Elements of Geometry and Trigonometry: With Notes |
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Page 8
... equal to four right angles : for if four right angles were formed about the point C , by means of two lines ... equal when an angle , and the two sides which contain it in the one , are respectively equal to an angle and the two sides ...
... equal to four right angles : for if four right angles were formed about the point C , by means of two lines ... equal when an angle , and the two sides which contain it in the one , are respectively equal to an angle and the two sides ...
Page 9
... equal to two angles and the interjacent side of the other . LET the side BC ( see the last figure ) be equal to the side EF , the angle B to the angle E , and the angle C to the angle F ; then will the triangle DEF be equal to the ...
... equal to two angles and the interjacent side of the other . LET the side BC ( see the last figure ) be equal to the side EF , the angle B to the angle E , and the angle C to the angle F ; then will the triangle DEF be equal to the ...
Page 10
... equal to DEF ( Prop . 6. ) , since , by construction , they have an equal angle in B- each , contained by equal sides ; therefore CG is equal to EF . C E D Now , there may be three cases in the proposition , according as the point G ...
... equal to DEF ( Prop . 6. ) , since , by construction , they have an equal angle in B- each , contained by equal sides ; therefore CG is equal to EF . C E D Now , there may be three cases in the proposition , according as the point G ...
Page 11
... equal to EDF , or less than it . In the first case , the side CB would ( Prop . 6. ) be equal to EF ; in the second , CB would be less than EF : but both of these results contradict the hypothesis ; therefore , BAC is greater than EDF ...
... equal to EDF , or less than it . In the first case , the side CB would ( Prop . 6. ) be equal to EF ; in the second , CB would be less than EF : but both of these results contradict the hypothesis ; therefore , BAC is greater than EDF ...
Page 12
... equal sides are equal . LET the side AB be equal to AC , the angle C will be equal to B. Join A the vertex , and D the middle point of the base BC . The triangles ADB , ADC , have all the sides of the one respectively equal to those of ...
... equal sides are equal . LET the side AB be equal to AC , the angle C will be equal to B. Join A the vertex , and D the middle point of the base BC . The triangles ADB , ADC , have all the sides of the one respectively equal to those of ...
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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.