Page images

II. A Line is a Length without Breadth, as the Line A B.

[blocks in formation]

Unto Quantity there appertain Three Dimenfions, viz. Length, Breadth and Depth (or Thickness;) of which, a Line is the firft, and hath Length only, without Breadth or Thickness; as the Line C D,




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 G


For a Line hath its beginning from a Point, and likewife endeth in a Point: So the Points G and 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; fo the Right Line G H, is the Shorteft Distance between the Points G and H.

V. Parallel (or Equidiftant) Right Lines are fuch, which being drawn upon the fame Plain, and infinitely produced, would ne

[blocks in formation]

Fig. I.

VI. A Plain Angle is the Inclination (or Bowing) of Two Right Lines, one to the other, and the one touching the other; and not being directly 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 reafon of the Inclination of the faid Two Lines) is made the Angle ABC; 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 here Note, That an Angle (generally) is noted with Three
Letters, of which, the middlemoft Letter reprefents the
Angular Point; fo, in this Angle ABC, 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 ftanding upon a Right Line maketh the Angles on either Side thereof Equal, then either of thofe Angles is a Right Angle; and the Right Line which ftandeth erected is called a Perpendicular Line to that Line upon which it ftandeth.

So upon the Right Line C D, fuppofe there do ftand another Fig. II. Right Line A B, in fuch fort, that it maketh the Angles A B C and A BD (on either fide of the Line A B) equal; then are either of thofe Angles, A BC and A B D, Right Angles; and the Line AB, which ftandeth erected upon the Line C D, (without inclining on either fide) is a Perpendicular to the Line C D.

VIII. An Obtufe Angle is that which is Greater than a
Right Angle:

So the Angle CBE is an Obtufe Angle, it being greater than the Right Angle ABC, 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 EBD is an Acute Angle, it being Less than the
Right Angle ABD, by the Quantity of the Angle A BE.

X. A Limit or Term is the End of any thing.

Forafmuch 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 Limits 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 respective Bounds or Limits.

A 2



Fig. IV.

Fig. V.

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, whofe 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 BCD, are
Equal. And that Point A is called the Centre of the Circle
B ̊C D.

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 à Diameter, because it paffeth from the Point E of the Circumference on the one Side, to the Point F on the other Side; and paffeth alfo 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 Circumference; Greater or Leffer than a Semicircle.

So the Right Line L M divideth the Circle EG FMHL into Two unequal Sections; namely, into the Section L GM above, Greater, and the Section L H M below, Leffer, 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 Circumference, which Lines are frequently called the Radius of the Circle.

[merged small][ocr errors]
« PreviousContinue »