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

### From inside the book

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**GEOMETRICAL**QUANTITIES , METHODS OF EXPRESSION , AND DEFINITIONS 1. Of Lines • 2. Of Surfaces or Figures 3. Of Angles . 191 192 196 201 SECTION XI . 207 PRINCIPLES OF**GEOMETRICAL**INVESTIGATION SECTION XII . Page INTERSECTION OF LINES ... Page 10

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**geometrical**reasoning , and one without which we should be unable to perform even the simplest operation in measuring . So also a mathematical line has neither breadth nor thickness , and therefore has no more real existence than a ... Page 27

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**geometrical**quantities are always such , that we can imagine them to exist and be visible , which is not the case with all quantities to which Algebra applies . It very often happens , however , that the very same mode of reasoning ... Page 28

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**geometrical**quantity , because we cannot say that it has either size or shape , and yet the law according to which it acts is a**geometrical**law . Thus all**geometrical**quantities must be such as that we can imagine them to exist in space ... Page 31

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**geometrical**principle . Thus , in the expression 111111111 , each of the characters has a different value ; this value is smallest in the character nearest our right hand , and it increases at a 32 SCALE OF NUMBERS . regular series of ...### 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.