Page images
[merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small]

Tho' a Point, strictly ta-

ken, has no Parts, or is of no Bigness; yet in Pra&ice, there is a Necessity of taking it of some Bigness, and that various, according to the Figure it is in or near : as upon Paper a Point is represented by a Prick with the Point of the Compasses, a Dott with the Pen, &c. but on the Ground by a Peg, Stake, c. And when we have occasion to mention it, we usually call it by the name of some Letter of the Alphabet, as the Point A.


2. A Line is Length without Breadth; as A B.

[blocks in formation]

SCHOLIU M. A Line is made by moving or drawing a Point from one place to another : it being the Mark or Trace that that point leaves behind it. As if I move or draw the. Point of my Compasses, Pen, or Pencil, &c. úpon Paper ; or a Peg, Stake, &c. upon the Ground, from the place or point A to B : then the Mark or Trace made thereby; which I call AB, is a Line, which will have fome Breadth and Thickness in Practice, because the Point defcribing it is of some Bignefs.

3. The Bounds of a Line are Points, as the Points A, B.

4. A Right 'Line is that which lies evenly-between its Points.

Ş. A Superficies is that which has only Length and Breadth.

SCHOL I U M. As the Motion of a Point makes a Line, ro the Motion of a Line makes a Superficies.


6. The Bound or Bounds of a Superficies are one or more

Lunes; as AB, BC, A


CD, AD. 7. A Plane Superficies is that which lies evenly between its Lines.

S C H 0 L T U M.. A plane Superficies is that to which a right Line may be apply'd all manner of ways, or which is made by the Motion of a streight Line.

8. A Plane Angle is the Inclination of two right

A Lines to one another, that are

in the Same Plane, and touch

one another ; yet not so that · B

both of them be in the same Dire&tion : as 'ABC.


с SCHOLIU M. An Angle is said to be so much the less, the nearer the Lines that make it are to one ano

ther. Take two Lines A

AB, BC, touching one

another in B: then if

A you conceive these two B

Lines to open like the

Legs of a Pair of ComC

passes, so as always to

remain fasten'd to one another in B, as by the Rivet of the Compasses, whilst the Extremity A moves from the Extremity C; you will perceive, that the more these Extremities move from each other, the greater Shall the Angle between the Lines AB, BC be; and on the contrary, the nearer you bring them to one another, the lesser will the Angle be.

Whence it must be observed, that the Big ness of Angles does not coniist in the bigness of the two Lines that form them, (which are called the sides of the Angle) but in the bigness of

their Inclination, or bow,D cing to one another : for

example, the Angle DAF is greater than the Angle CAB; tho' the Lines or

Sides AD, AF of the one B

are less than the Sides AC, F AB of the other : because


B 2

[ocr errors]

they do not incline or bow so much to one another, as the sides of the Angle CAB. To understand which, you need only conceive the Angle DAF to be laid upon the Angle CAB, as you may see by the dotted Lines representing the Angle DAF.

Here Note, That when I express an Angle by three Letters, -that Letter in the middle expresses the point wherein the sides meet, which is called the angular Point. As the Angle DAF thews the Angle formed by the two Lines or Sides DA, AF; it being the angular Point wherein the sides meet.

Moreover, right-lined Angles are such, whose Sides are right Lines ; and curved-lined ones such, whose Sides are crooked Lines.

9. When the Lines that contain or form an Angle are right ones, that Angle is called a Right-lined Angle. 10. When a right Line CG, standing upon d

a right Line AB, makes the Angles CGA, CGB, on each side equal to one another, each of those equal Angles is

callid á Right Angle ; A G

B and the right Line CG

thus standing, is called a Perpendicular to the Line AB, upon which it {tands.

II. An

[ocr errors]


11. An Obtuse Angle is that which is

greater than a right An:. gle; as ACB.

12. An Acute AnB

gle is that which is less than a right Angle ; as

ACD. 13. A Term or Bound is the Extremity or End of any thing.

14. A Figure is that which is contained under one or more Terms or Bounds.

15. A Circle is a plane Figure contained under one-Line, which is called the Circumference; to which all Lines that fall from a certain Point within the Figure, are equal to one another. 16. And that Point is called the Center of the


17. A Diameter of a Circle is a right Line

drawn through the Center EL

thereof, terminating both A


ways at the Circumference, and dividing the Circle into two equal Parts.

18. A Semi-circle is D

a Figure which is contained under the Diameter, and under that part of the Circumference which is cut off by the Diameter.

In the Circle EABCD, the Point E is the Center, the Line AC 'the Diameter, and ABC is a Semi-circle.

19. Right-lined Figures are such as are contained under right Lines.

20. Trilateral or three-fided Figures are such as are contained under three right Lines.

21. Quadrilateral or four-fided Figures are such as are contained under four right Lines.

B 3

22. Muz

« PreviousContinue »