| Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...inscribed circle, we may ghew that the rectangle contained by the sum of the perpendiculars and the sum of **the sides of the triangle, is equal to the rectangle contained by** the sum of the sides, and the sum of the radii of the inscribed and circumscribed circles. 20. Let... | |
| Euclides - 1848 - 52 pages
...angle. PROP. C. THEOREM. If from any angle of a triangle, a straight line be drawn perpendicular to **the base ; the rectangle contained by the sides of...the triangle, is equal to the rectangle contained by** the perpendicular and the diameter of the circle described about the triangle. PROP. D. THEOREM. The... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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...rectangle contained by the sides of the triangle is equal** loathe rectangle contained by the segments of the base, together with the square of the straight line... | |
| Euclides - Geometry - 1853 - 176 pages
...PROPOSITION C. — THEOREM. If from any angle of a triangle a straight line be drawn perpendicular to **the base, the rectangle contained by the sides of...the triangle is equal to the rectangle contained by** the perpendicular and the diameter of the circle described about the triangle. LET abc be a triangle,... | |
| Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...figure. 2. To cut a given straight line in extreme and mean ratio. 3. If an angle of a triangle he **bisected by a straight line which likewise cuts the...base, together with the square of the straight line** which bisects the angle. Section 3. 1. Show that equal triangles on equal bases have equal altitudes,... | |
| 1855 - 264 pages
...mean ratio. 3. If an angle of a triangle he bisected by a straight line which likewise cuts the hase, **the rectangle contained by the sides of the triangle...to the rectangle contained by the segments of the** ha;e, together with the square of the straight line which bisects the angle. SECT. III.— 1. Show... | |
| Euclides - 1855 - 270 pages
...&c. QED PROP. С. THEOREM. If from any angle of a triangle a straight line be drawn perpendicular to **the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by** the perpendicular and the diameter of the circle described about the triangle. Let AB С be a triangle,... | |
| Robert Potts - 1855 - 1050 pages
...sides of the triangle. 6. If from the angle of a triangle a straight line be drawn perpendicular to **the base, the rectangle contained by the sides of...the triangle is equal to the rectangle contained by** the perpendicular and the diameter of the circumscribing circle. 7. Draw a straight line perpendicular... | |
| Euclides - 1855 - 230 pages
...cor. . VI. 3. VI. 2. VI. A. (p. 76). If several parallels be drawn to the base of a triangle. If an **angle of a triangle be bisected by a straight line, which likewise cuts the base.** • Idem If a straight line bisects both the angle and base of a triangle. If from any angle of a triangle... | |
| Cambridge univ, exam. papers - 1856 - 200 pages
...Shew that each of the complements of the parallelograms is a mean proportional between them. 6. If an **angle of a triangle be bisected by a straight line,...the rectangle contained by the sides of the triangle** ia equal to the rectangle contained by the segments of the base, together with the square of the straight... | |
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