| Robert Potts - Geometry, Plane - 1860 - 380 pages
...PROPOSITION IV. THEOREM. The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides, that is, -ire the antecedents or consequents of the ratios. Let ABC, DCEhe equiangular triangles, having the... | |
| War office - 1861 - 260 pages
...ex aequali." Show that the sides about the equal angles of equiangular triangles are proportionals, and those which are opposite to the equal angles are homologous sides. 11. Define the cotangent of an angle, and trace its sign and extreme values between 0 and 180°. T>... | |
| Euclides - 1861 - 464 pages
...— THBOR. {Important.) The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides, ie, are the antecedents or the consequents of the ratios. OB, "Equiangular triangles have their sides... | |
| War office - 1861 - 714 pages
...triangle. 2. Prove that the sides about the equal angles of equiangular triangles are proportionals, and those which are opposite to the equal angles are homologous sides. What is the meaning of the term homologous in this proposition 1 3. If a straight line be at right... | |
| Euclides - 1863 - 122 pages
...angles (ABC and DCE, ACB and DEC, BAC and CDE) of equiangular triangbs (ABC and DCE) are proportionals; and those which are opposite to the equal angles are...are the antecedents or consequents of the ratios. Let the triangle DCE be placed so that its side CE may be contiguous to BC, and in tha same straight... | |
| Euclides - 1864 - 448 pages
...PROPOSITION IV. THEOREM. The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are...are the antecedents or consequents of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC equal to the angle DCE, and the angle ACB... | |
| University of Calcutta - 1864 - 388 pages
...their common tangent. 3. The sides about the equal angles of equiangular triangles are proportionals, and those which are opposite to the equal angles are homologous sides. Cut a given straight line in extreme and mean ratio. 4. Two straight lines which are each of them parallel... | |
| Euclides - 1865 - 402 pages
...PROP. IV.— THEOREM. The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are...are the antecedents or consequents of the ratios. (References— Prop. I. 17, 22, 28, 32, 34 ; v. 7, 16, 22 ; VI. 2.) Let ABC, DCE be equiangular triangles,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...The sides about the equal angles of triangles which are equiangular to one another are proportionals; and those which are opposite to the equal angles are...homologous sides, that is, are the antecedents or the consequents of the ratios. Let the triangle ABCbe equiangular to the triangle DCE, having the angle... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...equal angles of triangles which are equiangular to one another are proportionals; and those tehich are opposite to the equal angles are homologous sides, that is, are the antecedents or the consequents of the ratios. Let the triangle ABCbQ equiangular to the triangle DCE, having the angle... | |
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