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 16
... angles , taken in the same order , are equal , each to each . 23. A DIAGONAL ... right - angled and oblique - angled . 1st . A RIGHT - ANGLED TRIANGLE is one ... angle of an oblique - angled triangle 16 GEOMETRY .
... angles , taken in the same order , are equal , each to each . 23. A DIAGONAL ... right - angled and oblique - angled . 1st . A RIGHT - ANGLED TRIANGLE is one ... angle of an oblique - angled triangle 16 GEOMETRY .
Page 20
... 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 , let CE be drawn perpen- dicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles ...
... 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 , let CE be drawn perpen- dicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles ...
Page 22
... angle , all of the others are right angles also . For , ( P. I. , C. 1 ) , each of its adjacent angles is а right angle ; and from the proposition just demonstrated , its opposite angle is also angle . a right Cor . 2. If one line DE ...
... angle , all of the others are right angles also . For , ( P. I. , C. 1 ) , each of its adjacent angles is а right angle ; and from the proposition just demonstrated , its opposite angle is also angle . a right Cor . 2. If one line DE ...
Page 23
... angles which they form is equal to four right angles , and it is also equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III THEOREM . If two straight lines ...
... angles which they form is equal to four right angles , and it is also equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III THEOREM . If two straight lines ...
Page 24
... angles equal to two right angles , the two lines met form one and the same straight line . Let DC meet AC and BC at C , making the sum of the angles DCA and DCB equal to two right angles : then is CB the prolonga- tion of AC . A -B BE ...
... angles equal to two right angles , the two lines met form one and the same straight line . Let DC meet AC and BC at C , making the sum of the angles DCA and DCB equal to two right angles : then is CB the prolonga- tion of AC . A -B BE ...
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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.