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dividing the circle into two equal parts.

XVIII. A Semicircle 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, E is the center, AC the diameter, ABC the semicircle.

XIX. Right-lined figures are such as are contained under right lines.

XX. Three-lided or Trilateral figures are such as are contained under three right lines.

XXI. Four-sided or Quadrilateral figures are such as are contained under four right lines.

XXII. Many-fided figures are such as are contained under more right lines than four.

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XXVI. Of these Trilateral figures, a right-angled Triangle is that which has one right angle; as the

Triangle A. A B

XXVII. An Ainblygonium, or obtuse-angled Tri

angle, is that which has one angle obtuse; as B.

XXVIII.

An Oxygonium, or acute-angled Triangle, is that which

has three acute angles ; c

An Equiangular, or equal-angled figure is that whereof all the angles are

equal. Two figures are equiangular,if the several angles of the one figure be equal to the several angles of the other. The fame is to be understood of Equilateral figures. B

XXIX. Of Quadrilateral, or four-sided figures, a Square is that whole fides are equal, and angles right; as ABCD,

as C.

A

D

B

XXX. A figure on the one part longer, or a long {quare, is that which hath right angles, but not equal sides; as ABCD,

А

XXXI. A Rhombus, or diamond-figure , is

that which has four eА.

qual sides, but is not right-angled; as A.

H

M

XXXII. A Rhomboi des, or diamond-like figure, is that whose op

pofite fides, and oppoI lite angles, are equal;

but 'has neither equal nor right angles; as GLMH.

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XXXIV. Parallel, or A

equidistant rightlines are B

such, which being in the Came superficies, if infinitely produced, would never meet ; as A and B. H M XXXV.

A Parallelogram is a quadrilateral figure, whose oppofite fides are parallel, or equidistant;

as GLHM. G

I

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XXXVI. In a ParalA

EB lelogram ABCD, when a

diameter AC, and two lines EF, HI parallel to the fides, cutting the diameter in one and the same

point G, are drawn, lo C that the Parallelogram be

divided by them into four parallelograms ; those two DG, GB, through which the diameter pafseth not, are called Complements ; and the other two HE, FI, through which the diameter pafseth, the Parallelograms ftanding about the diameter.

A Problem is, when something is proposed to be done or effe&ted.

A Theoreme is, when something is proposed to be demonstrated.

A Corollary is a confe&tary, or some confequent truth gained from a preceding demonstration.

A Lemma is the demonstration of some premise, whereby the proof of the thing in hand becomes the foorter.

Poftulates or Petitions.
Rom any point to any point to draw a

right line. 2. To produce a right line finite, strait forth continually.

3. Upon any center, and at any diftance, to describe a circle.

Axioms, 1.

equal one other, As A-B-C. Therefore A=C. Or therefore all, A, B, C, are equal the one to the other.

Note, When several quantities are joined the one to the other continually with this mark =, the first quantity is by virtue of this axiome equal to the last, and every one to every one: In which cafe we often ab

stain

*F Right line

THinges equal to the same third, are also

stain from citing the axiome, for brevity's fake; al tho' the force of the consequence depend thereon.

2. If to equal things you add equal things, the wholes shall be equal.

3. If from equal things you take away equal things, the things remaining will be equal.

4. If to unequal things you add equal things, the wholes will be unequal.

5. If from unequal things you takeaway equal things, the remainders will be unequal.

6. Things which are double to the same third, or to equal things, are equal one to the other. Understand the fame of triple, quadruple, &c.

7. Things which are half of one and the fame thing, or of things equal, are equal the one to the other, Conceive the same of subtriple, subquadruple, &c.

8. Things which agree together, are equal one to the other,

The converse of this axiome is true in right lines and angles, but not in figures, unless they be like.

Moreover, magnitudes are faid to agree, when the parts of the one being applyed to the parts of the other, they fill up an equal or the same place.

9. Every whole is greater than its part.

10. Two right lines cannot have one and the same segment (or part) common to them both.

11. Iwo right lines meeting in the same point, if they be both produced, they shall neceffarily çut one the other in that point. 12.All right angles are equal the one to the other.

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А. 13. If a right line BA falling on two right lines

AD, CB,

A 4

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