 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...in the other. Let the triangles ABC and DEF have the angle BAC equal to EDF, the angle BCA to EFD, and a side of the one equal to a side of the other, whether it be interjacent or opposite to those equal angles; the triangles will be equal. First, let... | |
 | Daniel Cresswell - Geometry - 1816 - 352 pages
...spherical triangles, have two angles of the one equal to two angles of the other, each to each, and have a side of the one equal to a side of the other, namely, the sides adjacent to the equal angles, the other sides of the two triangles shall be equal,... | |
 | Euclides - 1821 - 294 pages
...the 13th.) .-. &c. •jy two triangles have two angles of the one respectively equal to two angles of the other, and a side of the one equal to a side of the other, whether it be adjacent or opposite to these equal angles, the remaining tides and angles are respectively... | |
 | Euclid - 1822 - 222 pages
...angles o/F;g.4o. the one respectively equal to lu'o angles of the other See N( K to D, and C to F), and a side of the one equal to a side of the other, whether it be adjacent (BCtoDF) or opposite ( BA to DE) to those equalangj.es, the remaining sides... | |
 | Euclides - 1826 - 226 pages
...circle which are parallel to one another. 1. If two isosceles triangles be of equal altitudes, and have a side of the one equal to a side of the other, then shall their bases be equal. PROPOSITION XV. THEOREM.* In a circle the greatest line is the diameter,... | |
 | Euclid - 1826 - 234 pages
...Therefore in a circle, &c. QED Deductions. 1. If two isosceles triangles be of equal altitudes, and have a side of the one equal to a side of the other, then shall their bases be equal. 2. There can only be drawn two equal right lines in a circle which... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...must be obtuse ; and if it be less than the sum of the other two it must be acute. (129) COR. 5. — If two triangles have two angles in the one respectively equal to two angles in the other, the remaining angles must be also equal. (130) COR. 6. — Isosceles triangles having equal vertical... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...together equal to a right angle ; and if one angle be equal to the other two, it is a right angle. Cor. 2. If two triangles have two angles in the one respectively equal to two angles in the other, the remaining angles are also equal. Cor. 3. In a right-angled isosceles triangle, each angle at the... | |
 | Dionysius Lardner - Geometry - 1838 - 382 pages
...DEF) have two angles of the one respectively equal to two angles of the other (B to D and C to F), and a side of the one equal to a side of the other similarly placed with respect to the equal angles, the remaining sides and angles are respectively... | |
 | Euclides - 1842 - 316 pages
...other side ; it follows that if two right-angled triangles have their hypotenuses equal, or common, and a side of the one equal to a side of the other, the remaining side of the one will be equal to the remaining side of the other. It follows also (8.... | |
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AFC. (in. 21.) Hence in the triangles ADE, AFC, there are two angles in the one respectively equal to two angles in the other, consequently, the third angle CAF is equal to the third angle DAB ; therefore the arc DB is equal to the arc CF, (in. 
