Elements of Geometry and Trigonometry |
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Page iii
... truths evolved . The term solid , used not only by LEGENDRE , but by many other authors , to denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a science , which deals only with the abstract.
... truths evolved . The term solid , used not only by LEGENDRE , but by many other authors , to denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a science , which deals only with the abstract.
Page 55
... denote their ratio . If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B mA A whence , mA : mB :: A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four quantities ...
... denote their ratio . If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B mA A whence , mA : mB :: A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four quantities ...
Page 86
... denote the given sides , and A the given angle . Draw the indefinite line DF , and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the side C , and on DE , lay off DG equal to the side B ; draw G ...
... denote the given sides , and A the given angle . Draw the indefinite line DF , and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the side C , and on DE , lay off DG equal to the side B ; draw G ...
Page 147
... AB at I and Prolong 40 to E be perpendicular to it . Let P denote the circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we shall have ( P. IX . ) , 2 P : p :: Õa2 : ÕÃ3 :: OK2 BOOK V. 147.
... AB at I and Prolong 40 to E be perpendicular to it . Let P denote the circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we shall have ( P. IX . ) , 2 P : p :: Õa2 : ÕÃ3 :: OK2 BOOK V. 147.
Page 149
... the inscribed polygon , and PQ the side of the circumscribed polygon of double the number of sides ( P. VII . ) . Draw CE , CP , CE , CP , CM , and CF E P M F D B A C Denote the area of the given inscribed polygon by p BOOK V. 149.
... the inscribed polygon , and PQ the side of the circumscribed polygon of double the number of sides ( P. VII . ) . Draw CE , CP , CE , CP , CM , and CF E P M F D B A C Denote the area of the given inscribed polygon by p BOOK V. 149.
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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...