Fig. 4.

10. An Obtuse Angle is greater than a Right Angle, as ADC, and an Acute Angle is less than a Right Angle; as CDB. Fig. 4.

B

D

NOTE-When an Angle is expressed by three letters, the middle letter represents the Angular Point. A Right Angle contains 90 degrees.

11. A Triangle is a figure bounded by three

Lines; as ABC. Fig. 5.

A

Fig. 5.

B

12. The most Natural Division of Triangles is into two kinds, viz:-That of Right Angled Triangles, and Oblique Angled Tri

angles.

14. A Triangle, constructed in any other manner, is an Oblique Triangle: as A B C Fig. 5 or 7.

15, In a Right Angled Triangle, the longest side is called the Hypothenuse, and the other two, the Legs or Base, and Perpendicu

lar. In Oblique Triangles, any side may be called the Base, and the other two, the Legs or Sides.

16. The Height of a Triangle is a Perpendicular Line, falling from any Angle to its opposite Side. AD is the Perpendicular Height of the Triangle ABC. Fig. 8.

B

17. If the Perpendicular fall without the Triangle, the Base must be continued to determine its Length. CE is the Perpendicular height of the Triangle, ABC; the Base being continued to E. Fig. 9.

Fig. 8.
Α

D

Fig. 9.
C

A

BE

18. If one foot of the Dividers be fixed at the Point C, and being open to a certain extent the other foot be carried round, the space comprehended is called a Circle, the Curve Line thereby described B is the Circumference or Periphery of the Circle, and the Point C its Centre. Fig. 10.

E

G

19. The extent in the Dividers, being the length of the Line C D, is Semidiameter or Radius. Whence it is manifest, from the construction that all Radii of the same Circle are equal. Fig. 10.

20. The Diameter of a Circle is a Right Line drawn from one side of the Circumference, through the Centre, to the other side, dividing the Circle into two equal parts, called Semicircles; as AB, or DE. Fig. 10.

21. An Arch, or Arc, is any part of the Circumference of a Circle; as DF, or AGE. Fig. 10.

22. A Chord is a Right Line, drawn from one end of an Arch

to the other end, and is the measure of the Arch. FG is the Chord of the Arch FAG. Fig. 10.

NOTE. The Chord of an Arch of 60 Degrees is equal, in length, to the Radius of the Circle.

23. A Segment of a Circle is the Space, or Area, comprehended between a Chord and the Circumference; as FAGF. Fig. 10.

24. A Quadrant is one quarter of a Circle; as BCD. Fig. 10

25. A Sector of a Circle is a part thereof contained between two Radii, and an Arch less than a Semicircle; as FCD, or F CE, Fig. 10.

26. The Complement of an Arch is what it wants of 90 Degrees, or a Quadrant. FD is the Complement of the Arch

AFD. Fig. 10.

27. The Supplement of an Arch is what it wants of 180 Degrees, or a Semicircle. BDF is the Supplement of the Arch FA. Fig. 10.

28. The Circumference of every Circle is supposed to be divid ed into 360 equal parts, called Degrees; each Degree into 60 equal parts, called Minutes; and these into Thirds, &c.

29. The measure of an Angle is the Arch of a Circle contained between two Lines which form the Angle, the Angular Point being the Centre; thus the Angle DCF is measured by the Arch D F. Fig. 10. Hence, an Angle is greater or less, according to the opening of the Lines which form it, without regarding their length.

30. A Square is a Figure bounded by four equal sides, and having four Right Angles.

Fig. 11.

Fig. 11.

31. A Parallelogram or Oblong Square is bounded by four Sides, the opposite ones being equal, and the Angles Right. Fig. 12.

Fig. 12.

Fig. 13.
A

inclined

32. A Rhombus is an Square, having its Angles Oblique.

Fig. 13.

B

33. A Rhomboides is an inclined Par allelogram, having its Angles Oblique. Fig. 14.

34. A Trapezoid is a part of a Triangle, cut by a Line Parallel to its Base, having two Parallel sides, though of unequal length. Fig. 15.

A

B

35. The Perpendicular Height of a Rhombus, Rhomboides, or Trapezoid is a Line drawn from one of its Angles to its opposite side, thus the dotted lines AB, in the three last figures, represent their Perpendicular Height.

36. A Trapezium is a Figure of four unequal Sides. Fig. 16.

Fig. 16.

A

B

37. A Diagonal is, a Line drawn between two opposite Angles; as the Line AB. Fig. 16.

38. Figures, consisting of more than four Sides, are called Polygons,; if the Sides be equal to each other, they are called Regular Polygons; if unequal, Irregular Polygons. They are sometimes named from the number of their sides. One of five sides is called a Pentagon; of six a Hexagon; of seven a Heptagon; of eight an Octagon, &c.

SECTION HI,

GEOMETRICAL PROBLEMS.

PROBLEM I. To bisect or divide into two equal parts, a given Right Line A AB. Fig. 17.

Fig. 17.

B

With any distance in the Dividers more than half the given Line, with one foot in A, describe an Arch above and below the Line; with the same distance, and one foot in B, describe Arches crossing the former; draw a Line through the intersection of those arches crossing AB; then AE=EB.

Fig. 18.
D

PROBLEM II. To erect a Perpendicular from the end, or any part of a given Line AB. Fig 18.

A

G

B

With any distance, set one foot of the Dividers on the Point from which the Perpendicular is to be erected, as at C, and describe an arch GEF; set off the same distance from G to C, and from E to F; upon E and F as Centres, describe two Arches at D; from their intersection to the point C draw CD a Perpendicular.

ANOTHER METHOD. Lay the Centre Point of the Protractor on the Point C, with the Arch upwards, and the edge exactly on the Line AB; at 90 degrees, on the Arch of the Protractor, make a Point in the paper; from which to the Point C, draw the Perpendicular.