Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
From inside the book
Results 1-5 of 34
Page v
... Measurement of Angles , ..... Problems relating to the First and Third Books , .. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book , ..... PAGE . 13 20 50 60 59 82 93 129 BOOK V. Regular ...
... Measurement of Angles , ..... Problems relating to the First and Third Books , .. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book , ..... PAGE . 13 20 50 60 59 82 93 129 BOOK V. Regular ...
Page 9
... measured . To measure a thing , is to find out how many times it contains some other thing of the same kind , taken as a stand- ard . The assumed standard is called the unit of measure . 2. In GEOMETRY , there are four species of ...
... measured . To measure a thing , is to find out how many times it contains some other thing of the same kind , taken as a stand- ard . The assumed standard is called the unit of measure . 2. In GEOMETRY , there are four species of ...
Page 13
... measurements of the Geo- metrical Magnitudes . 2. A POINT is that which has position , but not magni- tude . 3. A LINE is that which has length , but neither breadth nor thickness . Lines are divided into two classes , straight and ...
... measurements of the Geo- metrical Magnitudes . 2. A POINT is that which has position , but not magni- tude . 3. A LINE is that which has length , but neither breadth nor thickness . Lines are divided into two classes , straight and ...
Page 18
... measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn joining 18 GEOMETRY .
... measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn joining 18 GEOMETRY .
Page 26
... measured on any broken line AB , BC , A C is greater than the distance measured on the straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ; which was to be proved . Cor . If from both members of the inequality ...
... measured on any broken line AB , BC , A C is greater than the distance measured on the straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ; which was to be proved . Cor . If from both members of the inequality ...
Other editions - View all
Common terms and phrases
AB² ABCD AC² 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.