Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 11
... SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their use , their extent , or their limitation . I 13. An HYPOTHESIS is a supposition made , either INTRODUCTION . 11 Definitions, Propositions,
... SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their use , their extent , or their limitation . I 13. An HYPOTHESIS is a supposition made , either INTRODUCTION . 11 Definitions, Propositions,
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
... AC – BC < AB` ; as BC , for 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 .
... AC – BC < AB` ; as BC , for 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 ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following