 | Pierce Morton - Geometry - 1830 - 584 pages
...angles reciprocally proportional, are equal to one another; and, conversely, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional . 66 (j) Two triangles are similar,... | |
 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...Ratios that are the same to the same ratio, are the same to one another. 13. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. M. In a plane triangle, of which... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...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. Wherefore, if two triangles, &c. QED PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of tJie other, and the sides about two other angles proportionals, then, if each of the remaining angles... | |
 | 1834 - 578 pages
...: A b, that is, A c : A 6 : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that 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 are equiangular, and consequently similar ; we have seen... | |
 | Euclides - 1834 - 518 pages
...angles of the triangle BGC are together, -n- _ is impossible * : therefore the triangle • 17. 1. ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROPOSITION VIII. Let ABC be n right-angled triangle, having the right angle BAC ; and from the point A, let AD... | |
 | Euclid - 1835 - 540 pages
...DB is found. Which was to be done. a 11. 1. b 31. 3. PROP. XIV. THEOR. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And parallelograms that have one... | |
 | Mathematics - 1835 - 684 pages
...angles reciprocally proportional, are equal to one another; and, conversely, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional . .66 (g) Two triangles are similar,... | |
 | Mathematics - 1836 - 488 pages
...about the equal angles reciprocally proportional, are equal to one another. XV. 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... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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. Wherefore, if two triangles, &c. QED \ PROP. VIII. THEOR. In a right angled triangle, if a perpendicular be drawn from the right angle to... | |
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If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
