 | John Playfair - 1842 - 332 σελίδες
...the angle BAC is equal to the angle 'EDF (Hyp.) ; wherefore also the remaining angle at B is equal to the remaining angle at E. Therefore the triangle ABC is equiangular to the triangle DEF. PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the... | |
 | Euclides - 1842 - 320 σελίδες
...angles of the triangle BGC are together not less than two right angles, which is impossible (17.1.): therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the two triangles, &c. QED PROP. VIII. THEOR. IN a right-angled triangle, if a perpendicular be drawn... | |
 | 1843 - 570 σελίδες
...angle, and one of the other sides of a triangle are given ; construct it. 4. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and triangles which have one angle... | |
 | Scottish school-book assoc - 1845 - 434 σελίδες
...halves of parallelograms, upon the same base, and having the same altitude, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about these angles reciprocally proportional ; and if two triangles have one angle of... | |
 | Euclides - 1845 - 544 σελίδες
...same reason, the angle ACB is equal to the angle DFE, and the angle at A equal to the angle at D : therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one... | |
 | Euclid - 1845 - 218 σελίδες
...same reason, the angle ACB is equal to the angle DFE, and the angle at A equal to the angle at D : therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two triangles have one angle of the one equal to one... | |
 | Euclid, John Playfair - 1846 - 332 σελίδες
...the parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional ; And triangles which have one angle... | |
 | Euclides - 1846 - 272 σελίδες
...therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3.... | |
 | Euclides - 1846 - 292 σελίδες
...for the like reason, the angle ACB is equal to the angle DFE, and the angle at A to the angle at D : Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, If the sides to. QED s PROP. VI. THEOR. If two triangles have one angle of the one equal to one angle... | |
 | Dennis M'Curdy - 1846 - 168 σελίδες
...of two triangles, &c. QED Kecite (a) p. 23, 1; Wp.9,5; (4) 32, 1 ; (Op.8,1: p. 4, 6; ax. 1,1. 6 Th. If two triangles have one angle of the one equal to one of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,... | |
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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, and shall have those angles equal which are opposite to the homologous sides. 
