Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 95
... feet long is met at one extremity by a second line , making with it an angle of 30 ° ; find the centre of the circle of which the first line is a chord and the second a tangent . 6. How many degrees in an angle inscribed in an arc of ...
... feet long is met at one extremity by a second line , making with it an angle of 30 ° ; find the centre of the circle of which the first line is a chord and the second a tangent . 6. How many degrees in an angle inscribed in an arc of ...
Page 96
... feet long , con- struct a circular segment that shall contain an angle of 30 ° . 18. Show that parallel tangents to a circle include semi - circumferences between their points of contact . 19. Show that four circles can be drawn tangent ...
... feet long , con- struct a circular segment that shall contain an angle of 30 ° . 18. Show that parallel tangents to a circle include semi - circumferences between their points of contact . 19. Show that four circles can be drawn tangent ...
Page 141
... feet and 4 feet ; find the length of the perpendicular . 11. Two similar triangles , ABC and DEF , have the homologous sides AC and DF equal respectively to 4 feet and 6 feet , and the area of DEF is 9 square feet ; find the area of ABC ...
... feet and 4 feet ; find the length of the perpendicular . 11. Two similar triangles , ABC and DEF , have the homologous sides AC and DF equal respectively to 4 feet and 6 feet , and the area of DEF is 9 square feet ; find the area of ABC ...
Page 163
... feet ; find the radius of the circle . 2. The radius of a circle is 10 feet ; find the apothem of a regular inscribed hexagon . 3. Find the side of a square inscribed in a circle whose radius is 5 feet . 4. Draw a line whose length ...
... feet ; find the radius of the circle . 2. The radius of a circle is 10 feet ; find the apothem of a regular inscribed hexagon . 3. Find the side of a square inscribed in a circle whose radius is 5 feet . 4. Draw a line whose length ...
Page 164
... feet ; find the area of a sector whose arc is 120 ° . 15. The circumference of a circle is 200 feet ; find its area . 16. The area of a circle is 78.54 square yards ; find its diameter . 17. The radius of a circle is 10 feet , and the ...
... feet ; find the area of a sector whose arc is 120 ° . 15. The circumference of a circle is 200 feet ; find its area . 16. The area of a circle is 78.54 square yards ; find its diameter . 17. The radius of a circle is 10 feet , and the ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence