 | Mathematics - 1836 - 488 pages
...of the triangle. IV. Tiie 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. V. If the sides of two triangles, about each of their angles, be proportional, the triangles shall... | |
 | John Playfair - Geometry - 1836 - 148 pages
...&c. QED PROP. V. 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... | |
 | William Whewell - 1837 - 226 pages
...equal angles. *PROP. iv. 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. COR. to Prop. iv. Since it has been shewn (Lemma 2) that when quantities are proportionals geometrically,... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 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 die angle ABC equal to the angle DCE, and the angle... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...C. 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 DCE, and ACB to DEC, and consequently... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...THEOR. The sides about the equal angles of equiangular triangles are proportionals ; and those u,hich are opposite to the equal angles are homologous sides,...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 - 1838 - 264 pages
...QHD PROP. IV. THEOR. The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are...that is, are the antecedents or consequents of the proportions. Let ABC, DCE be equiangular triangles, having the angle ABC equal to the angle DCE, and... | |
 | Euclid - Geometry - 1838 - 470 pages
...therefore also EAD is equal to the angle CAD. Wherefore, if the outward, &c. Q,. KD PROP. IV. THEOR. are 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 ACB... | |
 | Euclides - 1840 - 192 pages
...BD : DC : : BA : AC. PROP. IV. THEOR. The sides about the angles of equiangular triangles (ABC, DCE) are proportional ; and those which are opposite to...are the antecedents or consequents of the ratios. Let the equiangular triangles ABC, DCE be so placed that two sides BC, CE opposite to equal angles... | |
 | Euclides - Geometry - 1841 - 378 pages
...&c. QED PROP. IV. THEOR. The rides 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. u 2 Let ABC, DCE be equiangular triangles, having the angle ABC equal to the angle DCE, and the angle... | |
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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... 
