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
... . or 12. A SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their use , their extent , or their limitation . 13. An HYPOTHESIS is a supposition made , either in INTRODUCTION . 11.
... . or 12. A SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their use , their extent , or their limitation . 13. An HYPOTHESIS is a supposition made , either in INTRODUCTION . 11.
Page 19
... ; 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.
... ; 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 26
... ( A. 5 ) , AC BC < AB ; - that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may re- present the sides of a triangle , the sum of 26 GEOMETRY .
... ( A. 5 ) , AC BC < AB ; - that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may re- present the sides of a triangle , the sum of 26 GEOMETRY .
Page 30
... Scholium . In triangles , equal in all their parts , the equal sides lie opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC be an ...
... Scholium . In triangles , equal in all their parts , the equal sides lie opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC be an ...
Page 41
... Scholium . Of the eight angles formed by a line cutting two parallel lines obliquely , the four acute angles are equal , and so , also , are the four obtuse angles . PROPOSITION XXI . THEOREM . If two straight lines intersect a third ...
... Scholium . Of the eight angles formed by a line cutting two parallel lines obliquely , the four acute angles are equal , and so , also , are the four obtuse angles . PROPOSITION XXI . THEOREM . If two straight lines intersect a third ...
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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