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

### From inside the book

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**mantissa**. 4. If , in Equation ( 3 ) , we make p successively equal to 0 , 1 , 2 , 3 , & c . , and also equal to 0 , −1 , −2 , — 3 , & c . , we may form the following -- - TABLE . log 1 = 0 log 10 = 1 log 100 log 1000 = 2 log .1 = log ... Page 5

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**mantissa**being always positive . This fact is indicated by writing the neg- ative sign over the characteristic : thus , 2.371465 , is equiv alent to 2.371465 . It is to be observed , that the characteristic cf the logarithm of a mixed ... Page 8

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**mantissa**, look in the column headed " N , ” for the first three figures of the number ; then pass along a horizontal line until you come to the column headed with the fourth figure of the number ; at this place will be found four ... Page 11

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**mantissa**in the table is 233504 ; the cor- responding number is 1712 , and the tabular difference is 253 . Given**mantissa**, OPERATION . Next less**mantissa**, • • · 233568 233504 · · 1712 25296 253 ) 6400000 ( ... The required mumber is ... Page 16

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**mantissa**. 2. Find the 4th root of .00000081 . The logarithm of .00000081 is 7.908485 , which is equal to 81.908485 , and one - fourth of this is 2.477121 . The number corresponding to this logarithm is 09 : hence , .03 is the root ...### Other editions - View all

### 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.