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 17
... rectangles 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . is a parallelogram 2d . A RHOMBOID whose angles are all oblique . A RHOMBUS is an equilateral rhomboid . 2 29 ...
... rectangles 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . is a parallelogram 2d . A RHOMBOID whose angles are all oblique . A RHOMBUS is an equilateral rhomboid . 2 29 ...
Page 99
... ( A. 7 ) ; which was to be proved . Cor . Triangles having equal bases and equal altitudes are equal , for they are halves of equal parallelograms . GEOMETRY . PROPOSITION III . THEOREM . Rectangles having equal BOOK 99 IV .
... ( A. 7 ) ; which was to be proved . Cor . Triangles having equal bases and equal altitudes are equal , for they are halves of equal parallelograms . GEOMETRY . PROPOSITION III . THEOREM . Rectangles having equal BOOK 99 IV .
Page 100
... Rectangles having equal altitudes , are proportional to their bases . There may be two cases : the bases may be commen- surable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose alti- tudes AD and HK ...
... Rectangles having equal altitudes , are proportional to their bases . There may be two cases : the bases may be commen- surable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose alti- tudes AD and HK ...
Page 101
... rectangles be incommensura- ble : then the rectangles are proportional to their bases . For , place the rectangle HEFK upon the rectangle ABCD , so that it shall take the position AEFD . Then , if the rectangles are not proportional to ...
... rectangles be incommensura- ble : then the rectangles are proportional to their bases . For , place the rectangle HEFK upon the rectangle ABCD , so that it shall take the position AEFD . Then , if the rectangles are not proportional to ...
Page 102
... rectangles are to each other as the products of their bases and altitudes . Let ABCD and AEGF be two rectangles : then ABCD is to AEGF , as AB X AD is to AE X AF . For , place the rectangles so that the angles ... rectangle 102 GEOMETRY .
... rectangles are to each other as the products of their bases and altitudes . Let ABCD and AEGF be two rectangles : then ABCD is to AEGF , as AB X AD is to AE X AF . For , place the rectangles so that the angles ... rectangle 102 GEOMETRY .
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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.