 | War office - 1861 - 714 pages
...perpendicular to the line touching the circle. Voluntary Portion. 1. To inscribe a square in a given circle. 2. 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 equiangular to one another, and... | |
 | War office - 1861 - 260 pages
...less than a right angle. 4. To describe an equilateral and equiangular hexagon in a given circle. 5. If two triangles have one angle of the one equal to one angle of the other and the sides about two other angles proportionals, and if each of the remaining angles be not less than a... | |
 | Woolwich roy. military acad - 1861 - 572 pages
...described on P 0 as diameter will pass through all the points of contact. 8. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional, and parallelograms that have one... | |
 | Euclides - 1861 - 464 pages
...into one Theorem, Prop. 1, VI, and might also be united here. PROP. 15. — THEOn. Equal angles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proD. 1 H. &C. 2 7. V. 3 1,V. 4 11, V. 5 Cone.... | |
 | Robert Potts - 1863 - 482 pages
...and the other two sides produced. Also describe a circle touching three sides of a parallelogram. 6. 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, triangle shall be equiangular, and shall have those... | |
 | Euclides - 1864 - 448 pages
...EC. (v. 9.) Therefore equal parallelograms, &c. QED PROPOSITION XV. THEOREM. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocallg proportional : and converselg, triangles which... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having one angle of the one equal to one angle of the other, and the sides about these angles proportional, are similar. HYPOTHESIS. £ B = $. G, and AB : BC : : FG : GH.... | |
 | Canada. Department of the Interior - 1888 - 756 pages
...figures. 13. Triangles and parallelograms having equal bases are to one another as their altitudes. 14. If two triangles have one angle of the one equal to one angle of tho other, the triangles are to each other in the ratio of the rectangles under the sides containing... | |
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If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
