| 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 - 282 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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