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

### From inside the book

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Page 248

... angles which it formed with the line DE at the point c , the one would be greater than a right angle , and the other ...

... angles which it formed with the line DE at the point c , the one would be greater than a right angle , and the other ...

**interior angle**at the one end of a line which falls upon or crosses two parallel lines , becomes , in all ... Page 250

... angles which are vertically opposite at the crossings are equal to each other , namely , AGE , BGH , GHC , and FHD ... interior , and opposite , as , for instance , CHG . The

... angles which are vertically opposite at the crossings are equal to each other , namely , AGE , BGH , GHC , and FHD ... interior , and opposite , as , for instance , CHG . The

**exterior angle**and the interior one opposite are also ... Page 251

... angles equal , the

... angles equal , the

**exterior angle**equal to the interior and opposite on the same side , or the**interior angles**on the same side together equal to two right angles , we may always conclude that the two straight lines , which answer any ... Page 253

...

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**angle**, without any regard whatever to the distance to which the lines would require to be produced in order to meet ; for the**angles**on one side of EF , 254 SUM OF THE**ANGLES interior**of A B and TWO LINES NOT PARALLEL . 253. Page 254

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**ANGLES interior**of A B and CD , are together exactly the measure of this**angle**more than two right**angles**, or 180o , and the sum of those on the other side is exactly the same measure less than two right**angles**, or 180o . The smaller ...### 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.