Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 70
Page 14
... vertex ; thus , the above is called the angle BAC , or simply , the angle A. 11. When one straight line meets another the two angles which they form are called adjacent angles . Thus , the A- angles ABD and DBC are adjacent . 12. A ...
... vertex ; thus , the above is called the angle BAC , or simply , the angle A. 11. When one straight line meets another the two angles which they form are called adjacent angles . Thus , the A- angles ABD and DBC are adjacent . 12. A ...
Page 25
... vertex B will coincide with the vertex E ; and because AC is equal to DF , the vertex C will coincide with the vertex F ; consequently , the side ' BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide ...
... vertex B will coincide with the vertex E ; and because AC is equal to DF , the vertex C will coincide with the vertex F ; consequently , the side ' BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide ...
Page 26
... vertex C will coincide with the vertex F ; and because the angle C is equal to the angle F , the side CA will take the direction FD . Now , the vertex A being at the same time on the lines ED D ( P. III . , C. ) and are and FD , it must ...
... vertex C will coincide with the vertex F ; and because the angle C is equal to the angle F , the side CA will take the direction FD . Now , the vertex A being at the same time on the lines ED D ( P. III . , C. ) and are and FD , it must ...
Page 30
... angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then will the angle C be equal to the angle B. Join the vertex A BC . Then , AB is 30 GEOMETRY .
... angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then will the angle C be equal to the angle B. Join the vertex A BC . Then , AB is 30 GEOMETRY .
Page 31
... vertex A BC . Then , AB is and the middle point D of the base equal to AC , by hypothesis , common , and BD equal to DC , by construction : hence , the triangles BAD , and DAC , have the three sides of the one equal to those of the ...
... vertex A BC . Then , AB is and the middle point D of the base equal to AC , by hypothesis , common , and BD equal to DC , by construction : hence , the triangles BAD , and DAC , have the three sides of the one equal to those of the ...
Other editions - View all
Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence