BOOK I.

On the Drawing of LINES.

PROPOSITIO N. I.

O raise a Perpendicular from a given Point in
the middle of a Right Line.

Plate 2.

Fig. 1.

Let C be the given Point in the middle of the Line AB, upon which the Perpendicular is to be raised.

PRACTICE.

From the given Point

C

Defcribe at Difcretion the Semi-Circle DE

From the Points

Make the Section

From the Point

Draw the Right Line required

Through the Section

DE.

I.

C

CO

I.

Thus the Line CO will be the perpendicular upon the given

Line AB, and raised from the given Point C.

PROPOSITION

II.

To raise a Perpendicular upon the Extremity of

a Right Line given.

Plate 2.
Fig. 2.

AB is the Right Line given, at the Extremity of which A, the Perpendicular is to be r ed.

Plate 2,

Fig. 3.

Otherwife,

From the Point A defcribe the Arch GHM.
From the Point G describe the Arch AH,
From the Point H defcribe the Arch AMN.
From the Point M defcribe the Arch HN.
Then draw the Line required

PROPOSITION III.

AN.

Upon an Angle given, to raise a Right Line, which fhall incline neither to the Right nor Left. Let BAC be the Angle upon which a Right Line is to be raised, that shall not incline either to the Right or Left.

PRACTICE,

From the Angle given

Defcribe at Difcretion the Arch
From the Points or Extremities
Make the Section

From the Point or Angle given

Draw the Right Line required
Through the Section

Thus the Right Line

Will be raised upon the Angle

A

BC.

B and C

D.

A

AD

D.

AD

BAC

Plate 2 Fig. 4.

Without inclining either to the Right or Left.

PROPOSITION IV.

To bring down a perpendicular Line upon a Right Line given, and from a Point at a Distance from the faid Right Line,

Let C be the Point from whence a Perpendicular Line is to be brought down upon the Line AB.

PROPOSITION V.

To draw a Line through a given Point, parallel to a Right Line given.

Plate 2. Fig.

5.

Let A be the Point through which a Line is to be drawn parallel to the Line BC.

PROPOSITION VI.

To divide a Right Line given of a determined Plate 2. Fig.

Length, into two equal Parts.

6.

Let AB be the proposed Right Line, to be divided equally in two.

It is neceffary these two Arches fhould interfect each other.

Draw the Right Line
Through the Sections

GH

G and H.

Thus the Line AB, will be divided into two equal Parts, at the Point O.

Plate 2. Fig.

7.

PROPOSITION VII.

To divide a given Rectilinear Triangle into two equal Parts.

Let BAC, be the Angle proposed to be divided into two equal Parts.

Which will divide the given Angle BAC into two equal

Parts.

Plate, 2, Fig.

PROPOSITION VIII.

To make a Rectilinear Angle, at the Extremity of a Right Line, equal to a Rectilinear Angle given.

Let A be the Extremity of the Line AB, at which an Angle is to be made, equal to the given Rectilinear Angle CDG.