Elements of Geometry and Trigonometry: With Notes |
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Page 55
... described on AB , since we made AF - AB : the second IGDH is the square described on BC ; for since we have ACA == E , and AB AF , the difference AC - AB must be equal to the difference AE - AF , which gives BC - EF ; but IG is equal to ...
... described on AB , since we made AF - AB : the second IGDH is the square described on BC ; for since we have ACA == E , and AB AF , the difference AC - AB must be equal to the difference AE - AF , which gives BC - EF ; but IG is equal to ...
Page 56
... described on AC will be equivalent to the square of AB , plus the square of BC , minus twice the rectangle con- tained by AB and BC ; that is to say , we shall have AC or ( AB - BC ) 2 = AB2 + BC2 —2 AB × BC . Construct the square ABIF ...
... described on AC will be equivalent to the square of AB , plus the square of BC , minus twice the rectangle con- tained by AB and BC ; that is to say , we shall have AC or ( AB - BC ) 2 = AB2 + BC2 —2 AB × BC . Construct the square ABIF ...
Page 57
With Notes Adrien Marie Legendre. The PROPOSITION XI . THEOREM . square described on the hypotenuse of a right - angled tri- angle is equivalent to the sum of the squares described on the two sides . Let the triangle ABC be right- angled ...
With Notes Adrien Marie Legendre. The PROPOSITION XI . THEOREM . square described on the hypotenuse of a right - angled tri- angle is equivalent to the sum of the squares described on the two sides . Let the triangle ABC be right- angled ...
Page 58
... described on the diago- nal AC , is double of the square described on the E side AB . B F This property may be exhibited more plainly , by drawing parallels to BD , through the points A and C , and parallels to AC , through the points B ...
... described on the diago- nal AC , is double of the square described on the E side AB . B F This property may be exhibited more plainly , by drawing parallels to BD , through the points A and C , and parallels to AC , through the points B ...
Page 67
... described on the hypotenuse BC is equal to the squares described on the two sides AB , AC . Thus we again arrive at the property of the square of the hypotenuse , by a path very different from that which formerly conducted us to it ...
... described on the hypotenuse BC is equal to the squares described on the two sides AB , AC . Thus we again arrive at the property of the square of the hypotenuse , by a path very different from that which formerly conducted us to it ...
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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.