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
... unit of measure of a quantity is of the same kind as the quantity measured , there are four kinds of units of measure , viz .: Units of Length , Units of Surface , Units of Volume , and Units of Angular Measure . 3. GEOMETRY is that ...
... unit of measure of a quantity is of the same kind as the quantity measured , there are four kinds of units of measure , viz .: Units of Length , Units of Surface , Units of Volume , and Units of Angular Measure . 3. GEOMETRY is that ...
Page 12
... unit an equal number of times . 15. Magnitudes are equal in all respects , when they may be so placed as to coincide throughout their whole extent ; they are equal in all their parts when each part of one is equal to the corresponding ...
... unit an equal number of times . 15. Magnitudes are equal in all respects , when they may be so placed as to coincide throughout their whole extent ; they are equal in all their parts when each part of one is equal to the corresponding ...
Page 76
... unit : then are they pro- portional to the intercepted arcs AB and DE . с B M m n Ρ Let the angle M be a common unit ; and suppose , for example , that this unit is contained 7 times in the angle ACB , and 4 times in the angle DOE ...
... unit : then are they pro- portional to the intercepted arcs AB and DE . с B M m n Ρ Let the angle M be a common unit ; and suppose , for example , that this unit is contained 7 times in the angle ACB , and 4 times in the angle DOE ...
Page 79
... unit . If , therefore , any angle is measured by one half or two thirds of a quadrant , it is equal to one half or two thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included ...
... unit . If , therefore , any angle is measured by one half or two thirds of a quadrant , it is equal to one half or two thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included ...
Page 94
... unit of measure for angles , being measured by a quadrant ( P. XVII . , S. ) , is said to be an angle B C A E of 90 ° ; an angle which is one third of a right angle is an angle of 30 ° ; an angle of 120 ° is or of a right angle , etc ...
... unit of measure for angles , being measured by a quadrant ( P. XVII . , S. ) , is said to be an angle B C A E of 90 ° ; an angle which is one third of a right angle is an angle of 30 ° ; an angle of 120 ° is or of a right angle , etc ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence