| Edinburgh Mathematical Society - 1899
...joined, the triangles EAB, DAC are halves of the parallelograms BE, CD. Hence, Two triangles which **have one angle of the one equal to one angle of the other** have to each other the same ratio as the rectangles contained by the sides about the equal angles.... | |
| University of Toronto - 1900
...the other, have their sides about the equal angles reciprocally proportional ; and triangles 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. Use this proportion... | |
| Great Britain. Board of Education - 1900 - 531 sider
...smaller circle. 7. Define the terms submultiple, ratio, homologous, duplicate ratio. 8. If two triangles **have one angle of the one equal to one angle of the other, and** the sides about the equal angles proportionals, the triangles shall be similar. In a given straight... | |
| Euclid, Micaiah John Muller Hill - 1900 - 143 sider
...about the equal angles reciprocally proportional, are equal in area. 49. (i) Equal triangles which **have one angle of the one equal to one angle of the other** have their sides about the equal angles reciprocally proportional. (ii) Triangles which have one angle... | |
| M. J. M. HILL - 1900
...PROPOSITION XLVIII. (i). (Euc. VI. 14, 1st Part.) ENUNCIATION. Parallelograms having equal areas and having **one angle of the one equal to one angle of the other** have the sides about the equal angles reciprocally proportional. Let the two parallelograms be placed... | |
| Macmillan & Co - 1901 - 776 sider
...addition, . a + b+e+ ... x+y+z+ ... or a:x 338 EUCLID'S ELEMENTS. PROPOSITION 6. THEOREM. If two triangles **have one angle of the one equal to one angle of the other, and** the sides about the equal angles proportionals, the triangles shall be similar. In the A' BAG, EOF,... | |
| Thomas Franklin Holgate - 1901 - 440 sider
...right angle which make equal angles with one of the sides. MISCELLANEOUS EXERCISES 1. If two triangles **have one angle of the one equal to one angle of the other, and** a second angle of the one supplementary to a second angle of the other, then the sides about the third... | |
| 1902
...pentagon is equal to the sum of a side and a diagonal of the smaller pentagon. 5. Equal triangles, which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional. 12, ABCD is a trapezium in which... | |
| 1903
...right angles to the straight line joining the middle points of AD and BC. 3. Show that if two triangles **have one angle of the one equal to one angle of the other, and** the sides about another angle of each proportional, the sides opposite the equal angles being homologous,... | |
| Olaus Henrici, George Charles Turner - 1903 - 204 sider
...the theorem is that of Euc. VI. vi., from which the general case follows at once. " If two triangles **have one angle of the one equal to one angle of the other and** the sides about the equal angles proportionals, the triangles shall be similar." For if one triangle... | |
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