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 DCB equal to two right an- gles . At C ...
... 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 DCB equal to two right an- gles . At C ...
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
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.