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SCHOLIU M.

Tho' a Point, strictly taken, has no Parts, or is of no

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Bignefs; yet in Practice, there is a Neceffity
of taking it of fome Bignefs, and that various,
according to the Figure it is in or near as
upon Paper a Point is reprefented by a Prick
with the Point of the Compaffes, a Dott with
the Pen, &c. but on the Ground by a Peg,
Stake, &c. And when we have occafion to men-
tion it, we ufually call it by the name of fome
Letter of the Alphabet, as the Point A.
B

2,

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

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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 Compaffes, Pen, or Pencil, &c. upon 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 A B, is a Line, which will have fome Breadth and Thickness in Practice, because the Point defcribing it is of fome 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.

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

SCHOLIUM.

As the Motion of a Point makes a Line, fo the Motion of a Line makes a Superficies.

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

SCHOLIU 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 ftreight Line.

8. A Plane Angle is the Inclination of two right

A

B

Lines to one another, that are in the fame Plane, and touch one another; yet not fo that both of them be in the Same Direction: as 'A BC.

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An Angle is faid to be fo much the lefs, the nearer the Lines that make it are to one ano

B

A

A

ther. Take two Lines AB, BC, touching one another in B: then if you conceive these two Lines to open like the Legs of a Pair of Compaffes, fo as always to remain faften'd to one another in B, as by the Rivet of the Compaffes, whilst the Extremity A moves from the Extremity C; you will perceive, that the more thefe Extremities move from each other, the greater fhall the Angle between the Lines AB, BC be; and on the contrary, the nearer you bring them to one another, the leffer will the Angle be.

D

Whence it must be obferved, that the Bignefs of Angles does not confift 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 bowcing to one another: for example, the Angle DAF is greater than the Angle CAB; tho' the Lines or Sides AD, AF of the one are less than the Sides AC, AB of the other because

F

B

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they do not incline or bow fo 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 fee by the dotted Lines representing. the Angle DAF.

Here Note, That when I exprefs an Angle by three Letters, that Letter in the middle expreffes the Point wherein the Sides meet, which is called the angular Point. As the Angle DAF fhews 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 fuch, whofe Sides are right Lines; and curved-lined ones fuch, whofe 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

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Line CG, ftanding upon a right Line AB, makes the Angles CGA, CGB, on each fide equal to one another, each of thofe equal Angles is call'd a Right Angle; B and the right Line CG thus ftanding, is called

a Perpendicular to the Line AB, upon which it

ftands.

11. An

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11. An Obtufe Angle is that which is greater than a right Angle; as ACB.

12. An Acute Angle 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 Circle.

-B

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D

17. A Diameter of a Circle is a right Line drawn through the Center thereof, terminating both ways at the Circumference, and dividing the Circle into two equal Parts.

18. A Semi-circle is 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.

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

B 3

22. Mul

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