Elements of Geometry and Trigonometry |
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Page 27
... triangle two straight lines be drawn to the extremities of any side , their sum will be less than that of the two remaining sides of the triangle . Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the ...
... triangle two straight lines be drawn to the extremities of any side , their sum will be less than that of the two remaining sides of the triangle . Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the ...
Page 28
... triangle ABC , it may be on the side BC , or it may be within the tri- angle ABC . Each case will be considered separately . 1o . When G is without the triangle ABC . In the triangles GIC and AIB , we have , B ( P. VII . ) , A D C F E ...
... triangle ABC , it may be on the side BC , or it may be within the tri- angle ABC . Each case will be considered separately . 1o . When G is without the triangle ABC . In the triangles GIC and AIB , we have , B ( P. VII . ) , A D C F E ...
Page 29
... triangle ABC . From Proposition VIII . , we have , BA + BC > GA + GC ; A D or , since GA = BA , and GC EF , B E we ... triangles ABC and DEF , the side AB is equal to the side DE , the side AC to DF , and BC greater than EF , then will ...
... triangle ABC . From Proposition VIII . , we have , BA + BC > GA + GC ; A D or , since GA = BA , and GC EF , B E we ... triangles ABC and DEF , the side AB is equal to the side DE , the side AC to DF , and BC greater than EF , then will ...
Page 30
... triangles , equal in all their parts , the equal sides lie opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle ...
... triangles , equal in all their parts , the equal sides lie opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle ...
Page 31
... triangle to the middle of the base , bisects the vertical angle , and is per- pendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal , and consequently ...
... triangle to the middle of the base , bisects the vertical angle , and is per- pendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal , and consequently ...
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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...