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 11
... THEOREM is a truth requiring demonstration . 7. An AXIOM is a self - evident truth . 8 . A PROBLEM is a question requiring solution . 9. A POSTULATE is a self - evident Problem . Theorems , Axioms , Problems , and Postulates , are all ...
... THEOREM is a truth requiring demonstration . 7. An AXIOM is a self - evident truth . 8 . A PROBLEM is a question requiring solution . 9. A POSTULATE is a self - evident Problem . Theorems , Axioms , Problems , and Postulates , are all ...
Page 19
... 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 meets another BOOK I. 19.
... 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 meets another BOOK I. 19.
Page 20
... THEOREM . If a straight line meets another straight line , the sum of the adjacent angles is equal to two right angles . Let DC meet AB at C : then is the sum of the angles DCA and DCB equal to two right an- gles . At C , let CE be ...
... THEOREM . If a straight line meets another straight line , the sum of the adjacent angles is equal to two right angles . Let DC meet AB at C : then is the sum of the angles DCA and DCB equal to two right an- gles . At C , let CE be ...
Page 23
... THEOREM . If two straight lines have two points in common , they coin- cide throughout their whole extent , and form one and the same line . Let A and B be be two points common to two lines : then the lines coincide throughout . E B ...
... THEOREM . If two straight lines have two points in common , they coin- cide throughout their whole extent , and form one and the same line . Let A and B be be two points common to two lines : then the lines coincide throughout . E B ...
Page 24
... THEOREM . If a straight line meets two other straight lines at a com- mon point , making the sum of the contiguous angles equal to two right angles , the two lines met form one and the same straight line . Let DC meet AC and BC at C ...
... THEOREM . If a straight line meets two other straight lines at a com- mon point , making the sum of the contiguous angles equal to two right angles , the two lines met form one and the same straight line . Let DC meet AC and BC at C ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence