I.

CHAP. I.

Of Geometrical Definitions.

Point, Geometrically confider'd, is the leaft affignable Part of Space, and abfolutely indivifible; and is denoted by a Tittle; as at A.

II. A Line, either ftrait or crooked, is a Length without Breadth or Thickness; and is generated by the Motion of a Point, as AB, CD.

III. A Superficies or Surface, is Length and Breadth without Thickness, and terminated by one or more Lines; as A, B, C.

IV. An Angle is the Inclination or Meeting of two Lines in one Point; B or the Space included between them; as the Angle A, B, C.

B

XII. A Semicircle (i. e half a Circle) is a Figure contained between the Diameter and half the Periphery of a Circle; as ABC.

XIII. A Quadrant is one Quarter of a Circle, or half the Semicircle; as the Figure BCD.

XIV. The Sector of a Circle is a Figure included between two Semidiameters and an Arch he Periphery as A OD.

XV. A Chord Line, or Subtenfe of an Arch is any Right Line dividing the Circle into two unequal Parts, and is lefs than the Diamiter; as A E.

XVI. A Segment of a Circle is the Figure included between the Chord Line and Arch of the Circle, and is greater or less than a Semicircle; as the Figure ADE, or AGE.

XVII. An Angle in the Segment of a Circle is that which toucheth the Periphery, and is fubtended by a Chord Line; as either of the three Angles A, B, or C.

B 2

B

G

F

E

C

XVIII. The Radius of a Circle, or Semidiameter, is half the Diamiter; as AC, or CE.

XIX. The Measure of an Angle, as the Angle OCE, is the Arch of the Circle OE. XX. The Sine of that Angle, is the Line O D.

XXI. The Tangent thereof, is the Line EF.

XXII: The Secant thereof, is the Line CF. XXIII. The Verfed Sine thereof, is the Line DE. XXIV. The Co-Sine, Co-Tangent, and Co-Secant, are the Sine, Tangent, and Secant of the Complement of that Arch to a Quadrant, viz. of the Arch AO; as BO, AG, and CG.

XXV A Triangle is a Figure bounded by, or included between three Lines, and having three Angles.

XXIX. An Ifoceles Triangle hath only two Sides equal; as the Figure DEF. That is, DE EF, (DF being greater or lefs.)

XXX. A Scalenous Triangle is that which hath all its three Sides unequal; as ABC.

XXXI. A Right-angled Triangle is that which hath one Right Angle; as AEC, Rightangled at E.

XXXII. An Obtufe-angled Triangle is that which hath one Angle Obtufe, (this is alfo call'd an Amblygon.) As DEG.

XXXIII. An Acute-angled Triang'e is that which hath its Angles acute, (this is alfo call'd an Oxygon.) As the Figure O.

XXXIV. The Height or Altitude of any Plain Triangle is the Length of a Perpendicular let fall from any one Angle the oppofite Side; and this Perpendicular may fall within or without the Triangle; as AE.