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 27
... extremities of any side , their sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then the sum ...
... extremities of any side , their sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then the sum ...
Page 35
... extremities of the line : 2. Any point , without the perpendicular , is unequally dis- tant from the extremities . Let AB be a given straight line , C its middle point , and EF the perpendicular . Then any point of EF is equally distant ...
... extremities of the line : 2. Any point , without the perpendicular , is unequally dis- tant from the extremities . Let AB be a given straight line , C its middle point , and EF the perpendicular . Then any point of EF is equally distant ...
Page 61
... extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . • 7. A SECTOR is a part of a circle ...
... extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . • 7. A SECTOR is a part of a circle ...
Page 63
... extremity , as A : then will AB be greater than AD . In the tri- Draw the radius CD . angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . this sum is equal to AB ( D. 3 ) : hence , AB is greater than AD ; which ...
... extremity , as A : then will AB be greater than AD . In the tri- Draw the radius CD . angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . this sum is equal to AB ( D. 3 ) : hence , AB is greater than AD ; which ...
Page 70
... extremity , it is tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it is perpendicular to the radius drawn to that point . 1 ° . Let BD be perpendicular to the radius CA , at A ...
... extremity , it is tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it is perpendicular to the radius drawn to that point . 1 ° . Let BD be perpendicular to the radius CA , at A ...
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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.