Elements of Geometry and Trigonometry |
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Page iii
... means of the diagrams employed in their demonstration . This departure from the method of EUCLID is much to be regretted . The propositions of Geometry are general truths , and ought to be stated in general terms , without reference to ...
... means of the diagrams employed in their demonstration . This departure from the method of EUCLID is much to be regretted . The propositions of Geometry are general truths , and ought to be stated in general terms , without reference to ...
Page 51
... means , and the fourth term , a fourth proportional to the other three . When the second term is equal to the third , it ... mean proportional between A and C , and Cis a third proportional to A and B. 5. Quantities are in proportion by ...
... means , and the fourth term , a fourth proportional to the other three . When the second term is equal to the third , it ... mean proportional between A and C , and Cis a third proportional to A and B. 5. Quantities are in proportion by ...
Page 52
... means will be equal to the product of the extremes . Assume the proportion , B D A : B :: C : D ; whence , ; A ... mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two quantities is equal ...
... means will be equal to the product of the extremes . Assume the proportion , B D A : B :: C : D ; whence , ; A ... mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two quantities is equal ...
Page 119
... mean propor- tional between the hypothenuse and the adjacent segment : 3 ° . The perpendicular will be a mean proportional between the two segments of the hypothenuse . 1o . Let ABC be a right - angled triangle , A the vertex of the ...
... mean propor- tional between the hypothenuse and the adjacent segment : 3 ° . The perpendicular will be a mean proportional between the two segments of the hypothenuse . 1o . Let ABC be a right - angled triangle , A the vertex of the ...
Page 120
... mean pro- portional between BC and BD ; and AC will be a mean propor- tional between CB and CD . For , the triangles ADB and BAC being similar , their homo- logous sides are proportional : hence , B BC : AB :: AB : BD . In like manner ...
... mean pro- portional between BC and BD ; and AC will be a mean propor- tional between CB and CD . For , the triangles ADB and BAC being similar , their homo- logous sides are proportional : hence , B BC : AB :: AB : BD . In like manner ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
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.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...