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DEF. 17. A PLANE FIGURE is a Space bounded on all fides by one or more Lines in the fame Plane.

2. Any Line, between two adjacent Angles, forming or bounding a Figure, is called a SIDE of that Figure.

N. B. If a Plane Figure be bounded by Right Lines, only, it is called a Right-lined Figure; as Z. And if it be formed of Right Lines and curved, it is called a mixed Figure. As AC.

DEF, 18. INTERNAL and EXTERNAL
ANGLES.

If any Side of a Plane Figure be drawn out beyond
the Figure, as A B to D, the Angle E, or ABC, with- A
in the Figure, is Internal; and the Angle F or CBD,
without the Figure, is called an External Angle.

DEF. 19. A CIRCLE is the fimpleft and most perfect of all Plane Figures, therefore the firft; it is bounded by one regular and uniform curved Line, falling again into itfelf; which is called the CIRCUMFERENCE of the Circle.

The curved Line ABD is the Circumference; the Space, included within it, is the Circle,

DEF. 20. CENTER of a Circle, or CENTRE,

is a Point in the middle of a Circle, or the middle. Point of a Circle; which is equally diftant, every way, from the Circumference. As C.

N. B. The genefis of a Circle is thus defined. If a Line, CD, be conceived to be revolved quite around, on one extreme, C, fixed to a Pin or Point; the other extreme, D, will, in its revolution, describe the Circumference of a Circle, ABD; and the Line CD, having gone over the whole fpace, has generated the Circle, bounded by that Circumference.

Hence, it is evident, that all Right Lines, drawn from the Center of a Circle to the Circumference, are equal.

C 2

B

N. B. 2.

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F

B

N. B. 2. Equal Right Lines describe equal Circies; but, it another Line, CE, or, if any Point, E, be affumed in the Line CD, another Circle will be defcribed, on the fame Center, and in the fame space of time; whose Circumference, EFG, is to that of the other Circle, defcribed by the Point D, in proportion to the Lines CE and CD, by which they were generated.

DEF. 21. DIAMETER, of a Circle, is a Right Line drawn through the Center, and terminated on both fides by the Circumference. As A B.

2. Half the Diameter of a Circle is called the RADIUS. As AC or CB.

N. B. Every Diameter divides the Circle, and alfo the Circumference, in two equal Parts.

B DEF. 22. A SEGMENT of a Circle, is any por-
tion cut off by a Right Line; which is called a
CHORD OF SUBTENSE.

As AD, making two Segments, AED and AFD.
N. B. A Diameter is alfo a Chord Line.

DEF. 23. A SEMICIRCLE is a Segment, made by a Diameter, AB. As AEB or AFB.

Therefore, the Segment AED, which is greater than a Semicircle, is called a greater Segment; and AFD a leffer Segment.

DEF. 24. An ARK, or ARCH, is any portion of the
Circumference of a Circle. As AB, BC, or ABC.

DEF. 25. A TANGENT is a Right Line drawn without a Circle, and touching it in a Point only; which is called the POINT OF CONTACT.

As AB, touching the Circle in B.

DEF. 26. A TRIANGLE is à Plane Figure bounded by three Right Lines, and contains as many Angles.

N. B. Not

N. B. Not less than three Right Lines can include a Space and form a Figure; wherefore, a Triangie is the first of all Right-lined Figures.

Triangles are of various kinds. As follows.

DEF. 27. 1. An EQUILATERAL TRIANGLE has all its three Sides equal, to one another.

DEF. 28. 2. An ISOSCELES TRIANGLE has only two equal Sides. AB and BC.

DEF. 29. 3. A SCALENE TRIANGLE has all its Sides unequal.

DEF. 30. 4. A RIGHT-ANGLED TRIANGLE A is one that has a Right Angle. B.

2. The Side A C, oppofite the Right Angle, is called the HYPOTHENUSE.

DEF. 31. 5. An OBTUSE ANGLED TRI-
ANGLE is one which has an Obtufe Angle. C.

