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 vii
... Parallelogram ,. The Area of a Triangle , Formula for the Sine of Half an Angle ,. Area of a Trapezoid , 106 106 ...... 108 112 ..... Area of a Quadrilateral , .... 112 Area of a Polygon , 113 Area of a Regular Polygon , ..... 114 To ...
... Parallelogram ,. The Area of a Triangle , Formula for the Sine of Half an Angle ,. Area of a Trapezoid , 106 106 ...... 108 112 ..... Area of a Quadrilateral , .... 112 Area of a Polygon , 113 Area of a Regular Polygon , ..... 114 To ...
Page 17
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A ...
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A ...
Page 43
... K are parallel , the angle HMB MBC ( P. XX . , C. 2 ) : hence , GHK is equal to ABC ; which was to be proved . Cor . The opposite angles of a parallelogram are equal . PROPOSITION XXV . THEOREM . In any triangle , the BOOK I. 43.
... K are parallel , the angle HMB MBC ( P. XX . , C. 2 ) : hence , GHK is equal to ABC ; which was to be proved . Cor . The opposite angles of a parallelogram are equal . PROPOSITION XXV . THEOREM . In any triangle , the BOOK I. 43.
Page 47
... parallelogram , the opposite sides are equal , each to each . Let ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . · Then , alternate D и A For , draw the diagonal BD . because AB and DC are parallel , the angle ...
... parallelogram , the opposite sides are equal , each to each . Let ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . · Then , alternate D и A For , draw the diagonal BD . because AB and DC are parallel , the angle ...
Page 48
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Then , the A Draw the diagonal DB . triangles ADB and CBD , will have D the sides of the one equal to the sides of the ...
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Then , the A Draw the diagonal DB . triangles ADB and CBD , will have D the sides of the one equal to the sides of the ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms centre chord circle circumference circumscribed complement cone consequently convex surface cosec cosine Cotang cylinder decimal denote diameter difference distance divided draw drawn edges equal to AC Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polar triangle pole polyedral angle polyedron prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium segment semi-circumference side BC similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triedral angle upper base vertex vertices volume whence
Popular passages
Page 101 - The area of a parallelogram is equal to the product of its base and altitude.
Page 92 - PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point 0 (Prob.
Page 48 - 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 45 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Page 106 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 33 - THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles.
Page 18 - A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle GH I.
Page 30 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the third sides will be unequal; and the greater side will belong to the triangle which has the greater included angle.
Page 8 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 156 - DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar arcs are to each other as their radii, and similar sectors are to each other as the squares of their radii.