 | Pierre Simon marquis de Laplace, Thomas Young - 1821 - 402 páginas
...A¿EB, those triangles are equal (86), BE and L ACDABE, L ADCAEB, and CDBE; but BDCE (16), therefore L BCDCBE (86), and L ACD—BCDABE—CBE (16), or L ACBABC....them are equal. A. Let L ABCBCD; then ACAB. If it be deA nied, take, in the greater AC, CD equal to the less. - AB; then, since L ABC=DCB, AB=DC¿ and BC... | |
 | Pierre Simon de Marquis Laplace, Thomas Young - 1821 - 372 páginas
...ACB=ABC. 88. THEOREM. If two angles of a triangle are cqtial, the sides opposite to them are equal. Let Z ABC^BCD ; then AC=AB. If it be denied, take, in the greater AC, CD equal to the less AB; then, since ¿_ ABC=DCB, AB=DC, ai^ BC is common, the triangle ABC=DCB (86), the whole to a part, which is impossible.... | |
 | Anna Cabot Lowell - 1846 - 216 páginas
...erected upon the middle point of the base of an isosceles triangle, bisects the opposite angle. 134. If two angles of a triangle are equal, the sides opposite to these angles are also equal. Dem. (fig. 86.) Let angle A = B. Upon the middle point of the base AB... | |
 | 1857 - 198 páginas
...erected upon the middle point of the base of an isosceles triangle, bisects the opposite angle. 134. If two angles of a triangle are equal, the sides opposite to these angles are also equal. Dem. (fig. 86.)" Let angle A = B. Upon the middle point of the base AB... | |
 | Horatio Nelson Robinson - 1860 - 470 páginas
...|_ B. Hence the theorem; if two sides of a triangle are equal, the angles, etc. Cor. 1. Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle it itosceles* For, if AC is not equal to BC, suppose BC to be tne greater, and make... | |
 | Adrien Marie Legendre - 1863 - 464 páginas
...middle of the base, bisects the vertical angle, and is perpendicular to the base. PROPOSITION XII. THEOREM. If two angles of a triangle are equal, the sides opposite , to them are also equal, and consequently, the triangle is isosceles. In the triangle ABC, let the angle AB G be... | |
 | Evan Wilhelm Evans - 1862 - 116 páginas
...still more, then, is it greater than BAG. Therefore, the greater of two unequal sides, etc. Cor. Hence, if two angles of a triangle are equal, the sides opposite to them can not be unequal. THEOEEM X. If two triangles have tivo sides of the one equal to two sides of the... | |
 | Horatio Nelson Robinson - 1865 - 474 páginas
...[_ B. Hence the theorem; if two sides of a triangle are equal, the angles, etc. Cor. 1. Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle is isosceles. For, if AC is not equal to BC, suppose BC to he the greater, and make... | |
 | Euclides - 1865 - 80 páginas
...ACB. Cor. Hence the less angle of every triangle is opposite to the less side. PROPOSITION XIX. THEOE. If two angles of a triangle are equal, the sides opposite to them are also equal. Let ABC be a triangle having the angle B equal to the angle C, the side AB is also equal... | |
 | Euclides - 1867 - 384 páginas
...all three angles are equal. PROP. 6 is the converse of this. If A=B, then a=b; and, generally, if any two angles of a triangle are equal, the sides opposite to them are equal. Also, if all three angles are equal, the three sides are alt equal. PEOP. 18 shows that, if the sides... | |
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BCD=CBE (86), and L ACD—BCD=ABE—CBE (16), or L ACB=ABC. 88. Theorem. If two angles of a triangle are equal, the sides opposite to them are equal. A Let L ABC=BCD ; then AC=AB. If it be denied, take, in the greater AC, CD equal to the less AB ; then,... 
