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 & Company, 1854 - 432 σελίδες |
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Σελίδα 19
... half of the angle A. 3 8. The square of the line AB is designated by AB ; its cube by AB . What is meant by the square and cube of a line , will be explained in its proper place . 9. The sign indicates a root to be extracted ; thus ✓2 ...
... half of the angle A. 3 8. The square of the line AB is designated by AB ; its cube by AB . What is meant by the square and cube of a line , will be explained in its proper place . 9. The sign indicates a root to be extracted ; thus ✓2 ...
Σελίδα 32
... half of ABF , is shorter than AC , the half of ACF ; hence , the perpendicular is shorter than any oblique line . Secondly . Let us suppose BC = BE ; then 32 GEOMETRY .
... half of ABF , is shorter than AC , the half of ACF ; hence , the perpendicular is shorter than any oblique line . Secondly . Let us suppose BC = BE ; then 32 GEOMETRY .
Σελίδα 33
... half of the broken line FDA , is greater than AC , the half of FCA : consequently , the oblique line which cuts off the greater distance , is the longer . Cor . 1. The perpendicular measures the shortest distance of a point from a line ...
... half of the broken line FDA , is greater than AC , the half of FCA : consequently , the oblique line which cuts off the greater distance , is the longer . Cor . 1. The perpendicular measures the shortest distance of a point from a line ...
Σελίδα 64
... half of equal to the side DG , the half of DE : hence , the triangles are equal , and CF is equal to CG ( B. I. , P. 17 ) ; consequently , the two equal chords AB , DE , are equally distant from the centre . N K H Secondly . Let the ...
... half of equal to the side DG , the half of DE : hence , the triangles are equal , and CF is equal to CG ( B. I. , P. 17 ) ; consequently , the two equal chords AB , DE , are equally distant from the centre . N K H Secondly . Let the ...
Σελίδα 72
... half the circumference . Scholium 3. It appears most natural to measure a quan- tity by a quantity of the same species ; and upon this principle it would be convenient to refer all angles to the right angle . This being made the unit of ...
... half the circumference . Scholium 3. It appears most natural to measure a quan- tity by a quantity of the same species ; and upon this principle it would be convenient to refer all angles to the right angle . This being made the unit of ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang 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 oblique lines 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 sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 27 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Σελίδα 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 26 - The sum of any two sides of a triangle is greater than the third side.
Σελίδα 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Σελίδα 93 - The area of a parallelogram is equal to the product of its base and altitude.
Σελίδα 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Σελίδα 323 - 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.
Σελίδα 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.