Elements of Geometry and Trigonometry |
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Page 94
... square described on the linear unit , as a side . PROPOSITION I. THEOREM . Parallelograms which have equal bases and equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and equal altitudes : then will the ...
... square described on the linear unit , as a side . PROPOSITION I. THEOREM . Parallelograms which have equal bases and equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and equal altitudes : then will the ...
Page 101
... square described on the sum of two lines is equal to the sum of the squares described on the lines , increased by twice the rectangle of the lines . Let AB and BC be two lines , and AC their sum : then will 2 AC2 = AB2 + BC2 + 2AB × BC ...
... square described on the sum of two lines is equal to the sum of the squares described on the lines , increased by twice the rectangle of the lines . Let AB and BC be two lines , and AC their sum : then will 2 AC2 = AB2 + BC2 + 2AB × BC ...
Page 102
... square Cor . If the lines AB and BC are equal , the four parts of the square on AC square described on a line is described on half the line . PROPOSITION IX . THEOREM . The square described on the difference of two lines is equal to the ...
... square Cor . If the lines AB and BC are equal , the four parts of the square on AC square described on a line is described on half the line . PROPOSITION IX . THEOREM . The square described on the difference of two lines is equal to the ...
Page 103
Adrien Marie Legendre Charles Davies. the square EFLK : then will EK be equal to BC , and EFLK will be equal to the square of BC . The whole figure ABILKE is equal to the sum of the squares described on AB and BC . The part CBIG is equal ...
Adrien Marie Legendre Charles Davies. the square EFLK : then will EK be equal to BC , and EFLK will be equal to the square of BC . The whole figure ABILKE is equal to the sum of the squares described on AB and BC . The part CBIG is equal ...
Page 104
... square BG AH on the side AB , and the square AI on the side 40 ; from A draw AD , perpendicular to BC , and prolong it to E : then will DE be parallel to BF ; draw AF and HC . In the triangles HBC and ABF , we have HB equal to AB ...
... square BG AH on the side AB , and the square AI on the side 40 ; from A draw AD , perpendicular to BC , and prolong it to E : then will DE be parallel to BF ; draw AF and HC . In the triangles HBC and ABF , we have HB equal to AB ...
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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
AB² ABCD AC² 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...