Elements of Geometry and Trigonometry: With Notes |
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Page 28
... determine the position of a straight line ; hence every straight line which passes through two of the points just mentioned , will necessarily pass through the third , and be perpendicular to the chord . It follows , likewise , that the ...
... determine the position of a straight line ; hence every straight line which passes through two of the points just mentioned , will necessarily pass through the third , and be perpendicular to the chord . It follows , likewise , that the ...
Page 48
... determining the true meaning of propositions , and dissipating any obscurity that may occur either in the enunciations or the proofs . The proportion A : B :: C : D being given , it is well known A short sketch of the subject has been ...
... determining the true meaning of propositions , and dissipating any obscurity that may occur either in the enunciations or the proofs . The proportion A : B :: C : D being given , it is well known A short sketch of the subject has been ...
Page 84
... determine whether the lines AC , CB have or have not a common mea- sure . There is a very simple way , however , of avoiding these decreasing lines , and obtaining the result , by operating only upon lines which remain always of the ...
... determine whether the lines AC , CB have or have not a common mea- sure . There is a very simple way , however , of avoiding these decreasing lines , and obtaining the result , by operating only upon lines which remain always of the ...
Page 86
... determined by the number of sides , as that of an equiangular polygon ( 28. I. ) PROPOSITION II . THEOREM . Any regular polygon may be inscribed in a circle , and circum- scribed about one . Let ABCDE , & c . be a regular polygon ...
... determined by the number of sides , as that of an equiangular polygon ( 28. I. ) PROPOSITION II . THEOREM . Any regular polygon may be inscribed in a circle , and circum- scribed about one . Let ABCDE , & c . be a regular polygon ...
Page 97
... determined ex- cept approximately ; but the approximation has been carried so far , that a knowledge of the exact ratio would afford no real advantage whatever beyond that of the approximate ratio . Ac cordingly , this problem , which ...
... determined ex- cept approximately ; but the approximation has been carried so far , that a knowledge of the exact ratio would afford no real advantage whatever beyond that of the approximate ratio . Ac cordingly , this problem , which ...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
Common terms and phrases
ACē adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cosē cosine cylinder demonstration determined diagonal diameter draw drawn equal angles equation equivalent faces figure formulas frustum greater homologous sides hypotenuse inclination inscribed intersection isosceles join less likewise manner measure multiplied number of sides opposite parallel parallelepipedon parallelogram perpendicular plane MN polyedron prism PROBLEM Prop PROPOSITION quadrilateral quantities radii radius ratio rectangle rectilineal triangle regular polygon right angles right-angled triangle SABC Scholium sector segment shew shewn side BC similar sinē sines solid angle sphere spherical polygon spherical triangle square straight line suppose tang tangent THEOREM third side three angles three plane angles triangle ABC triangular pyramids vertex vertices
Popular passages
Page 152 - AMB be a section, made by a plane, in the sphere, whose centre is C. From the...
Page 24 - THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 62 - Similar triangles are to each other as the squares of their homologous sides.
Page 211 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Page 187 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 140 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Page 150 - The radius of a sphere is a straight line, drawn from the centre to any point...
Page 168 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 135 - XII.) ; in like manner, the two solids AQ, AK, having the same base, AOLE, are to each other as their altitudes AD, A M.