Imágenes de páginas
PDF
EPUB

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.

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

A

fig. 9.

B

I

[ocr errors]

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.

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

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

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

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

24. Or obtuse angled, having one

fig. 10.

A

fig. 11.

A D B

fig. 12,

C

fig. 13.

A

fig. 14.

25. Or acute angled, having all the angles acute, as F. fig. 15.

fig. 15.

F

26. Acute and obtuse angled triangles are in general called oblique angled triangles, in all which any side may be called the base, and the other two the sides.

[blocks in formation]

Hence all triangles between the same parallels have the same height, since all the perpendiculars are equal from the nature of parallel lines.

28. Any figure of four sides is called a quadrilateral figure.

29. Quadrilateral figures whose opposite sides are parallel, are called parallelograms: thus ABCD is a parallelogram. fig. 3. 17. and fig.

18. 19.

[see fig. 3.

page 25.]

30. A parallelogram whose sides. are all equal and angels right, is called a square, as ABCD. fig. 17.

[blocks in formation]

31. A parallelogram whose opposite sides are equal and angles right, is called a rectangle or an oblong, as ABCD, fig. 3.

32. A rhombus is a parallelogram of equal sides, and has its angles oblique, as fig. 18.

33. A rhomboides is a parallelogram whose opposite sides are equal and angles oblique; as B fig. 19.

34. Any quadrilateral figure that is not a parallelogram, is called a trapezium. fig. 100.

fig. 18.

A

fig. 19. B

fig. 100.

B

C

[blocks in formation]

35. Figures which consist of more than four sides are called polygons: if the sides are all equal to each other, they are called regular polygons. They sometimes are named from the number of their sides, as a five-sided figure is called a pentagon, one of six sides a hexagon, &c. but if their sides are not equal to each other, then they are called irregular polygons

36. Four quantities are said to be in proportion when the product of the extremes is equal to that of means thus if A multiplied by D, be equal to B multiplied by C, then A is said to be to B as C is to D.

POSTULATES OR PETITIONS.

1. That a right line may be drawn from any one given point to another.

2. That a right line may be produced or continued at pleasure.

3. That from any centre and with any radius, the circumference of a circle may be described.

4. It is also required that the equality of lines and angles to others given, be granted as possible: that it is possible for one right line to be perpendicular to another, at a given point or distance; and that every magnitude has its half, third, fourth, &c. part.

Note. Though these postulates are not always quoted, the reader will easily perceive where, and in what sense they are to be understood.

AXIOMS OR SELF-EVIDENT TRUTHS.

1. Things that are equal to one and the same thing, are equal to each other.

2. The whole is greater than its part.

« AnteriorContinuar »