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 19
... perpendicular may be drawn to a given straight line , either from a point without , or from a point on the line . 7. A straight line may be drawn , making with a given straight line an angle equal to a given angle . 8. A straight line ...
... perpendicular may be drawn to a given straight line , either from a point without , or from a point on the line . 7. A straight line may be drawn , making with a given straight line an angle equal to a given angle . 8. A straight line ...
Page 22
... perpendicular to the first DE . For , the angles DCA and DCB are right angles , by definition ( D. 12 ) ; and from what has just been proved , the angles ACE and BCE are also right angles . Hence , the two lines are mutually perpen ...
... perpendicular to the first DE . For , the angles DCA and DCB are right angles , by definition ( D. 12 ) ; and from what has just been proved , the angles ACE and BCE are also right angles . Hence , the two lines are mutually perpen ...
Page 23
... perpendicular to each other , the sum of the angles which they form is equal to four right angles , and it is also equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles ...
... perpendicular to each other , the sum of the angles which they form is equal to four right angles , and it is also equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles ...
Page 31
... perpendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isosceles . In the triangle ABC , let the angle ABC be equal ...
... perpendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isosceles . In the triangle ABC , let the angle ABC be equal ...
Page 33
... perpendicular can be drawn to a given straight line . no Let A be a given point , and AB a perpendicular to DE : then can other perpendicular to DE be drawn from A. D O A F B יח For , suppose a second perpendicular AC to be drawn ...
... perpendicular can be drawn to a given straight line . no Let A be a given point , and AB a perpendicular to DE : then can other perpendicular to DE be drawn from A. D O A F B יח For , suppose a second perpendicular AC to be drawn ...
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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.