...triangle is equal to the side of an equilateral triangle inscribed in a circle whose diameter is the base. 25. If an equilateral triangle be inscribed in a circle,...points of bisection will be trisected by the sides. 26. If any triangle be inscribed in a circle, and from the vertex a line be drawn parallel to a tangent...

...cotemporary variations of the angles of incidence and refraction are to each other as n -fi : i. 6. It an equilateral triangle be inscribed in a circle,...points of bisection will be trisected by the sides. 7. The sum of the distances of a star from two known star» is a minimum, and its declination, which...

...coteraporary variations of the angles of incidence and refraction are to each other as n -f- i : i. 6. If an equilateral triangle be inscribed in a circle,...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 known stara is a minimum,...

...cotemporary variations of the angles of incidence and refraction are to each other as n -t- 1 : 1 . 6. If an equilateral triangle be inscribed in a circle,...points of bisection will be trisected by the sides. 7. The sum of the distances of a star from two known stars is a minimum, and its declination, which...

...circumscribed ; to determine the ratio which they bear to each other. 400. If an A be inscribed in a ©, and the adjacent arcs cut off by two of its sides be bisected ; the line joining the (.)' of bisection will be trisected by the sides. 401 . To draw an Arithmetic Mean between two given...

...triangles, and shew that the line joining any two points of contact is parallel to the remaining side. 4. If an equilateral triangle be inscribed in a circle,...bisected, the line joining the points of bisection shall be trisected by the sides. 5. If perpendiculars A a, Bb, Cc be drawn from the angular points...

...chord be drawn, shew that its middle point will always lie in the circumference of a given circle. 64. If an equilateral triangle be inscribed in a circle,...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 inscribed...

...object, such as a pond, which does not obstruct the sight, but which impedes the chaining of the line. 4. If an equilateral triangle be inscribed in a circle,...points of bisection will be trisected by the sides. 5. Using the same notation as before, prove the formula : — е- т> 6 sin A Sin В =6. An elliptical...

...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...points of bisection will be trisected by the sides. Prop. 6. The side of an equilateral triangle inscribed in a circle is to the radius, as the square...

...upon a given base and between the same parallels, the isosceles has the greatest vertical angle. 14. If an equilateral triangle be inscribed in a circle,...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 right-angled...