Elements of Geometry and Trigonometry: With Notes |
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Page 1
... solid or body is that which combines all the three dimensions of space . IX . When two straight lines , AB , AC ... angle ; the point of intersection A is the vertex of the A angle ; the lines AB , AC , are its sides . A ن The angle is ...
... solid or body is that which combines all the three dimensions of space . IX . When two straight lines , AB , AC ... angle ; the point of intersection A is the vertex of the A angle ; the lines AB , AC , are its sides . A ن The angle is ...
Page 73
... angled , the one at D , the other at E A ; also the angle B - E ; these triangles are therefore similar , and they ... solid , for a reason that shall be seen afterwards . Its value is easily con- ceived , by imagining that the lines are ...
... angled , the one at D , the other at E A ; also the angle B - E ; these triangles are therefore similar , and they ... solid , for a reason that shall be seen afterwards . Its value is easily con- ceived , by imagining that the lines are ...
Page 110
... angle or mutual inclination of two planes is the quantity , greater or less , by which they are separated from each other ; this quantity is measured ( 7. IV . ) by the angle contained between two perpendiculars drawn in ... Solid Angles,
... angle or mutual inclination of two planes is the quantity , greater or less , by which they are separated from each other ; this quantity is measured ( 7. IV . ) by the angle contained between two perpendiculars drawn in ... Solid Angles,
Page 122
... solid angle is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires demonstra- tion only when the plane angle , which is compared to the sum of the other two , is ...
... solid angle is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires demonstra- tion only when the plane angle , which is compared to the sum of the other two , is ...
Page 123
... angles which form a solid angle , is al- ways less than four right angles . Cut the solid angle S by any plane ABCDE ; from O , a point in that plane , draw to the several angles straight lines AO , OB , OC , OD , OE . The sum of the angles ...
... angles which form a solid angle , is al- ways less than four right angles . Cut the solid angle S by any plane ABCDE ; from O , a point in that plane , draw to the several angles straight lines AO , OB , OC , OD , OE . The sum of the angles ...
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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.