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Practical Geometry.
T

HIS First Part consists only of such DEFINITIONS,
PROBLEMS and THEOREMS, GEOMETRICAL,
which of Necessity ought to be understood and pra-

Eticed, before farther Progress be made in any other
Mathematical Science : And so I will begin It with these following

Geometrical Definitions.

I. A Point is that which hath no Part.

That is, it hath no Parts into which it may be divided ; It being the least thing that by Mind and Understanding can be imagined or conceived; than which there can be nothing A iefs : As the point in the Margin, noted with the Letter A over it: It being neither Quantity, nor any part of QuanTity; but only the Term or End of Quantity.

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II. A Line is a Lengıh without Breadth; as the Line A B.

A

-B
Unto Quantity there appertain Three Dimensions, viz. Length,
Breadth and Depth (or Thickness ;) of which, a Line is the first,
and hath Length only, without Breadth or Thickness; as the Line

E F
CI

1

ID
which may be divided into Parts; either Equally, in the Point E;
or Unequally, in the Point F.
III. The Ends, or Limits, of a Line, are Points Gm H.

For a Line hath its beginning from a Point, and likewise
endeth in a Point: So the Points Gand H are the Ends of the
Line G H, and are no Parts of it.
IV. A Right Line is that which lyeth Equally between its Points.

Or, it is the Shorteft Distance that can be drawn between Point and Point so the Right Line G H, is the shortest Distance between the Points G and H.

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V. Parallel (or Equidistant) Right Lines are such, təbich being

draton upon the same Plain, and infinitely produced, would ne

ver meet.

And such are these two.
Lines, A B and C D.

A
C

-B
D

Fig. I.

VI. A Plain Angle is the Inclination for Bowing) of Two Right

Lines, one to the other, and the one touching ihe other; and not being direilly joined together.

So the Two Lines A B and B C incline one to the other, and touch each other in the Point B; in which Point (by reason of the Inclination of the said Two Lines) is made the Angle A BC; But if the Two Lines which incline one to the other, do (when they meet) make one Streight Line, then do they make no Angle at all: As the Lines D E and EF incline one to the other, and meet each other in the Point E, and yet they make no Angle.

And,

a

And here Note, That an Angle (generally) is noted with Three

Letters, of which, the middlemoft Letter represents the
Angular Point; so, in this Angle A BC, the Letter B de-
notes the Angular Point. —And of Angles there are Three

Kinds; viz. Right, Acute and Obtufe.
VII. When a Right Line Standing upon a Right Line maketh the

Angles on either Side thereof Equal, then either of those Angles
is a Right Angle; and the Right Line which standeıb ere&ted is
called a Perpendicular Line to that Line upon which it ftandeth,

So upon the Right Line C D, suppose there do fand another Fig. II. Right Line A B, in such fort, that it maketh the Angles ABC and A BD (on either side of the Line A B) equal; then are either of those Angles, A BC and A B D, Right Angles; and the Line A B, which standeth ere£ted upon the Line CD, (without inclining on either side) is a Perpendicular to the Line CD. VIII. An Obtuse Angle is that which is Greater than a

Right Angle:
So the Angle CBE is an Obtuse Angle, it being greater than
the Right Angle A BC, by the Quantity of the Angle A B E.
IX. An Acute Angle is that which is Less than a Right Angle.

So the Angle E B D is an Acute Angle, it being Less than the
Right Angle A BD, by the Quantity of the Angle A B E.

X. A Limit or Term is the End of any thing. Forasmuch as there is no Quantity (or Magnitude) of which Geometry treateth, but it hath Bounds or Limits : And as Points are the Bounds or Limits of Lines, fo Lines are the Bounds or Li. mits of Plains or Superficies; and Plains (or Superficies) of Solids' (or Bodies.) XI. A Figure is that which is contained under One Term,

or Limit; or Many. So A is a Figure contained under one Line or Limit: B is a Fig. III. Figure under Three Lines or Limits: C under Four : D under Five, &c. which are their respe&tive Bounds or Limits.

A 2

XII. A

Fig. IV.

XII. A Circle is a Plain Figure contained under One Line, which

is called a Circumference or Periferie; unto which all Right
Lines drawn from one certain Point within the Figure unto the
Circumference, are equal one to the other.

So the Figure BCD contained under One crooked Line, is a
Circle, whose Circumference or Periferie is BCD. In the mid-
dle whereof there is a Point A, from which all the Right Lines,
A B, AC, A D, being drawn to the Circumference B CD, are
Equal. And that Point A is called the Centre of the Circle
B C D

Fig. V.

XIII. The Diameter of a Circle is any Right Line drawn through

the Centre, and ending at the Circumference on either Side,
dividing the Circle into Two Equal Parts.

So the Line E K F is á Diameter, because it passeth from the
Point E of the Circumference on the one side, to the Point F on
the other Side; and passeth also by the Point K, which is the
Centre of the Circle : And moreover, it divideth the Circle into
Two equal Parts, viz. into the Part E G F above, and EHF
below, the Diameter; which Two Parts are termed Semicircles.
XIV. A Section, Segment or Portion, of a Circle, is a Figure

contained under one Right Line, and a Part of the Circumfe-
rence ; Greater or Lesser than a Semicircle.

So the Right Line L M divideth the Circle EGFMHL in-
to Two unequal Sections; namely, into the Section L GM above,
Greater, and the Sektion L H M below, Lejer, than a Semicircle.
XV. The Semidiameter of a Circle, is half of the Diameter

of that Circle.
So KE or KF are semidiameters of the Circle EGFH: And
fo is any Right Line drawn from K the Center to the Circumfe-
rence; which Lines are frequently called the Radius of the Circle.

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