 | Daniel Cresswell - Geometry - 1816 - 352 pages
...proposition, of the first Book of Euclid's Elements. (Art. 99.) PROP. XI. (99.) Theorem. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, the three sides of the one shall, also, be equal to the three sides of the other, each to each, to... | |
 | Daniel Cresswell - Geometry - 1819 - 486 pages
...manifest, therefore, that DAB is the triangle which was to be constructed. PROP. XVI. 24. THEOREM. If two right-angled triangles have the three angles...triangle be equal to the hypotenuse of the former. Let ACB and EDF be two right angled ^, AD C EG F DEF, is equal to the hypotenuse AB, of the A ABC.... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...manifest,. therefore, that DAB is the triangle which was to be constructed. PROP. XVI. 24. THEOREM. If two right-angled triangles have the three angles...side of the one be equal to the perpendicular let fail from the right angle upon the hypotenuse of the other, then shall a side of this latter triangle... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...C, the angle В А С is likewise equal to the ande EDF. Therefore, &c. PROP. 16. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the othrr, each to... | |
 | Mathematics - 1835 - 684 pages
...А' С, the angle BAG is likewise equal to the angle ED F. Therefore, &c. PROP. 1C. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the other, each to... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...triangles, &c. PROP. XXVI. THEOR. IF two angles of one triangle be equal to two angles of another, each to each, and if a side of the one be equal to a side of the other similarly situated in respect to those angles ; then (1.) the remaining sides are... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...triangles, &c. PROP. XXVI. THEOR. — If two angles of one triangle be equal to two angles of another, each to each, and if a side of the one be equal to a side of the other similarly situated with respect to those angles; (1) the remaining sides are equal,... | |
 | James Hamblin Smith - Trigonometry - 1870 - 286 pages
...given, we cannot determine the sides, because an infinite number of triangles may be constructed with the three angles of the one equal to the three angles of the other, each to each. 173. "We shall denote the angles of a triangle by the letters A, Б, C ; the sides respectively opposite... | |
 | 1880 - 594 pages
...in K. Then AH, HD are parallelograms. Now in the triangles AFB, DFC, the three angles of the one are equal to the three angles of the other, each to each, and the side AB to DC ; therefore BF is equal to FD and AF to FC (I. 26). Then in the two triangles FBH,... | |
 | Edinburgh Mathematical Society - Mathematics - 1894 - 284 pages
...of the ordinary " ambiguous case " of Plane Geometry. § 7. The polar theorem of Euclid I. 8. If two triangles have the three angles of the one equal to the three angles of the other, the triangles are either congruent or symmetric. The polar theorems of Euclid I. 24 and I. 25. § 8.... | |
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If two triangles have the three angles of one equal to the three angles of the other, each to each, do you think the two triangles are necessarily alike in every respect ? 5. 
