Elements of Geometry and Trigonometry |
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Page 11
... less than the cube root of B. The opening of the sign is towards the greater quantity . The sign , ... is used as an abbreviation of the word hence , or consequently . 5. The general truths of Geometry are deduced by a course of logical ...
... less than the cube root of B. The opening of the sign is towards the greater quantity . The sign , ... is used as an abbreviation of the word hence , or consequently . 5. The general truths of Geometry are deduced by a course of logical ...
Page 14
... two classes , acute angles , and obtuse angles . 15. An OBTUSE ANGLE is greater than a right angle. 14. An AcUTE ANGLE is less than a right angle NOTE . In making references , the following abbreviations are 14 GEOMETRY .
... two classes , acute angles , and obtuse angles . 15. An OBTUSE ANGLE is greater than a right angle. 14. An AcUTE ANGLE is less than a right angle NOTE . In making references , the following abbreviations are 14 GEOMETRY .
Page 18
... drawn between any two points . 2. A straight line may be prolonged to any length . 3. If two lines are unequal , the length of the less may be laid off on the greater 4. A line may be bisected ; that is , 18 GEOMETRY .
... drawn between any two points . 2. A straight line may be prolonged to any length . 3. If two lines are unequal , the length of the less may be laid off on the greater 4. A line may be bisected ; that is , 18 GEOMETRY .
Page 26
... , AC - BC < AB ; that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may represent the sides of a triangle , the sum of any 26 GEOMETRY .
... , AC - BC < AB ; that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may represent the sides of a triangle , the sum of any 26 GEOMETRY .
Page 27
... less than the third . PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines be drawn to the extremities of any side , their sum will be less than that of the two remaining sides of the triangle . Let O ...
... less than the third . PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines be drawn to the extremities of any side , their sum will be less than that of the two remaining sides of the triangle . Let O ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cos²a cosec cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment semi-circumference similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...