Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page v
... BOOK I. BOOK II . BOOK III . The Circle , and the Measurement of Angles , ..... Problems relating to the First and Third Books , .. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book ...
... BOOK I. BOOK II . BOOK III . The Circle , and the Measurement of Angles , ..... Problems relating to the First and Third Books , .. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book ...
Page vi
... BOOK VIII . PAGE . 210 BOOK IX . 235 PLANE TRIGONOMETRY . INTRODUCTION . Definition of Logarithms , Rules for Characteristics , General Principles , ..... Table of Logarithms , .... Manner of Using the Table , Multiplication by ...
... BOOK VIII . PAGE . 210 BOOK IX . 235 PLANE TRIGONOMETRY . INTRODUCTION . Definition of Logarithms , Rules for Characteristics , General Principles , ..... Table of Logarithms , .... Manner of Using the Table , Multiplication by ...
Page 12
... tains the same unit an equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to coincide throughout their whole extent . ELEMENTS OF OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . 12 GEOMETRY .
... tains the same unit an equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to coincide throughout their whole extent . ELEMENTS OF OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . 12 GEOMETRY .
Page 13
... made up of straight lines , not lying in the same direction , is called a broken line . 7. A SURFACE is that which has length and breadth without thickness . Surfaces are divided into two classes , plane and curved BOOK Definitions,
... made up of straight lines , not lying in the same direction , is called a broken line . 7. A SURFACE is that which has length and breadth without thickness . Surfaces are divided into two classes , plane and curved BOOK Definitions,
Page 15
... . 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 direction , the first side of the one is equal to the first side BOOK I. 15.
... . 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 direction , the first side of the one is equal to the first side BOOK I. 15.
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - 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 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - 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 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
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 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.