 | Robert Simson - Trigonometry - 1827 - 546 pages
...«. ED PROP. IV. THEOR. 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... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...ED, ex cequali (XXII, Book V.), AB is to AC as DC to DE, therefore the sides about the equal angles are proportional, and those which are opposite to the equal angles are homologous. (538) It is evident that the sides opposite to equal angles are proportional, for since AB : AC = DC... | |
 | John Playfair - Geometry - 1829 - 210 pages
...THEOREM. The sides about the equal angles of equiangular triangles are proportional ; and the sides which are opposite to the equal angles are homologous sides, that is, they are the antecedents or the consequents of the ratios. Let ABC, DCB be equiangular triangles, having... | |
 | University of Cambridge - 1830 - 554 pages
...sum of the squares described upon the sides containing the right angle. 2. The sides about the equal angles of equiangular triangles are proportional, and those which are opposite to the equal angles arc homologous sides. 3. Divide 1532 feet 9,^ inches by 81 feet 9 inches. 4. Find the amount of an... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...&c. QED PROP. IV. THEOR. 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, are the antecedents or con' sequents of the ratios. Let ABC, DCE, be equiangular triangles, having the angle ABC equal to... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...AC as CE to ED, ex aequali (7), AB is to AC as DC to DE ; therefore the sides about the equal angles are proportional, and those which are opposite to the equal angles are homologous. Schol. It is evident that the triangles BAC and CDE are similar ; and also that the sides, which are... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...angles of equiangular triangles arc proportionals ; and those which are opposite to Ike equal angles arc homologous sides, that is, 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... | |
 | Euclides - 1834 - 518 pages
...THEOR. — The tides about the equal angles of equiangular triangles are proportionals; and those whick are opposite to the equal angles are homologous sides,...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... | |
 | Euclid - 1835 - 540 pages
...QED PROP. IV. THEOR. 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... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...CAD. PROP. IV. THEOR. The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are, homologous sides, thai is, are the antecedents or consequents of the ratios. Let ABC, DCE, be equiangular triangles,... | |
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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, are the antecedents or consequents of the ratios Let ABC, DCE, be equiangular triangles, having... 
