 If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.  Self-examinations in Euclid - Page 175by John Martin Frederick Wright - 1829 - 188 pagesFull view - About this book
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...inscribed in a circle whose diameter is the base. 25. If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected ; the line joining the points of bisection will be trisected by the sides. 26. If any triangle be inscribed in a circle, and... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...right angle, and AC=AB = DG, .-. CO = DE. (25.) If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected; the line joining the points of bisection will be trisected by the sides. Let ABC be an equilateral triangle inscribed in... | |
 | Thomas Leybourn - Mathematics - 1819 - 430 pages
...refraction are to each other as n -f- i : i. 6. If an equilateral triangle be inscribed in a circle, and the adjacent arcs, cut off by two of its sides, be bisected; the line joining the points of bisection wilt be trisected by the sides. 7. The sum of the distances of a star from two... | |
 | University of Cambridge - Mathematics - 1821 - 254 pages
...refraction are to each other as n -t- 1 : 1 . 6. If an equilateral triangle be inscribed in a circle, and the adjacent arcs, cut off by two of its sides, be bisected; the line joining the points of bisection will be trisected by the sides. 7. The sum of the distances of a star from two... | |
 | Euclides - 1845 - 546 pages
...contact is parallel to the remaining side. 4. If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides. 5. If perpendiculars A a, Bb, Cc be drawn from... | |
 | Euclides - 1846 - 292 pages
...lie in the circumference of a given circle. 64. If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of section will be trisected by the sides. 65. The vertical angle of any oblique-angled triangle... | |
 | 1853 - 768 pages
...but which impedes the chaining of the line. 4. If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection will be trisected by the sides. 5. Using the same notation as before, prove the... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...is double that of the other. Prop. 5. If an equilateral triangle be inscribed in a circle, and the arcs cut off by two of its sides be bisected, the line joining the points of bisection will be trisected by the sides. Prop. 6. The side of an equilateral triangle inscribed... | |
 | Thomas Stantial - Examinations - 1859 - 352 pages
...isosceles has the greatest vertical angle. 14. If an equilateral triangle be inscribed in a circle, and the adjacent arcs (cut off by two of its sides) be bisected, the line joining the points of section will be trisected by the sides. 8. EXEECISES IN GEOMETRY. III. 1. What is the only... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...whose diameter is the base. Required proof. 7. If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides. 8. If an equilateral triangle be inscribed in... | |
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