Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 14
... meets another the two angles which they form are called adjacent angles . Thus , the A angles ABD and DBC are adjacent . 12. A RIGHT ANGLE is formed by one straight line meeting another so as to make the adjacent angles equal . The ...
... meets another the two angles which they form are called adjacent angles . Thus , the A angles ABD and DBC are adjacent . 12. A RIGHT ANGLE is formed by one straight line meeting another so as to make the adjacent angles equal . The ...
Page 15
... meet , how far soever , either way , both may be produced . They then have the same direction . 17. A PLANE FIGURE is a portion of a plane bounded by lines , either straight or curved . 18. A POLYGON is a plane figure bounded by ...
... meet , how far soever , either way , both may be produced . They then have the same direction . 17. A PLANE FIGURE is a portion of a plane bounded by lines , either straight or curved . 18. A POLYGON is a plane figure bounded by ...
Page 19
... Postu- late ; and S. for Scholium . In referring to the same Book the number of the Book is not given ; in referring to any other Book , the number of the Book is given . PROPOSITION I. THEOREM . If a straight line meet another BOOK I. 19.
... Postu- late ; and S. for Scholium . In referring to the same Book the number of the Book is not given ; in referring to any other Book , the number of the Book is given . PROPOSITION I. THEOREM . If a straight line meet another BOOK I. 19.
Page 20
... meet another straight line , the sum of the adjacent angles will be equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA and DCB be equal to two right angles . At C , let CE be drawn per- pendicular to ...
... meet another straight line , the sum of the adjacent angles will be equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA and DCB be equal to two right angles . At C , let CE be drawn per- pendicular to ...
Page 23
... reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a straight line meet BOOK I. 23.
... reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a straight line meet BOOK I. 23.
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Common terms and phrases
ABē ACē 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 straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence