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 afterwards , 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 afterwards , with ...
Page 11
... Propositions . 10. A LEMMA is an auxiliary proposition . 11. A COROLLARY is an obvious consequence of one more propositions . or 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 more propositions . or 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 meet another straight line , the sum of the adjacent angles will be equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA and DCB be equal to two right angles ...
... PROPOSITION I. THEOREM . If a straight line meet another straight line , the sum of the adjacent angles will be equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA and DCB be equal to two right angles ...
Page 21
... proposition just demonstrated , is equal to two right angles . DEFINITIONS . If two straight lines intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each ...
... proposition just demonstrated , is equal to two right angles . DEFINITIONS . If two straight lines intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each ...
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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