Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 11
... equation . part on the left of the sign of equality , is called the first member ; that on the right , the second member . The Sign of Inequality , < : Thus , √A < / B , indicates that the square root of A is less than the cube root of ...
... equation . part on the left of the sign of equality , is called the first member ; that on the right , the second member . The Sign of Inequality , < : Thus , √A < / B , indicates that the square root of A is less than the cube root of ...
Page 52
... AD = BC , by changing the members of the equation , we have , BC = AD ; dividing both members by AC , we have , B D Ā C = or A : B :: C : D ; which was to be proved . PROPOSITION III . THEOREM . If four quantities are in 52 GEOMETRY .
... AD = BC , by changing the members of the equation , we have , BC = AD ; dividing both members by AC , we have , B D Ā C = or A : B :: C : D ; which was to be proved . PROPOSITION III . THEOREM . If four quantities are in 52 GEOMETRY .
Page 58
... equations , member by member , we have , BF DH = AE CG ; BF :: whence , AE : which was to be proved . CG : DH ; Cor . 1. If the corresponding terms of two proportions are equal , each term of the resulting proportion will be the square ...
... equations , member by member , we have , BF DH = AE CG ; BF :: whence , AE : which was to be proved . CG : DH ; Cor . 1. If the corresponding terms of two proportions are equal , each term of the resulting proportion will be the square ...
Page 109
... equations , member to member ( A. 2 ) , recollect . ing that BE is equal to EC , we have , 2 AB2 + AC2 2BE2 + 2EA2 ; which was to be proved . = Cor . Let ABCD be a parallelogram , and BD , AC , its diagonals . Then , since the diagonals ...
... equations , member to member ( A. 2 ) , recollect . ing that BE is equal to EC , we have , 2 AB2 + AC2 2BE2 + 2EA2 ; which was to be proved . = Cor . Let ABCD be a parallelogram , and BD , AC , its diagonals . Then , since the diagonals ...
Page 151
... Equation ( 2 ) , we can find P ' . PROPOSITION XII . PROBLEM . To find the approximate area of a circle whose radius ... Equations ( 1 ) and ( 2 ) of Proposition XI . , inscribed octagon ; p ' = √8 = 2.8284271 • 16 P ' = = 3.3137085 ...
... Equation ( 2 ) , we can find P ' . PROPOSITION XII . PROBLEM . To find the approximate area of a circle whose radius ... Equations ( 1 ) and ( 2 ) of Proposition XI . , inscribed octagon ; p ' = √8 = 2.8284271 • 16 P ' = = 3.3137085 ...
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Common terms and phrases
ABē ABCD ACē 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.