 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...PROPOSITION IV. THF.OR. Tke 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... | |
 | Euclides - Geometry - 1853 - 176 pages
...the equal anijles of equiangular triangles are proportionals ; and those which are opposiie to tlie equal angles are homologous sides, that is, are the antecedents or consequents oftlie ratios. LET abc, dce he equiangular triangles, having the angle abc equal to the angle dce,... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...IT.— THEOBEM. The sides about the equal angles of equiangular triangles (ABC, DCE) are proportionals ; and those which are opposite to the equal angles are homologous sides ; that is, arc the antecedents, or the consequents of the ratios. Let the angle ABC = DCE ; ACB =DEC ; and consequently... | |
 | Euclides - 1855 - 270 pages
...base. 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. Let ABС and D С E be equiangular triangles, haying the angle ABС equal to the angle D С E, and... | |
 | John Playfair - Euclid's Elements - 1855 - 340 pages
...PROP. IV. THEOR. The sides about the equal angles of equiangular triangles are proportionals ; ana those which are opposite to the equal angles are homologous...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... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...Through two given points draw a circle which shall touch a given circle. 12. The sides about the equal angles of equiangular triangles are proportional,...are the antecedents or consequents of the ratios. THURSDAY, January 15, 1857. 12^ to 3£. SECOND DIVISION.— (A.) 1. To bisect a given rectilineal angle,... | |
 | John Playfair - Euclid's Elements - 1856 - 346 pages
...CAD PROP. IV. THEOR. The sidesabout the equalangles of equiangular triangles are proportionals ; ana those which are opposite to the equal angles are homologous sides, that is, ai e the antecedents or consequents of the ratios Let ABC, DCE.be equiangular triangles, having the... | |
 | Cambridge univ, exam. papers - 1856 - 200 pages
...rectilineal angle. 12. The sides about the equal angles of equiangular triangles are proportionals; and those which are opposite to the equal angles are homologous sides. FIRST DIVISION (B.) 1. FROM the greater of two given straight lines to cut off a part equal to the... | |
 | Euclid - 1859 - 150 pages
...yuíviaç, KU¡ «'i/íóXuym ai viro raç iaof ywviaç viroTtívovaai irXeupaí. The sides about the equal angles of equiangular triangles are proportional;...are opposite to the equal angles, are homologous, Statement. — Let ABC and DCE be equiangular triangles, having the angle ABC equal to the angle DCE,... | |
 | Royal University of Ireland - Universities and colleges - 1859 - 490 pages
...a given point without it. 15. Prove that in equiangular triangles the sides about the equal angles are proportional, and those which are opposite to the equal angles are homologous. 16. Assuming that the arc of a circle is greater than its chord and less than the sum of the tangents... | |
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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... 
