Elements of Geometry and Trigonometry |
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Page 49
... Scholium . In a rhombus , the sides AB , BC , being equal , the triangles AEB , EBC , have the sides of the one equal to the corresponding sides of the other ; they are , therefore , equal : hence , the angles AEB , BEC , are equal ...
... Scholium . In a rhombus , the sides AB , BC , being equal , the triangles AEB , EBC , have the sides of the one equal to the corresponding sides of the other ; they are , therefore , equal : hence , the angles AEB , BEC , are equal ...
Page 65
... Scholium . The centre C , C , the middle point D of the chord AB , and the middle point G of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a straight line ( A. 11 ) ...
... Scholium . The centre C , C , the middle point D of the chord AB , and the middle point G of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a straight line ( A. 11 ) ...
Page 67
... Scholium . All the propositions relating to chords and arcs of equal circles , are also true for chords and arcs of one and the same circle . For , any circle may be regarded as made up of two equal circles , so placed , that they ...
... Scholium . All the propositions relating to chords and arcs of equal circles , are also true for chords and arcs of one and the same circle . For , any circle may be regarded as made up of two equal circles , so placed , that they ...
Page 72
... Scholium . From the preceding propositions , we infer that two circles may have any one of six positions with respect to each other , depending upon the distance between their centres : 1o . When the distance between their centres is ...
... Scholium . From the preceding propositions , we infer that two circles may have any one of six positions with respect to each other , depending upon the distance between their centres : 1o . When the distance between their centres is ...
Page 77
... Scholium . Since the intercepted arcs are proportional to the corresponding angles at the centre , the arcs may be taken as the measures of the angles . That is , if a circum- ference be described from the vertex of any angle , as a cen ...
... Scholium . Since the intercepted arcs are proportional to the corresponding angles at the centre , the arcs may be taken as the measures of the angles . That is , if a circum- ference be described from the vertex of any angle , as a cen ...
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Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence