Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 52
Page 51
... proportional to the other three . When the second term is equal to the third , it is said to be a mean proportional between the extremes . In this case , there are but three different quantities in the proportion , and the last is ...
... proportional to the other three . When the second term is equal to the third , it is said to be a mean proportional between the extremes . In this case , there are but three different quantities in the proportion , and the last is ...
Page 53
... , the consequents will be proportional . For , the antecedents of the second couplets may be made the consequents of the first , by alternation ( P. III . ) . PROPOSITION V. THEOREM . If four quantities are in proportion BOOK II . 53.
... , the consequents will be proportional . For , the antecedents of the second couplets may be made the consequents of the first , by alternation ( P. III . ) . PROPOSITION V. THEOREM . If four quantities are in proportion BOOK II . 53.
Page 55
... proportional to the quan- tities themselves . B Let A and B be any two quantities ; then will denote their ratio . A If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , MB B = mA : 1 ...
... proportional to the quan- tities themselves . B Let A and B be any two quantities ; then will denote their ratio . A If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , MB B = mA : 1 ...
Page 56
... proportional to the quantities themselves . We have , Prop . VII . , A : B :: mA : mB . If we make m 1 ± , q in which P is any fraction , q we shall have , A : B :: A + A which was to be proved . P q : B ± _B ; q PROPOSITION X. THEOREM ...
... proportional to the quantities themselves . We have , Prop . VII . , A : B :: mA : mB . If we make m 1 ± , q in which P is any fraction , q we shall have , A : B :: A + A which was to be proved . P q : B ± _B ; q PROPOSITION X. THEOREM ...
Page 58
... proportional , their squares will be proportional . Cor . 2. If the principle of the proposition be extended to three or more proportions , and the corresponding terms of each be supposed equal , it will follow that , like powers of ...
... proportional , their squares will be proportional . Cor . 2. If the principle of the proposition be extended to three or more proportions , and the corresponding terms of each be supposed equal , it will follow that , like powers of ...
Other editions - View all
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
ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cos²a cosec cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment semi-circumference similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume 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...