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N. B. Not lefs than three Right Lines can include a Space and form a Figure; wherefore, a Triangle 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 species of Triangles, but only a particular kind; which ftill 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 Ifofceles.

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

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

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

B

DEF. 33.

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DEF. 33. A PARALLELOGRAM is a Quadrilateral, whofe oppofite Sides are parallel.

DEF. 34. A RECTANGLE is a Parallelogram,
whofe Angles are all Right ones. As X.

DEF. 35. A SQUARE is a Rectangle, whose
Sides are all equal, to one another.

Z.

N.B. All Rectangles and Squares are Parallelograms. DEF. 36. A RHOMBUS is a Parallelogram, whofe Sides are all equal, and its Angles not Right ones.

z. If the Sides of a Parallelogram are not all equal, and the Angles not Right ones, it is called a RHOм

BOIDES.

DEF. 37. A DIAGONAL is a Right Line drawn between any two Angles, that are oppofite, in any right-lined or mixed Figure; i. e. from one Angle to the other. As AC.

N. B. In Parallelograms, the Diagonal is ufually called a Diameter; because it paffes through the Center (the middle Point, E, where the two Diagonals, AC and BD, interfect) and, as in a Circle, it divides the Parallelogram into two equal Parts.

Any Right Line, cutting a Parallelogram through its Center, is a Diameter.

DEF. 38. COMPMENTS of a Parallelogram.

If any Point, as E, be taken in the Diagonal of a Parallelogram, and, chrough that Point, two Right Lines are drawn parallel to the Sides, both ways (AB and CD) it will be divided into four Parallelograms, V, X, Y, and Z; the two, X and Z, which touch the Diameter, in the Point E, only, are called the COMPLEMENTS; which, with either of the other, about the Diameter, taken together (as XYZ or XVZ) is called a GNOMON.

DEF. 39.

DEF. 39. A TRAPEZIUM is an irregular four-
fided Figure.

Wherefore, every Quadrilateral which is not a
Parallelogram, is, confequently, a Trapezium.
As ABCD.

DEF. 40. A POLIGON. All right-lined or other Plane Figures, having more than four Sides, have the general appellation of Poligons, fignifying many Sides.

N. B. Ordinate or regular Poligons' are fuch as have all their Sides and Angles equal; about which a Circle may be circumfcribed, whofe Circumference fhall pass through every Angle of the Poligon; and, a Circle may allo be infcribed, which fhall touch every Side.

Poligons have various Names, derived to them. from the Number of their Sides; as follows.

I. A PENTAGON is one that has five Sides.
2. A HEXAGON has fix Sides.

3. A HEPTAGON has feven Sides.
4. An OCTAGON has eight Sides.
5. A NONAGON has nine Sides.
6. A DECAGON has ten Sides.

7. A DUODECAGON has twelve Sides.

8. A QUINDECAGON has fifteen Sides.

These eight are the moft effential, in Geometry, and the most useful amongst Mechanics. To fpecify every kind of Poligon would be infinite.

DEF. 41. PERIMETER is the fum or meafure of all the Sides of a Poligon, or other right-lined or mixed Figure, in one Sum; which is fometimes called its Circumference, or PERIPHERY,

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DEF. 42.

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DEF. 42. EQUIANGULAR FIGURES are fuch as have an equal number of Angles; and the Angles of one alfo equal, respectively, to the Angles of the other, each to its corresponding Angle.

As, a equal A, b equal B, and c equal C.

CDEE.

C

43. CONGRUOUS FIGURES are fuch as have all their Angles equal, refpectively; also, the Sides, which contain equal Angles, or which are between equal Angles, are equal.

If the Angle a be equal A, b equal B, c equal C, and d equal D; and, if the Side ab is equal AB, bc equal BC, cd equal CD, and ad to AD; then, the Figures abcd, ABCD, are congruous,

DEF. 44. EQUAL FIGURES are fuch as have an equal Area. See Def. 47.

N. B. If two Figures of different Denominations have an equal Area, they are called equal Figures. So, the Parallelogram ABDE is equal to the Triangle ABC.

Congruous Figures are equal and fimilar.

DEF. 45. BASE, of a Plane Figure, is the Side on which it is fuppofed to ftand erect. As AB.

N. B. It may be any Side, at difcretion; but is generally applied to the lower Side, or that which is next towards us.

DEF. 46. ALTITUDE, of a Figure, is its perpendicular height from the Base.

As ED, perpendicular to the Bafe AB, is the Altitude of the Trapezium ADCB; or of the Triangle ADB.

B DEF. 47. AREA of a Plane Figure, or other Surface, is its fuperficial Contents; i. e. the meafure, or quantity of Space contained within the bounds of the Figure, expreffed in square Feet, Yards, or any other known measure, of length.

DEF. 48.

DEF. 48. SEGMENT of a Line, is any portion of a Line.

As AC, or CB, of the Line AB.

DEF. 49. SUBTEND. The Side of a Triangle which is oppofite to any Angle is faid to fubtend that Angle.

Thus, AB fubtends the Angle C, AC fubtends the Angle B, and BC fubtends the Angle A.

So likewife, the Chord or Subtenfe AB, fubtends the Ark ACDB; and CB fubtends the Ark CDB.

DEF. 50. To BISECT, is to cut or divide a Line or Angle, &c. into two equal Parts.

Thus AB is bifected in the Point C; and the Angle BAD, is bifected by the Line AE.

2. TO TRISECT, is to cut, equally, into three Parts.

DEF. 51. To PRODUCE, is to draw out a Line or Plane, or to lengthen it at pleasure.

Thus, the Line AB is produced to C.

DEF. 52. To DESCRIBE, is to draw a Line,
Circle, or other Figure.

DEF. 53. To INSCRIBE, is to draw a Figure touching every Side of another Figure, internally; or, whofe Angles fhall all touch the Circumference of a Circle.

DEF. 54. To CIRCUMSCRIBE, is to defcribe a Circle or other Figure paffing through all the Angles of another Figure. As ABCD.

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DEF. 55.

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