Elements of Geometry and Trigonometry from the Works of A. M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes, 1857 - 432 σελίδες |
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Σελίδα ii
... PASS , PLANE - TABLE , and LEVEL ; also , Maps of the TOPOGRAPHICAL SIGNS adopted by the Engineer Department - an explanation of the method of surveying the Public Lands , Geodesic and Maritime Surveying , and an Elementary Treatise on ...
... PASS , PLANE - TABLE , and LEVEL ; also , Maps of the TOPOGRAPHICAL SIGNS adopted by the Engineer Department - an explanation of the method of surveying the Public Lands , Geodesic and Maritime Surveying , and an Elementary Treatise on ...
Σελίδα 57
... passes through the centre , and is terminated , on both sides , by the circumference , is called a diameter . From ... passing through the centre , is called a chord , or subtense of the arc . * 4. A SEGMENT is the part of a circle ...
... passes through the centre , and is terminated , on both sides , by the circumference , is called a diameter . From ... passing through the centre , is called a chord , or subtense of the arc . * 4. A SEGMENT is the part of a circle ...
Σελίδα 62
... passes through two of these points , will necessarily pass through the third , and be perpendicular to the chord . It follows , also , that the perpendicular raised at the middle point of a chord passes through the centre of the circle ...
... passes through two of these points , will necessarily pass through the third , and be perpendicular to the chord . It follows , also , that the perpendicular raised at the middle point of a chord passes through the centre of the circle ...
Σελίδα 63
... pass through the three given points , A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the sa.ne straight line : we say farther , that but one can be described through ...
... pass through the three given points , A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the sa.ne straight line : we say farther , that but one can be described through ...
Σελίδα 67
... pass through B. In the same manner it may be shown , that the circumfer ence described about the centre D , with the radius DA , will also pass through B. Cor . If two circumferences intersect each other , they will intersect in two ...
... pass through B. In the same manner it may be shown , that the circumfer ence described about the centre D , with the radius DA , will also pass through B. Cor . If two circumferences intersect each other , they will intersect in two ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² cosine Cotang cubes cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar similar triangles sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM three angles triangle ABC triangular prism triedral angles vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 34 - If two right-angled triangles have the hypothenuse and a side of the one, equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Σελίδα 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Σελίδα 278 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Σελίδα 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 1 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.
Σελίδα 43 - BtSL hence the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides.
Σελίδα 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Σελίδα 30 - B : hence the two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each : hence, the two triangles are equal (Th.
Σελίδα 97 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.