Elements of Geometry and Trigonometry |
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Page 21
... intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each other . are 1o . ADJACENT ANGLES those which lie on the same side of one line , and on opposite ...
... intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each other . are 1o . ADJACENT ANGLES those which lie on the same side of one line , and on opposite ...
Page 23
... intersect in only one point . NOTE . The method of demonstration employed above , is called the reductio ad absurdum . It consists in assuming an hypothesis which is the contradictory of the proposition to be proved , and then ...
... intersect in only one point . NOTE . The method of demonstration employed above , is called the reductio ad absurdum . It consists in assuming an hypothesis which is the contradictory of the proposition to be proved , and then ...
Page 26
... intersection D ( P. III . , C. ) : hence , the triangles coincide throughout , therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . and are PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is ...
... intersection D ( P. III . , C. ) : hence , the triangles coincide throughout , therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . and are PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is ...
Page 39
... AGHI are equal , because they are verti- cal angles ( P. II . ) ; and consequently , AGH and GHD are equal : hence , from Cor . 1 , AB and CD are parallel . PROPOSITION XX . THEOREM . If a straight line intersect BOOK I. 39.
... AGHI are equal , because they are verti- cal angles ( P. II . ) ; and consequently , AGH and GHD are equal : hence , from Cor . 1 , AB and CD are parallel . PROPOSITION XX . THEOREM . If a straight line intersect BOOK I. 39.
Page 40
Adrien Marie Legendre. PROPOSITION XX . THEOREM . If a straight line intersect two parallel straight lines , the sum of the interior angles on the same side will be equal to two right angles Let the parallels AB , CD , be cut FE : then ...
Adrien Marie Legendre. PROPOSITION XX . THEOREM . If a straight line intersect two parallel straight lines , the sum of the interior angles on the same side will be equal to two right angles Let the parallels AB , CD , be cut FE : then ...
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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