Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 9
... four species of quantity , called GEOMETRICAL MAGNITUDES , ViZ . , LINES , SUR- FACES , VOLUMES , and ANGLES : hence , there are four kinds of units of measure , viz . , Units of Length , Units of Surface , Units of Volume , and Units ...
... four species of quantity , called GEOMETRICAL MAGNITUDES , ViZ . , LINES , SUR- FACES , VOLUMES , and ANGLES : hence , there are four kinds of units of measure , viz . , Units of Length , Units of Surface , Units of Volume , and Units ...
Page 15
... four sides , a quadrilateral ; of five sides , a pentagon ; one of six sides , a hexagon ; one of seven sides , a hepta- gon ; one of eight sides , an octagon ; one of ten sides , a decagon ; one of twelve sides , a dodecagon , & c . 20 ...
... four sides , a quadrilateral ; of five sides , a pentagon ; one of six sides , a hexagon ; one of seven sides , a hepta- gon ; one of eight sides , an octagon ; one of ten sides , a decagon ; one of twelve sides , a dodecagon , & c . 20 ...
Page 21
... four angles about the point of intersection , which have received different names , with respect to each other . 1o . ADJACENT ANGLES those which lie on the same side of one line , and on opposite sides of the other ; thus , ACE and ECB ...
... four angles about the point of intersection , which have received different names , with respect to each other . 1o . ADJACENT ANGLES those which lie on the same side of one line , and on opposite sides of the other ; thus , ACE and ECB ...
Page 22
... mutually perpendicular to each other . Cor . 3. The sum of all the angles ACB , BCD , DCE , ECF , FCA , that can be formed about a point , is equal to four right angles , B For , if two lines be drawn through the point 22 GEOMETRY .
... mutually perpendicular to each other . Cor . 3. The sum of all the angles ACB , BCD , DCE , ECF , FCA , that can be formed about a point , is equal to four right angles , B For , if two lines be drawn through the point 22 GEOMETRY .
Page 23
... four right angles , and it will also be equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have two points in common ...
... four right angles , and it will also be equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have two points in common ...
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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