Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

If to the square of this root we add the remaining figures 20551, we shall have our given square, whose root was required. What is the square root of 16007.3104?

Answer 126.52.

What is the square root of 348.17320836 ?

Answer 18.6594 What is the square root of 12345678987654321 ?

Answer 111111111.

The application of this will hereafter be shewn.

THE ELEMENTS OF

PLANE GEOMETRY.

DEFINITIONS.

GEOMETRY

EOMETRY is that science wherein we consider the properties of magnitude.

2. A point is position without magnitude, as A.

fig. 1.

3. A line is length without breadth, as AB. fig. 1. and 2.

A

B

4. The extremities of a line are points, as the extremities of the line AB are the points A and B.

5. A right line is the shortest thật can be drawn between any two points, as the line A

B. If it be not the shortest, it is then called a curve line, as AB. fig. 2.

[merged small][merged small][merged small][merged small][ocr errors]

6. A superfices, or surface, is that which has length and breadth, without thickness, as ABCD. fig. 3.

[ocr errors]

7. The extremities of a superfices are lines.

[merged small][ocr errors][merged small]

8. The inclination of two lines meeting one another, or the opening between them, is called an angle. Thus fig. 4. the inclination of the line AB to the line BC meeting each other in the point B, or the opening of the two lines BA and BC, is called an angle, as ABC.

Note, when an angle is expressed by three letters, the middle one is that at the angular point.

fig. 5.

B

10. When the lines that form the angle are right ones, it is then called a right-lined angle, as ABC. fig. 4. If one of them be right and the other curved, it is called a mixed-angle, as B. fig. 5. If both of them be curved it is called a curved line or a spherical angle, as C. fig. 6.

fig. 6.

7. C.

E

11. If a right line, CD. fig. 7. stand upon another right line, AB, so as to make the angles ADC, CDB, on each side, equal to each other, these angles are called right angles, and the line CD a perpendicular.

А

12. An obtuse angle is that which is greater than a right one, as the angle ADE, fig. 7. and an acute

13. Acute and obtuse angles in general are called oblique angles.

14. If a right line CB, fig. 8. be fastened at the end C, and the other end B, be carried quite round, then the space comprehended is called a circle; and the curve line described by the point B, is called the circumference, or the periphery of the circle ; the fixed point C is called its centre.

[blocks in formation]

15. The describing line CB. is called the semidiameter, or radius, or any line from the centre to the circumference; whence all radii of the same, or of equal circles are equal.

16. The diameter of a circle is a right line drawn through the centre, and terminated on both sides by the circumference; and it divides the circle and circumference into two equal parts called semicircles ; and is double the radius, as AB or DE, fig. 8.

fig. ,

B

17. Parallel lines are such as are every where equidistant from each other, as AB, CD. fig. 9.

I

18. A figure is a space bounded by a line or lines. If the lines be right it is called a rectilineal figure, if curved it is called a curvilineal figure ; but if they be partly right and partly curved lines, it is called a

mixt figure.

19. The most simple rectilineal figure is a triangle, being composed of three right lines, and is considered in a double capacity ; 1st, with respect to its sides ; and 2d, to its angles.

fig. 10.

20. In respect to its sides it is either equilateral, having the three sides equal, as A. fig. 10.

A.

fig. 11.

с

21. Or isosceles, having two equal sides, as B. fig. 11.

[ocr errors][merged small][merged small][merged small][merged small]

22. Or scalene, having the three sides unequal, as C. fig. 12.

C

fig. 13.

23. In respect to its angles, it is either right-angled, having one right angle, as D. fig. 13.

D

Ag. 14

21. Or obtuse angled, having one

« ΠροηγούμενηΣυνέχεια »