N. B. The two last are not diftinct fpecies of Triangles, but only a particular kind; which still come under the general Denomination of Ifofceles or Scalene.

An Ifofceles or Scalene Triangle may be either right or obtufe angled, or have all its Angles acute.

The Triangle ADB is right-angled; ACB is obtufe-angled; and AEB has all its Angles acute; yet, they are all Isofceles.

So likewife, the Figures of icy vo laft Definitions are Scalene Triangles.

DEF. 32. A QUADRILATERAL or QUA-
DRANGLE is a Plane Figure which has four
Sides, and four Angles.

These are fynonimous Terms; the first exprefing it by the number of its Sides, the other by its Angles.

B

C

DEF. 33.

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DEF. 14. EQUAL ANGLES. Angles are equal, when the Lines, which form them, have the fame Inclination each to the other, respectively.

In the Angles abc, ABC; if the Vertex, b, of the one, be applied to the Vertex, B, of the other, in fuch wife, that the Side ab falling on AB, cb alfo falls on CB; then, there is the fame inclination of cb to ab as of CB to AB, and the Angles abc, ABC are equal.

N. B. The length of the Lines, or Sides, is not confidered or regarded in the equality of the Angles, but only their inclination to each other.

Angles have other Denominations, which are derived to them only from their Situation, in respect of each other; yet ftill retain the general appellation of Right, Acute, or Obtufe Angles. Such are the following.

DEF. 15. VERTICAL and CONTIGUOUS
ANGLES.

If two Lines, AB and CD, cut and cross each other, there are made four Angles, at the Point, E, of their mutual Interfection; either two of which, AED, CEB, or AEC and DEB, touching at their Vertices, only, are called Vertical Angles.

Any other two, as AEC, AED, or AEC and CEB, &c. having one Side, CE or AE, common to both Angles, are called Contiguous or Adjoining Angles.

DEF. 16. ALTERNATE ANGLES, and others.

If a Line croffes or interfects two Lines, there are made eight Angles, A, B, C, D, &c.; of which C and F, alfo E and D, between the two Lines, one on each Side of the cutting Line, are called Alternate Angles.

Cand E, alfo D and F, are called INTERNAL ANGLES on the fame Side.

E and A, F and B, C and G, or D and H are called INTERNAL and OPPOSITE ANGLES, on the fame Side.

DEF.

DEF. 17. A PLANE FIGURE is a Space bounded on all fides by one or more Lines in the fame Plane.

2. Any Line, between two adjacent Angles, forming or bounding a Figure, is called a SIDE of that Figure. N. B. If a Plane Figure be bounded by Right Lines, only, it is called a Right-lined Figure; as Z. And if it be formed of Right Lines and curved, it is called a mixed Figure. As AC.

DEF, 18. INTERNAL and EXTERNAL
ANGLES.

If any Side of a Plane Figure be drawn out beyond the Figure, as A B to D, the Angle E, or ABC, within the Figure, is Internal; and the Angle F or CBD, without the Figure, is called an External Angle.

DEF. 19. A CIRCLE is the fimpleft and most

perfect of all Plane Figures, therefore the first; it is bounded by one regular and uniform curved Line, falling again into itfelf; which is called the CIRCUMFERENCE of the Circle.

The curved Line ABD is the Circumference; the Space, included within it, is the Circle,

DEF. 20. CENTER of a Circle, or CENTRE, is a Point in the middle of a Circle, or the middle. Point of a Circle; which is equally diftant, every way, from the Circumference. As C.

N. B. The genesis of a Circle is thus defined.

If a Line, CD, be conceived to be revolved quite around, on one extreme, C, fixed to a P'in or Point; the other extreme, D, will, in its revolution, defcribe the Circumference of a Circle, ABD; and the Line CD, having gone over the whole fpace, has generated the Circle, bounded by that Circumference.

Hence, it is evident, that all Right Lines, drawn from the Center of a Circle to the Circumference, are equal.

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