Elements of Geometry and Trigonometry: With Notes |
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Page 25
... polygon is circumscribed about a circle , when all its sides are tangents to the circumference ( see the diagram of Prop . 6. IV . ) : in the same case , the circle is said to be inscribed in the polygon . PROPOSITION I. THEOREM . Every ...
... polygon is circumscribed about a circle , when all its sides are tangents to the circumference ( see the diagram of Prop . 6. IV . ) : in the same case , the circle is said to be inscribed in the polygon . PROPOSITION I. THEOREM . Every ...
Page 69
... polygon ABCDE , draw diagonals AC , AD B to the other angles . From the corresponding angle A F , in the other polygon FGHIK , draw diagonals FH , FI to the other angles . E These polygons being similar , the angles ABC , FGH , which ...
... polygon ABCDE , draw diagonals AC , AD B to the other angles . From the corresponding angle A F , in the other polygon FGHIK , draw diagonals FH , FI to the other angles . E These polygons being similar , the angles ABC , FGH , which ...
Page 70
... polygon ABCDE , is to the sum of the consequents FGH + FHI + FIK , or to the polygon FGHIK , as one antecedent ABC is to its consequent FGH , or as AB2 is to FG2 ; hence the surfaces of similar polygons are to each other as the squares ...
... polygon ABCDE , is to the sum of the consequents FGH + FHI + FIK , or to the polygon FGHIK , as one antecedent ABC is to its consequent FGH , or as AB2 is to FG2 ; hence the surfaces of similar polygons are to each other as the squares ...
Page 79
... polygon . Let ABCDE be the given polygon . Draw first the diagonal CE cutting off the triangle CDE ; through the point D , draw DF parallel to CE , and meeting AE produced ; join CF : the polygon ABCDE will be equivalent to the poly ...
... polygon . Let ABCDE be the given polygon . Draw first the diagonal CE cutting off the triangle CDE ; through the point D , draw DF parallel to CE , and meeting AE produced ; join CF : the polygon ABCDE will be equivalent to the poly ...
Page 80
... polygon ABCDE equivalent to the polygon ABCF . The angle B may in like manner be cut off , by substituting for the triangle ABC the equivalent triangle AGC , and thus the pentagon ABDE will be changed into an equivalent tri- angle GCF ...
... polygon ABCDE equivalent to the polygon ABCF . The angle B may in like manner be cut off , by substituting for the triangle ABC the equivalent triangle AGC , and thus the pentagon ABDE will be changed into an equivalent tri- angle GCF ...
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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
AC² adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cos² 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 sin² 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.