... angles equal; and conversely if two angles of a triangle are equal, two of the sides are equal. 3. If two triangles have the three sides of one equal to the three sides of the other, each to each, do you think the two triangles are alike in every... A Supplement to the Elements of Euclid - Page 2by Daniel Cresswell - 1819 - 410 pagesFull view - About this book
| 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 - Euclid's Elements - 1817 - 454 pages
...the other, that which has the greater surface shall have the greater perimeter. PROP. XXVI. (xiv.) **If two right-angled triangles have the three angles...triangle be equal to the hypotenuse of the former.** (XV.) If the sides of any given equilateral and equiangular figure of more than four sides, be produced... | |
| 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.... | |
| George Cunningham Edwards - Geometry - 1895 - 330 pages
...BC is not parallel to DE is an erroneous one. 64. THEOREM. If two triangles have the three angles of **one equal to the three angles of the other, each to each,** the ratio of any two sides of one will equal the ratio of the corresponding * sides of the other. Fio.... | |
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