 | War office - 1861 - 714 σελίδες
...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... | |
 | Euclides - 1861 - 464 σελίδες
...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.... | |
 | Woolwich roy. military acad - 1861 - 572 σελίδες
...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... | |
 | Robert Potts - 1863 - 482 σελίδες
...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 σελίδες
...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... | |
 | Simon Somerville Laurie - 1865 - 432 σελίδες
...to two right angles." ft. To inscribe an equilateral and equiangular pentagon in a given circle. 0. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proper tionals, the triangles shall be equiangular. 7. Similar polygons... | |
 | Euclides - 1865 - 402 σελίδες
...equiangular, and shall have those angles equal which are opposite to the homologous sides. Prop. 7. If two triangles have one angle of the one equal to one angle of tha other, and the sides about two other angles proportionals ; then, if each of the remaining angles... | |
 | George Bruce Halsted - 1886 - 394 σελίδες
...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 σελίδες
...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. 
