## Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and Geometry, in Their Relations and Uses |

### From inside the book

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**Reciprocal**Proportion Proportions involving a Constant Quantity Changes of Proportional Quantities SECTION XIV . POWERS AND ROOTS OF QUANTITIES Involution Evolution The Square Roots of Numbers The Cube Roots of Numbers 264 273 277 283 ... Page 125

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**reciprocal**of that quantity , and that division by any quantity is the same as multiplication by its**reciprocal**. We need hardly repeat that the**reciprocal**...**RECIPROCALS**. between any quantity and its**reciprocal**, AND DIVISION . 125. Page 126

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**reciprocal**of 4 , is = 1 4 ' 15 = 32 . 4 The product of any quantity by its**reciprocal**is always = 1 , for it is always a fraction of which the numerator and denomi- nator are equal . The quotient by the**reciprocal**is the square of the ... Page 127

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**reciprocal**of d C 1 ; therefore adbc . The principles which have been stated contain the foundation of the ...**reciprocals**, SUMMARY OF PRINCIPLES . 127. Page 128

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**reciprocals**, which is done by invert- ing the terms , and then treat them as in multiplication . When there is a number of multiplications and divisions to be performed , it is often very convenient to throw them into a general ...### Other editions - View all

Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ... Robert Mudie No preview available - 2017 |

### Common terms and phrases

adjacent angles Algebra angular space answering apply bisects breadth called centre circle circumference co-efficients compound quantity consequently considered consists contain cube root decimal point denominator diameter difference direction divide dividend division divisor drawn equi-multiples Euclid's Elements evident exactly equal exponent expressed factors follows four fraction geometrical geometrical series greater hypotenuse inclination instance integer number interior angles kind least common multiple length less letters logarithm magnitude mathematical means measure meet metical multiplicand multiplier natural numbers necessary number of figures obtained operation opposite parallel parallelogram performed perpendicular plane position principle proportion quan quotient radius ratio reciprocal rectangle relation remaining right angles round a point salient angle scale of numbers second term segment sides simple solid space round square root stand straight line subtraction surface taken third tion triangle truth whole

### Popular passages

Page 396 - Upon a given straight line to describe a segment of a circle, which shall contain aa angle equal to a given rectilineal angle.

Page 473 - Prove it. 6.If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced together with the -square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Page 416 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.

Page 380 - If two angles of a triangle are equal, the sides opposite those angles are equal. AA . . A Given the triangle ABC, in which angle B equals angle C. To prove that AB = A C. Proof. 1. Construct the AA'B'C' congruent to A ABC, by making B'C' = BC, Zfi' = ZB, and Z C

Page 494 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Page 138 - Generalising this operation, we have the common rule for finding the greatest common measure of any two numbers : — divide the greater by the less, and the divisor by the remainder continually till nothing remains, and the last divisor is the greatest common measure.

Page 259 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.

Page 489 - But let one of them BD pass through the centre, and cut the other AC, which does not pass through the centre, at right angles, in the...

Page 102 - COR. 1. Hence, because AD is the sum, and AC the difference of ' the lines AB and BC, four times the rectangle contained by any two lines, together with the square of their difference, is equal to the square ' of the sum of the lines." " COR. 2. From the demonstration it is manifest, that since the square ' of CD is quadruple of the square of CB, the square of any line is qua' druple of the square of half that line.