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 15
... parallel , when they lie in the same plane and can not meet , how far soever , either way , both may be produced . They then have the same direction . 17. A PLANE FIGURE is a portion of a plane bounded by lines , either straight or ...
... parallel , when they lie in the same plane and can not meet , how far soever , either way , both may be produced . They then have the same direction . 17. A PLANE FIGURE is a portion of a plane bounded by lines , either straight or ...
Page 17
... parallel . 28. A PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are and rhomboids . two varieties of parallelograms : rectangles 1st . A RECTANGLE is a parallelogram whose angles are all ...
... parallel . 28. A PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are and rhomboids . two varieties of parallelograms : rectangles 1st . A RECTANGLE is a parallelogram whose angles are all ...
Page 18
... another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn joining 18 GEOMETRY .
... another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn joining 18 GEOMETRY .
Page 19
... parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz .: A. for Axiom ; B. for Book ; C. for Corollary ; D. for Definition ; I. for Introduction ; P. for Proposition ; Prob . for Problem ...
... parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz .: A. for Axiom ; B. for Book ; C. for Corollary ; D. for Definition ; I. for Introduction ; P. for Proposition ; Prob . for Problem ...
Page 37
... parallel . Let the two lines AC , BD , be perpendicular to AB : then they are parallel . For , if they could meet in a point O , there would be two perpendiculars OA , OB , drawn from the same point to the same straight line ; which is ...
... parallel . Let the two lines AC , BD , be perpendicular to AB : then they are parallel . For , if they could meet in a point O , there would be two perpendiculars OA , OB , drawn from the same point to the same straight line ; which is ...
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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.