Elements of Geometry and Trigonometry: With Notes |
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Page xii
... results from making the first of them numerator , and the second denominator . It is in this sense , that one ratio is said to be equal to or less or greater than another ratio . IV . The first and third terms of a proportion are called ...
... results from making the first of them numerator , and the second denominator . It is in this sense , that one ratio is said to be equal to or less or greater than another ratio . IV . The first and third terms of a proportion are called ...
Page 11
... results contradict the hypothesis ; therefore , BAC is greater than EDF . PROPOSITION XI . THEOREM . Two triangles are equal , when the three sides of the one are re- spectively equal to the three sides of the other . LET the side AB ...
... results contradict the hypothesis ; therefore , BAC is greater than EDF . PROPOSITION XI . THEOREM . Two triangles are equal , when the three sides of the one are re- spectively equal to the three sides of the other . LET the side AB ...
Page 49
... results in a similar manner from the lines B and C. The magnitudes A and B may be of one species , for ex- ample , lines ... result from them . We must also premise , that several of our demonstrations are grounded on some of the simpler ...
... results in a similar manner from the lines B and C. The magnitudes A and B may be of one species , for ex- ample , lines ... result from them . We must also premise , that several of our demonstrations are grounded on some of the simpler ...
Page 54
... result AB + CD which is expressed thus : ABCD = EF × 2 Scholium . If through I , the middle point of BC , the line IH be drawn parallel to the base AB , the point H will also be the middle of AD . For , because the figure AHIL is a ...
... result AB + CD which is expressed thus : ABCD = EF × 2 Scholium . If through I , the middle point of BC , the line IH be drawn parallel to the base AB , the point H will also be the middle of AD . For , because the figure AHIL is a ...
Page 59
... results BD2 = BC2 + CD2 + 2 BC × CD . Adding AD to both , and reducing the sums as in the last theorem , we find AB2 - BC + AC2 + 2BC × CD . Scholium . The right - angled triangle is the only one in which the squares of two sides are ...
... results BD2 = BC2 + CD2 + 2 BC × CD . Adding AD to both , and reducing the sums as in the last theorem , we find AB2 - BC + AC2 + 2BC × CD . Scholium . The right - angled triangle is the only one in which the squares of two sides are ...
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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.