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 páginas |
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Página 13
... means of such measurement , the properties and relations of geometrical magnitudes . 3. A POINT is that which has place , or position , but not magnitude . 4. A LINE is length , without breadth or thickness . 5. A STRAIGHT LINE is one ...
... means of such measurement , the properties and relations of geometrical magnitudes . 3. A POINT is that which has place , or position , but not magnitude . 4. A LINE is length , without breadth or thickness . 5. A STRAIGHT LINE is one ...
Página 17
... means of a demonstration . 4. A problem is a question proposed , which requires a solution . 5. A lemma is a subsidiary truth , employed for the demonstration of a theorem , or the solution of a problem 6. The common name , proposition ...
... means of a demonstration . 4. A problem is a question proposed , which requires a solution . 5. A lemma is a subsidiary truth , employed for the demonstration of a theorem , or the solution of a problem 6. The common name , proposition ...
Página 19
... means the square - root of 2 ; √AXB means the square - root of the product of A and B. AXIOMS . 1. Things which are equal to the same thing , are equal to one another . 2. If equals be added to equals , the wholes will be equal ...
... means the square - root of 2 ; √AXB means the square - root of the product of A and B. AXIOMS . 1. Things which are equal to the same thing , are equal to one another . 2. If equals be added to equals , the wholes will be equal ...
Página 49
... together are called the terms of the propor tion . The first and last terms are called the two extremes , and the second and third terms , the two means . 7. Of four proportional quantities , the last is said 4 BOOK II . 49.
... together are called the terms of the propor tion . The first and last terms are called the two extremes , and the second and third terms , the two means . 7. Of four proportional quantities , the last is said 4 BOOK II . 49.
Página 50
... mean proportional between the other two . 9. Magnitudes are in proportion by alternation , or alter- nately , when antecedent is compared with antecedent , and consequent with consequent . 10. Magnitudes are in proportion by inversion ...
... mean proportional between the other two . 9. Magnitudes are in proportion by alternation , or alter- nately , when antecedent is compared with antecedent , and consequent with consequent . 10. Magnitudes are in proportion by inversion ...
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Términos y frases comunes
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
Pasajes populares
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 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...
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 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.
Página 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.
Página 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'.
Página 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.
Página 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Página 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.
Página 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.