| Robert Simson - Trigonometry - 1827 - 546 pages
...angle EBC: and the angle AEG is •15.1. equal* to the angle BEH: therefore the triangles AEG, BEH have two angles of the one equal to two angles of the other, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another: • 26. 1.... | |
| Thomas Kerigan - Nautical astronomy - 1828 - 776 pages
...opposite angle CBF, — Euclid, Book I., Prop. 29. And, since the two triangles AFD and FBC have, thus, two angles of the one equal to two angles of the other, viz., the angle AFD to the angle FBC, and the angle FAD to the angle BFC, and the side AF of the one... | |
| James Hayward - Geometry - 1829 - 228 pages
...mO' and M'N'O' are equal. The angle N'O'M' is common to the two triangles nmO' and N'M'O'; and having two angles of the one equal to two angles of the other, the other angles must be equal, that is, the angle O'M'N' is equal to the angle O' nm ; and this intersection... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...equal to the arc В С (12.); therefore the angle В О a is equal to BO b. Therefore BO a, BO b are triangles which have two angles of the one equal to two angles of the other, each to each, and the interjacent side О В common to both : consequently, (I. 5.) they are equal... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...be proved in all other triangles under the same conditions. Wherefore, universally, if two triangles have two angles of the one, equal to two angles of the other respectively ; &c. Which was to be demonstrated. PROPOSITION XXVII. THEOREM. — If a straight line... | |
| William Sullivan - Ethics - 1833 - 380 pages
...it. It is a truth, for example, but not a self-evident one, that if one draw two triangles, having two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either of the sides adjacent to the equal angles,... | |
| Euclides - 1834 - 518 pages
...and the right angle FHC equal to the right angle FKC, therefore in the triangles FHC, FKC there are two angles of the one, equal to two angles of the other, each to each ; and the side FC, which is opposite to one of the equal angles in each, is common to... | |
| Mathematics - 1835 - 684 pages
...the arc В С (12.); therefore the angle В О a is equal to BO b. Therefore В О а, В О b are triangles which have two angles of the one equal to two angles of the other, each to each, and the interjacent side О В common to both : consequently, (I. 5.) they are equal... | |
| Euclid - 1835 - 540 pages
...by BD, and because the right angle BED is equal to the right angle BFD, the two triangles EBD, FBD have two angles of the one equal to two angles of the other, and the side BD, which is opposite to one of the equal angles in each, is common to both; therefore... | |
| John Playfair - Geometry - 1836 - 148 pages
...therefore all the exterior angles are equal to four right angles. PROP. VI. THEOR. If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, the triangles shall be equivalent. Let ABC, DEF be two... | |
| |