangle ABC is similar to the triangle DEF. PROPOSITION 18. If two triangles have an angle of the one equal to an angle of the other, and the sides containing those angles proportionals, the triangles shall be similar. Fig. 25. Let ABC and... | |
 | William Chauvenet - 1871 - 380 pagina’s
...other are to each other as the products of the sides including the equal angles. Two triangles which have an angle of the one equal to an angle of the other may be placed with their equal angles in coincidence. Let ABC, ADE, be the two triangles having the... | |
 | William Chauvenet - 1871 - 380 pagina’s
...of the ratio of similitude of the triangles. PROPOSITION VIII.— THEOREM. 22. Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Two triangles which have... | |
 | Euclides, James Hamblin Smith - 1872 - 376 pagina’s
...each other proportionally. And Conversely, Triangles, which home one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let the sides about the equal / s be reciprocally proportional, that is,... | |
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... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another. 
