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 iii
... propositions of Geometry are general truths , and ought to be stated in general terms , without reference to particular diagrams . In the following work , each proposition is first enunciated in general terms , and afterward with ...
... propositions of Geometry are general truths , and ought to be stated in general terms , without reference to particular diagrams . In the following work , each proposition is first enunciated in general terms , and afterward with ...
Page 11
... Propositions . 10. A LEMMA is an auxiliary proposition . 11. A COROLLARY is an obvious consequence of one or more propositions . 12. A SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their ...
... Propositions . 10. A LEMMA is an auxiliary proposition . 11. A COROLLARY is an obvious consequence of one or more propositions . 12. A SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their ...
Page 19
... Proposition ; Prob . for Problem ; Post . for Postulate ; 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 ...
... Proposition ; Prob . for Problem ; Post . for Postulate ; 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 ...
Page 20
... PROPOSITION I. 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 ... proposition 20 GEOMETRY . Propositions,
... PROPOSITION I. 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 ... proposition 20 GEOMETRY . Propositions,
Page 21
... proposition just demonstrated , the sum of any two adjacent angles is equal to two right angles . PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles are equal . Let AB and DE ...
... proposition just demonstrated , the sum of any two adjacent angles is equal to two right angles . PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles are equal . Let AB and DE ...
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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