Elements of Geometry and Trigonometry: With Notes |
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Page 12
... DBC must be equal to ACB . But the part cannot be equal to the whole ; hence there is no inequality between the sides AB , AC ; hence the triangle ABC is isosceles . B PROPOSITION XIV . THEOREM . Of two sides of a 12 GEOMETRY .
... DBC must be equal to ACB . But the part cannot be equal to the whole ; hence there is no inequality between the sides AB , AC ; hence the triangle ABC is isosceles . B PROPOSITION XIV . THEOREM . Of two sides of a 12 GEOMETRY .
Page 14
... whole . PROPOSITION XVI . THEOREM . If from a point A ( see the preceding figure ) , situated without the straight line DE , a perpendicular AB be let fall on that straight line , and several oblique lines AE , AC , AD , be drawn to ...
... whole . PROPOSITION XVI . THEOREM . If from a point A ( see the preceding figure ) , situated without the straight line DE , a perpendicular AB be let fall on that straight line , and several oblique lines AE , AC , AD , be drawn to ...
Page 31
... whole arc HMK = HPK . It is farther evi- dent that each of these arcs is a semicircumference . PROPOSITION XI . THEOREM . If two circles cut each other in two points , the line which passes through their centres , will be perpendicular ...
... whole arc HMK = HPK . It is farther evi- dent that each of these arcs is a semicircumference . PROPOSITION XI . THEOREM . If two circles cut each other in two points , the line which passes through their centres , will be perpendicular ...
Page 33
... whole , which is absurd : hence the angle ACB is equal to DCE . PROPOSITION XVI . THEOREM . In the same circle , or in equal circles , if two angles at the centre ACB , DCE are to each other in the proportion of two whole numbers , the ...
... whole , which is absurd : hence the angle ACB is equal to DCE . PROPOSITION XVI . THEOREM . In the same circle , or in equal circles , if two angles at the centre ACB , DCE are to each other in the proportion of two whole numbers , the ...
Page 34
... whole arc AB will be to the whole arc DE as 7 is to 4. But the same reasoning would evidently apply , if in place of 7 and 4 any numbers whatever were employed ; hence , if the ratio of the angles ACB , DCE can be expressed in whole ...
... whole arc AB will be to the whole arc DE as 7 is to 4. But the same reasoning would evidently apply , if in place of 7 and 4 any numbers whatever were employed ; hence , if the ratio of the angles ACB , DCE can be expressed in whole ...
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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.