of which there is but one Diameter that divides it equally in

two.

D. a Volute, which is a Figure or Superficies contained in a spiral Line.

E. a Cylindrical Superficies.

F. an irregular curvilinear Figure, composed of feveral unequal curve Lines.

Of Mixed FIGUREs.

As a Semi-circle, of a Circle Plate 1. Fig.

as is contained from its Diameter either way.

II.

B. a Portion of a Circle, being composed of a Right Line and Part of a Circle.

F. a great Portion of a Circle, containing more than half of it.

it.

G. a small Portion of a Circle, containing less than half of

C. A Sector, which is a Figure compofed of two SemiDiameters, with more or less than half of the Circle. D. Concentric Figures, are those whose Centers are the fame.

E. Excentric Figures, are thofe contained in fome meafure within each other, but which have not the fame Center,

Of Regular and Irregular FIGURES.

A Regular Figure, is that whofe oppofite Sides Plate 1. Fig. are equal and the fame.

AA

12.

B. An Irregular Figure, is that composed of unequal Sides and Angles.

EE. Similar Figures are thofe, of which the Lines of one are proportioned to the Lines of the other, tho' one may be greater or leffer than the other.

FF. Equal Figures, are those whofe Contents are the fame, and which may be either fimilar or diffimilar.

C. An Equiangular Figure, has all its Angles equal. EE. One Figure is Equiangular to another, when all the Angles of one are equal to all the Angles of the other.

Č.D. An Equilateral Figure, is that whofe Sides are all equal.

GG. Similar Curvilinear Figures, are thofe in which may be infcribed, or round which may be cucumfcribed fnnilar Polygons,

L 2

AXI

Plate 1. Fig. 13.

AN

AXIOM S.

N Axiom, is fuch a common, plain, felf-evi dent, and received Notion, that it cannot be made more plain and evident by Demonftration, because it is itself better known than any thing that can be brought to prove it.

I.

Things equal to one fingle Thing, are in themselves equal. The Lines AC, AC, which are equal to AB, are alfo equal to themselves.

II.

If equal Things are added to Things that are equal, the Whole will be equal.

The Lines AC, AC, are equal,

The Lines added, CD, CD, are equal,

Therefore the Whole, AD, AD, are alfo equal.

III.

If equal Things are taken from Things that are equal, the Remainder will be equal.

From the equal Lines AD, AD.

Take away the equal Parts AC, AC.

The remaining Parts CD, CD.

Are equal.

IV.

If equal Things are added to Things that are unequal, the Whole will be unequal.

To the unequal Lines DE, DE.

Add the equal Lines AD, AD.

And the whole

Will be unequal.

AE, AE.

V.

Plate 1. If equal Things are taken away from Things Fig. 14. which are unequal, the Remainder will be unequal.

From the unequal Lines

AE, AE.

Take away the equal Parts AD, AD.

The Remainder

Are unequal.

DE, DE..

VI.

Things which are double the Proportion of another, are in themselves equal.

The Right Lines DD, DD.

Which are double the Line AD.
Are in themselves equal.

VII.

Things which have but half the Proportion of other equal things, are in themselves equal.

The Lines

AD, AD.

Which are only half the Length of the Lines DD, DD.
Are in themselves equal.

What is here faid with regard to Lines, is equally true with respect to Numbers, Superficies and Solids.

Refolutions of fome Questions neceffary to facilitate the Practice of GEOMETRY,

Apply the Ruler even with the Points A and B.

Then draw the Line required

By drawing your Pen or Pencil along

The Side of the Ruler, from the Point
To the Point

II.

To prolong infinitely the Line
From the Extremity

PRACTICE.

Join the Ruler close to the Line
Continue infinitely the faid Line
From the Extremity

By drawing the Pen along the Side
Of the Ruler towards

L 3

AR

AB,

Α

B.

III.

Plate 1. Fig. 16.

To defcribe a Circle from the Point A
And from the Distance

AB

PRACTICE.

Place one of the Points of the. Compass in the Point A Open the Compaffes and extend the other into the Point B Turn the Compaffes in the Point

A

And by drawing or turning them round from the Point B Defcribe the Circle required

IV,

To defcribe a Section from the given Points

PRACTICE.

BCD

EF.

Open the Compaffes at Difcretion, but in fuch a manner nevertheless, that the Distance between its two Points, may be greater than half the Distance between the two given Points E and F.

Having opened the Compaffes,

From the Point E defcribe the Arch LM
From the Point F defcribe the Arch HI

The Section

Is what is required.

G

BOOK