## Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |

### From inside the book

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Page vii

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**Formulas**of Relation between Functions and Arcs , ... Functions of Double and Half Arcs , Additional**Formulas**...**Formula**for the Sine of Half an Angle , .. 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a ... Page 207

... abcde :: AB3 · ab ' ; which was to be proved . Cor . Similar pyramids are to each other as the cubes of their altitudes , or as the cubes of any other homologous lines . GENERAL

... abcde :: AB3 · ab ' ; which was to be proved . Cor . Similar pyramids are to each other as the cubes of their altitudes , or as the cubes of any other homologous lines . GENERAL

**FORMULAS**. If we denote the volume of any BOOK VII . 207. Page 208

From the Works of A.M. Legendre Adrien Marie Legendre. GENERAL

From the Works of A.M. Legendre Adrien Marie Legendre. GENERAL

**FORMULAS**. If we denote the volume of any prism by V , its base by B , and its altitude by II , we shall have ( P. XIV . ) , V = B X II · • • ( 1. ) If we denote the volume ... Page 233

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**FORMULAS**. If we denote the convex surface of a cylinder by S , its volume by V , the radius of its base by R , and its alti . tude by H , we have ( P. I. , II . ) , S = 2R × H • V = TR2 x H • ( 1. ) ( 2. ) If we denote the convex ... Page 3

... equal to the exponent of that power : hence the

... equal to the exponent of that power : hence the

**formula**, log ( 10 ) " = p . ( 3. ) If a number is an exact power of 10 , its logarithm is a whole number . ว If a number is not an exact power of 10 PLANE TRIGONOMETRY INTRODUCTION.### Other editions - View all

### Common terms and phrases

AB² ABCD AC² 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.