Elements of Geometry and Trigonometry: With Notes |
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Page 129
... faces of a poly- edron is called the side or edge of the polyedron . III . A regular polyedron is one whose faces are all equal regular polygons , and whose solid angles are all equal to each other . There are five such polyedrons ...
... faces of a poly- edron is called the side or edge of the polyedron . III . A regular polyedron is one whose faces are all equal regular polygons , and whose solid angles are all equal to each other . There are five such polyedrons ...
Page 130
... faces parallelograms ; it is named a parallelepipedon . ( See the diagram of Prop . 4. VI . ) The parallelepipedon is rectangular when all its faces are rectangles . X. Among rectangular parallelepipedons , we distinguish the cube , or ...
... faces parallelograms ; it is named a parallelepipedon . ( See the diagram of Prop . 4. VI . ) The parallelepipedon is rectangular when all its faces are rectangles . X. Among rectangular parallelepipedons , we distinguish the cube , or ...
Page 131
... faces in each are respectively similarly placed , and equally inclined to each other . Thus , supposing the angles ... face or on the base of a polyedron , then the vertices of the different solid angles of the polyedron , which are ...
... faces in each are respectively similarly placed , and equally inclined to each other . Thus , supposing the angles ... face or on the base of a polyedron , then the vertices of the different solid angles of the polyedron , which are ...
Page 132
... face , when produced , can in no case cut the solid ; the polyedron therefore cannot be in part above the plane of any face , and in part below it ; it must lie wholly on the same side of this plane . PROPOSITION I. THEOREM . Two ...
... face , when produced , can in no case cut the solid ; the polyedron therefore cannot be in part above the plane of any face , and in part below it ; it must lie wholly on the same side of this plane . PROPOSITION I. THEOREM . Two ...
Page 133
... faces are respec- tively equal , and the inclination of two adjacent faces in one of those solids is equal to the inclination of the two homolo- gous faces in the other . Let ABCDE be the common base of the two polyedrons ; M and N the ...
... faces are respec- tively equal , and the inclination of two adjacent faces in one of those solids is equal to the inclination of the two homolo- gous faces in the other . Let ABCDE be the common base of the two polyedrons ; M and N the ...
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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.