12. An acute angle is that which is less than a right angle.

13. A term or boundary is the extremity of any thing.

14. A figure is that which is inclosed by one or more boundaries.

15. A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another,

16. And this point is called the centre of the circle,

17. A diameter of a circle is a straight line down thing we sh*tw and terminated both ways by the circumteigia,

18. A semicircle is the figure contained by a diameter, and the part of the circunference cut off by the diameter.

19. The centre of a semicircle is the same with that of the circle.

20. Rectilineal figures are those which are contained by straight lines.

21. Trilateral figures, or triangles, by three straight lines.

22. Quadrilateral, by four straight lines.

23. Multilateral figures, or polygons, by more than four straight lines.

24. Of three-sided figures, an equilateral triangle is that which has three equal sides.


25. An isosceles triangle is that which has two sides equal.

26. A scalene triangle is that which has three unequal sides.

27. A right-angled triangle is that which has a right angle.

28. An obtuse-angled triangle is that which has an obtuse angle.

29. An acute-angled triangle is that which has three acute angles.

30. Of quadrilateral or four-sided figures, a square has all its sides equal, and all its angles right angles.

31. An oblong is that which has all its angles right angles, but has not all its sides equal.

32. A rhombus has all its sides equal, but its angles are not right angles.

33. A rhomboid has its opposite sides equal to each other, but all its sides are not equal, nor its angles right angles.


All other four-sided figures besides these, are called Trapeziums.

35. Parallel straight lines are such as are in the same plane, and which, being produced ever so far both ways, do not meet.

A. A parallelogram is a four-sided figure, of which the opposite sides are parallel ; and the diameter, or the diagonal, is the straight line joining two of its opposite angles.


1. LET it be granted that a straight line may be drawn from any one point to any other point.

2. That a terminated straight line may be produced to any length in a straight line.

3. And that a circle may be described from any centre, at any distance from that centre.


1. THINGS which are equal to the same thing are equal to one another.

2. If equals be added to equals, the wholes are equal.

3. If equals be taken from equals, the remainders are equal.

4. If equals be added to unequals, the wholes are unequal.

5. If equals be taken from unequals, the remainders are unequal.

6. Things which are double of the same, are equal to one another.

7. Things which are halves of the same, are equal to one another.

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