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 49
... are compared 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.
... are compared 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.
Σελίδα 50
... proportional quantities , the last is said to be a fourth proportional to the other three , taken in order . The first and second terms , are called the first couplet of the proportion ; and the third and fourth terms , the second ...
... proportional quantities , the last is said to be a fourth proportional to the other three , taken in order . The first and second terms , are called the first couplet of the proportion ; and the third and fourth terms , the second ...
Σελίδα 51
... proportional quantities , the product of the extremes will be equal to the square of the mean ( D. 8 ) . For , if N = P , we have 2 MXQ = N ° or P2 . PROPOSITION II . THEOREM . If the product of two magnitudes be equal to the product of ...
... proportional quantities , the product of the extremes will be equal to the square of the mean ( D. 8 ) . For , if N = P , we have 2 MXQ = N ° or P2 . PROPOSITION II . THEOREM . If the product of two magnitudes be equal to the product of ...
Σελίδα 52
... proportional magnitudes , and four other pro- portional magnitudes , having the antecedents the sume in both , the consequents will be proportional . Let M N P Q , giving MX Q = N × P , and MRP : S , giving RX P = MXS , then will N : Q ...
... proportional magnitudes , and four other pro- portional magnitudes , having the antecedents the sume in both , the consequents will be proportional . Let M N P Q , giving MX Q = N × P , and MRP : S , giving RX P = MXS , then will N : Q ...
Σελίδα 54
... proportional magnitudes , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of the two consequents , such equimultiples will be proportional . Let M , N , P , Q , be four magnitudes in proportion ; and ...
... proportional magnitudes , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of the two consequents , such equimultiples will be proportional . Let M , N , P , Q , be four magnitudes in proportion ; and ...
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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.