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 v
... Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , 59 82 93 129 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons , .... 178 Cylinder , Cone , and Sphere , BOOK VIII .
... Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , 59 82 93 129 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons , .... 178 Cylinder , Cone , and Sphere , BOOK VIII .
Page vii
... Regular Polygon , ..... 114 To find the Circumference of a Circle , 116 To find the Diameter of a Circle , To find the length of an Arc , 116 117 .... Area of a Circle , .... 117 Area of a Sector , ..... Area of a Segment , ..... Area ...
... Regular Polygon , ..... 114 To find the Circumference of a Circle , 116 To find the Diameter of a Circle , To find the length of an Arc , 116 117 .... Area of a Circle , .... 117 Area of a Sector , ..... Area of a Segment , ..... Area ...
Page viii
... of the Frustum of a Pyramid , Volume of a Sphere , Volume of a Wedge , ..... Volume of a Prismoid , ...... Volumes of Regular Polyedrons , .... ELEMENTS OF GEOMETRY . INTRODUCTION . DEFINITIONS OF TERMS . viii CONTENTS .
... of the Frustum of a Pyramid , Volume of a Sphere , Volume of a Wedge , ..... Volume of a Prismoid , ...... Volumes of Regular Polyedrons , .... ELEMENTS OF GEOMETRY . INTRODUCTION . DEFINITIONS OF TERMS . viii CONTENTS .
Page 15
... REGULAR POLYGON , is one which is both equilateral and equiangular . 21. Two polygons are mutually equilateral , when their sides , taken in the same order , are equal , each to each : that is , following their perimeters in the same ...
... REGULAR POLYGON , is one which is both equilateral and equiangular . 21. Two polygons are mutually equilateral , when their sides , taken in the same order , are equal , each to each : that is , following their perimeters in the same ...
Page 135
... as a side , homologous to A or B , construct a polygon similar to the given polygons , and it will be equal to their sum or difference ( P. XXVII . , C. 2 ) . 13 BOOK V. REGULAR POLYGONS . - AREA OF THE CIRCLE BOOK IV . 135.
... as a side , homologous to A or B , construct a polygon similar to the given polygons , and it will be equal to their sum or difference ( P. XXVII . , C. 2 ) . 13 BOOK V. REGULAR POLYGONS . - AREA OF THE CIRCLE BOOK IV . 135.
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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.