Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 59
... arc and its chord . 7. A SECTOR is a part of a circle included within an an arc and the radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is BOOK III The Circle, and the Measurement of Angles,
... arc and its chord . 7. A SECTOR is a part of a circle included within an an arc and the radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is BOOK III The Circle, and the Measurement of Angles,
Page 60
From the Works of A.M. Legendre Adrien Marie Legendre. 8. An INSCRIBED ANGLE is an angle whose vertex is in the circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the circum ...
From the Works of A.M. Legendre Adrien Marie Legendre. 8. An INSCRIBED ANGLE is an angle whose vertex is in the circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the circum ...
Page 77
... inscribed angle is measured by half of the arc included between its sides . There may be three cases : the centre of the circle may lie on one of the sides of the angle ; it may lie within the angle ; or , it may lie without the angle ...
... inscribed angle is measured by half of the arc included between its sides . There may be three cases : the centre of the circle may lie on one of the sides of the angle ; it may lie within the angle ; or , it may lie without the angle ...
Page 78
... inscribed angle , and let the centre lie within it then will the angle be measured by half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB ...
... inscribed angle , and let the centre lie within it then will the angle be measured by half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB ...
Page 79
... inscribed in a segment less than a semi - circle , is B B obtuse ; for it is measured by half the arc BAC , greater than a semi - circumference . Cor . 4. The opposite angles A and C , of an inscribed quadrilateral ABCD , are together ...
... inscribed in a segment less than a semi - circle , is B B obtuse ; for it is measured by half the arc BAC , greater than a semi - circumference . Cor . 4. The opposite angles A and C , of an inscribed quadrilateral ABCD , are together ...
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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.