Elements of Geometry and Trigonometry: With Notes |
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Page 25
... circumscribe such a figure . VII . A secant is a line which meets the cir- cumference in two points . AB is a secant ... circumscribed about a circle , when all its sides are tangents to the circumference ( see the diagram of Prop . 6 ...
... circumscribe such a figure . VII . A secant is a line which meets the cir- cumference in two points . AB is a secant ... circumscribed about a circle , when all its sides are tangents to the circumference ( see the diagram of Prop . 6 ...
Page 73
... circumscribed circle , and the perpendicular AD let fall upon the third side BC . For , joining AE , the triangles ABD , AEC are right - angled , the one at D , the other at E A ; also the angle B - E ; these triangles are therefore ...
... circumscribed circle , and the perpendicular AD let fall upon the third side BC . For , joining AE , the triangles ABD , AEC are right - angled , the one at D , the other at E A ; also the angle B - E ; these triangles are therefore ...
Page 86
... circumscribed circles , may also be regarded as the centre of the polygon ; and upon this principle the angle AOB is called the angle at the centre , being formed by two radii drawn to the extremities of the same side AB . Since all the ...
... circumscribed circles , may also be regarded as the centre of the polygon ; and upon this principle the angle AOB is called the angle at the centre , being formed by two radii drawn to the extremities of the same side AB . Since all the ...
Page 89
... circumscribed lygon GHIK & c . , similar to the inscribed one . po- It is evident , in the first place , that the three N P K T E M F points O , B , H , lie in the same straight line ; for the right - angled It was long supposed , that ...
... circumscribed lygon GHIK & c . , similar to the inscribed one . po- It is evident , in the first place , that the three N P K T E M F points O , B , H , lie in the same straight line ; for the right - angled It was long supposed , that ...
Page 90
... circumscribed polygon are all equal ; hence this polygon is regular , and similar to the inscribed one . : = Cor . 1. Reciprocally , if the circumscribed polygon GHIK & c . were given , and the inscribed one ABC & c . were required to ...
... circumscribed polygon are all equal ; hence this polygon is regular , and similar to the inscribed one . : = Cor . 1. Reciprocally , if the circumscribed polygon GHIK & c . were given , and the inscribed one ABC & c . were required to ...
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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.