Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page ii
... less time to give the subject . Davies ' Legendre's Geometry . - Acknowledged the only satisfactory treatise of its grade . 300,000 copies have been sold . Davies ' Analytical Geometry and Calculus . - The shorter treatises , combined ...
... less time to give the subject . Davies ' Legendre's Geometry . - Acknowledged the only satisfactory treatise of its grade . 300,000 copies have been sold . Davies ' Analytical Geometry and Calculus . - The shorter treatises , combined ...
Page 11
... less than the cube root of B. The opening of the sigu is towards the greater quantity . The sign , ... is used as an abbreviation of the word hence , or consequently . The symbols , 1o , 2o , etc. , mean , 1st , 2d , etc. 5. The general ...
... less than the cube root of B. The opening of the sigu is towards the greater quantity . The sign , ... is used as an abbreviation of the word hence , or consequently . The symbols , 1o , 2o , etc. , mean , 1st , 2d , etc. 5. The general ...
Page 14
... as to make the adjacent angles unequal . B D Oblique angles are subdivided into two classes , acute angles , and obtuse angles . 14. An ACUTE ANGLE is less than a right angle 15. An OBTUSE ANGLE is greater than a right angle 14 GEOMETRY .
... as to make the adjacent angles unequal . B D Oblique angles are subdivided into two classes , acute angles , and obtuse angles . 14. An ACUTE ANGLE is less than a right angle 15. An OBTUSE ANGLE is greater than a right angle 14 GEOMETRY .
Page 19
... less may be laid off on the greater . 4. A straight line may be bisected ; that is , divided into two equal parts . 5. An angle may be bisected . 6. A perpendicular may be drawn to a given straight line , either from a point without ...
... less may be laid off on the greater . 4. A straight line may be bisected ; that is , divided into two equal parts . 5. An angle may be bisected . 6. A perpendicular may be drawn to a given straight line , either from a point without ...
Page 26
... < AB ; as BC , for 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 re- present the sides of a triangle , the sum of 26 GEOMETRY .
... < AB ; as BC , for 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 re- present the sides of a triangle , the sum of 26 GEOMETRY .
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
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 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
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.