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 are 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 are 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 140
... feet , each of the equal sides is 5 feet ; find the area . 2. The parallel sides of a trapezoid are 8 and 10 feet , and the altitude is 6 feet ; what is the area ? 3. The sides of a triangle are 60 , 80 , and 100 feet , the diameter of ...
... feet , each of the equal sides is 5 feet ; find the area . 2. The parallel sides of a trapezoid are 8 and 10 feet , and the altitude is 6 feet ; what is the area ? 3. The sides of a triangle are 60 , 80 , and 100 feet , the diameter of ...
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 ...
... 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 ...
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 ...
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Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.