 | Euclides - 1848 - 52 pages
...circumferences on which they stand have to one another : so also have the sectors. PROP. B. THEOREM. If an angle of a triangle be bisected by a straight line which likewise cuts the base; the rectangle contained by the sides of the triangle is equal to the rectangle... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...base are between the same parallels (39. 1.); therefore DE is parallel to BC. PROP. III. THEOR. If the angle of a triangle be bisected by a straight line which also cuts the bate ; the segments of the base shall have the same ratio which the other sides of the triangle have... | |
 | Education - 1850 - 488 pages
...inscribe a circle in a given triangle. 3. If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base : the segments of the base shall have the same ratio which the other sides of the triangle have to one another : and conversely, if... | |
 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...angles are as the numbers 2, 5 and 8. 5. If the angle of a triangle be divided into two equal angles by a straight line which also cuts the base, the segments of the base have the same ratio which the other sides of the triangle have to one another. If A, B, C be three... | |
 | Francis James Jameson - Mathematics - 1851 - 144 pages
...inscribed in the circle ACD. 1851. (A). If the angle of a triangle be divided into two equal angles by a straight line, which also cuts the base, the segments of the base have the same ratio which the other sides of the triangle have to one another, (vi. 3.) (JB). If A,... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...circumference EF, so is the sector BGC to the sector EHF. Wherefore, in equal circles, etc. QED PROPOSITION B. THEOR. If an angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal loathe rectangle... | |
 | Euclides - Geometry - 1853 - 176 pages
...the sector bgc to the sector ehf. Wherefore, in equal circles, &c. QED PROPOSITION B. — THEOREM. If an angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle... | |
 | Euclides - Geometry - 1853 - 334 pages
...the same parallels (i. 39), that is, DE is parallel to BC. Which was to be proved. PEOP. III. THEOE. If an angle of a triangle be bisected by a straight line cutting the opposite side : then the two parts into which this side is divided shall have the same... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...with two given sides shew that that is the greatest in which the two sides form a right angle. (22) If an angle of a triangle be bisected by a straight line which also cuts the opposite side, shew that the two parts into which this side is divided will be in the same ratio as... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...emancipation ? HIGHER MATHEMATICS.— No. I. (Three Hours allowed for this Paper.) Section 1. 1. If the angle of a triangle be bisected by a straight line,...also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have. 2. If two triangles have one angle... | |
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IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square of the... 
