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 a solution . 9. A POSTULATE is a problem whose solution is self- evident . Theorems , Axioms , Problems , and ...
... THEOREM is a truth requiring demonstration . 7. An AXIOM is a self - evident truth . 8. A PROBLEM is a question requiring a solution . 9. A POSTULATE is a problem whose solution is self- evident . Theorems , Axioms , Problems , and ...
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 meet 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 meet another BOOK I. 19.
Page 21
... THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . Let AB and DE intersect at C : then will the opposite . or vertical angles be equal . The sum of the adjacent angles ACE and ACD , is ...
... THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . Let AB and DE intersect at C : then will the opposite . or vertical angles be equal . The sum of the adjacent angles ACE and ACD , is ...
Page 23
... THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines coincide throughout ...
... THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines coincide throughout ...
Page 24
... THEOREM . If a straight line meet 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 will form one and the same straight line . Let DC meet AC and BC ...
... THEOREM . If a straight line meet 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 will form one and the same straight line . Let DC meet AC and BC ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence