Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 16
... vertices of two angles , not consecutive . 24. A BASE of a polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference either to their sides , or their angles . When ...
... vertices of two angles , not consecutive . 24. A BASE of a polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference either to their sides , or their angles . When ...
Page 60
... vertices are all in the circum- ference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line which touches the circumference in one point only . This ...
... vertices are all in the circum- ference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line which touches the circumference in one point only . This ...
Page 89
... vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle . There may be two cases : the given point may lie on the circumference of the given circle ...
... vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle . There may be two cases : the given point may lie on the circumference of the given circle ...
Page 110
... vertices at the same point E , have a common altitude : hence , ( P. VI . , C. ) AED : DEB :: AD : DB . B The triangles AED and EDC , have their bases in the same line AC , and their vertices at the same point D ; they have , therefore ...
... vertices at the same point E , have a common altitude : hence , ( P. VI . , C. ) AED : DEB :: AD : DB . B The triangles AED and EDC , have their bases in the same line AC , and their vertices at the same point D ; they have , therefore ...
Page 133
... vertices B and G lie in the same line BG parallel to the base , their altitudes are equal , and consequently , the triangles are equal : hence , the polygon GCDE is equal to the polygon ABCDE . A E Again , draw CE ; produce AE and draw ...
... vertices B and G lie in the same line BG parallel to the base , their altitudes are equal , and consequently , the triangles are equal : hence , the polygon GCDE is equal to the polygon ABCDE . A E Again , draw CE ; produce AE and draw ...
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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.