Elements of Geometry and Trigonometry |
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Page 12
... are equal , when they are equal in measure . When they may be so placed as to coincide through- out their whole extent , they are equal in all their parts . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
... are equal , when they are equal in measure . When they may be so placed as to coincide through- out their whole extent , they are equal in all their parts . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
Page 63
... placed upon the sector EOG , so that the angle ACD shall coincide with the angle EOG , the sectors will coincide throughout ; and , consequently , the arcs AMD and ENG will coincide : hence , they will be equal ; which was to be proved ...
... placed upon the sector EOG , so that the angle ACD shall coincide with the angle EOG , the sectors will coincide throughout ; and , consequently , the arcs AMD and ENG will coincide : hence , they will be equal ; which was to be proved ...
Page 66
... at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
... at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
Page 67
Adrien Marie Legendre Charles Davies. For , let the circle KLG be placed upon ACH , so that the centre R shall fall upon the ... placed , that they coincide in all their parts . PROPOSITION IX . THEOREM . If a straight line is BOOK III . 67.
Adrien Marie Legendre Charles Davies. For , let the circle KLG be placed upon ACH , so that the centre R shall fall upon the ... placed , that they coincide in all their parts . PROPOSITION IX . THEOREM . If a straight line is BOOK III . 67.
Page 75
... be proportional to the arcs AB and FH . For , let the less angle FOH , angle ACB , SO that it shall AA Α DIOB F II be placed upon the greater take the position ACD . Then , if the proposition is not true , let BOOK II . 75.
... be proportional to the arcs AB and FH . For , let the less angle FOH , angle ACB , SO that it shall AA Α DIOB F II be placed upon the greater take the position ACD . Then , if the proposition is not true , let BOOK II . 75.
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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...