## Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising Definitions of All the Terms Employed in Mathematics - an Analysis of Each Branch, and of the Whole, as Forming a Single Science |

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Page 19

... two stations . scribed with the radius 1 , which measures the When the stations

are near each other , and error committed in measuring the angle of but one set

of observations can be made at a elevation , and dh is the

... two stations . scribed with the radius 1 , which measures the When the stations

are near each other , and error committed in measuring the angle of but one set

of observations can be made at a elevation , and dh is the

**corresponding**error ... Page 21

Four hyperbola the squares of the ordinates of any pairs only are known at the

present time . two points are to each other as the rectanA - MOUNT ' . In

Arithmetic the sum or gles of the

two or more ...

Four hyperbola the squares of the ordinates of any pairs only are known at the

present time . two points are to each other as the rectanA - MOUNT ' . In

Arithmetic the sum or gles of the

**corresponding**distances from the sum total oftwo or more ...

Page 30

a a a + ) | To use the table , look at the top for the Present value of third payment

is ( 1 + r ) heading which

column opposite the fourth ( 1 + r ) * number

a a a + ) | To use the table , look at the top for the Present value of third payment

is ( 1 + r ) heading which

**corresponds**to the given rate of interest ; then , in thatcolumn opposite the fourth ( 1 + r ) * number

**corresponding**to the number of & c . Page 38

If the given triangle is equilateral , AB = a , and from the construction will give only

the triangle it- A on AE , the disself . tance AE = b ; draw The second value of x

If the given triangle is equilateral , AB = a , and from the construction will give only

the triangle it- A on AE , the disself . tance AE = b ; draw The second value of x

**corresponds**to a EB ; lay off from A on AB , the distance second construction ... Page 40

y – 4bpa = 0 , and the

equation . In the equa- to each other , and set off on the line AB the Draw two

lines AB and CD at right angles tion of the fourth degree , if two of the roots are ...

y – 4bpa = 0 , and the

**corresponding**construction will give the roots of a cubicequation . In the equa- to each other , and set off on the line AB the Draw two

lines AB and CD at right angles tion of the fourth degree , if two of the roots are ...

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### Common terms and phrases

algebraic angle application assumed axes axis base becomes branch called centre chords circle co-efficients co-ordinates common cone considered constructed contains continued corresponding course curve decimal denote described determined diameter differential direction distance divided division draw drawn elements ellipse equal equation expression extremity factors figure fixed formula fraction function Geometry give given greater hence horizontal indicated infinite intersection known latitude length less limit manner means measure meridian method multiplied nature operation parallel pass perpendicular plane polygon portion positive powers principles problem projection quantity radius ratio reduced referred relation remaining represent respect result right angles roots rule scale sides sphere square straight line substitute suppose surface survey taken tangent term third tion triangle unit variable vertex vertical whole

### Popular passages

Page 87 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.

Page 275 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 26 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.

Page 454 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 82 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.

Page 4 - This cyclopaedia of mathematical science defines, with completeness, precision, and accuracy, every technical term ; thus constituting a popular treatise on each branch and a general view of the whole subject. 50 The National Teachers

Page 462 - In any quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the diagonals, plus four times the square of the line joining the middle points of the diagonals.

Page 134 - Subtract the cube of this number from the first period, and to the remainder bring down the first figure of the next period for a dividend.

Page 453 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.

Page 516 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.