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TAB. XV. Shewing the Time of ihe Sun, Moon, and Star's

Setting when they have North Declination, and the Time

of their Rising when they have South Declination

TAB. XVI. For finding the Latitude by two Altitudes of the Sun

TAB. XVII. Of Natural Sines

TAB. XVIII. For turning Degrees and Minutes, into Time

and the contrary

Tab. XIX. The Proportional Logarithms
TAB. XX. For computing the Effects of Parallax on tbe Moon's

Distance from the Sun or fixed Stars

TAB. XXI. Of Logarithms

TAB. XXII. Of artificial Sines, Tangents, and Secants.

E R R Α Τ Α.

Page 111, In the second Line under the Table, reject 55 Miles of


Page 109, In the Answer to the seventh Question, for as Diff. of

Lat. 786, read Diff. of Long.

Page 139. In finding the Number of the Month, for 7 read 8.

Page 200. The fifth Line from the Bottom, for Boards read Boats.

Page 240, Question 6. Make the supposed Longitude 8o W. the re-

duced Time sh. 22' 57", the true Time will be 4h. 38' 7", and

the true Distance 77° 38' 27". Find the Distances between 3

and 6 Hours, and the Longitude will be 7° 59' & West.

N. B. The rapid Sale this Book has had since its first Publication, has

induced Persons in Scotland and other places to copy it, many of which
have been distributed in different Parts of the World, particularly in
tinerica; in order to prevent such fpurious and erroneous Editions being
imposed on the Public in future, a striking Likeness of the Author will be
affixed to each Book of the new Edition : all without it are pirated and
cannot be depended on.





G E O M E T R Y.


EOMETRY is that Science by which we compare such

and Solids, whose original is from a Point.

I. -
A Point hath no Parts; that is, a Geometrical Point is

A. not any Quantity, but only an affignable Place in a Quantity denoted by a Point, as at A.

Such a Place may be conceived fo infinitely small, as to be void of Length, Breadth, and Thickness; and therefore a Point may • be said to have no Parts.'

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A Right Line is the nearest Distance between two
Points, which limit its Length, as A B.

Circular Lines are those which lie bending between two Points.

Parallel Lines are those that are equally distant in
all their Parts, which being infinitely extended on the
Same Plane, will never micet.


V. Lines

V. Lines not parallel, but inclining towards each other, whether they are right Lines or circular, will, if they are extended, meet, and make an A Angle; the point where they meet is called the Angular Point, as at A; and according as such Lines stand nearer or farther off each other, the Angle is said to be greater or less, whether the Lines that include the Angle be long or short.

All Angles included between Right Lines, are called Right-lined Angles, and fall under these three Denominations; viz. A Right Angle, an Obtufe Angle, and an Acute Angle.


D A Right Angle is that which is included between two Lines that meet each other perpendicular, as DC meets A B.



VII. An Obtufe Angle is that which is greater than a Right Angle, such as the Angle included between the Lines A Cand C B.

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Segment Chord Line

IX. A Circle is a perfect round Figure ; the Point C in the Middle is the Centre, and is bounded by a round Line called its Circumference, or. Periphery.

A Right Line, drawn from the Centre to the circumference, is called the Radius, or it is the Distance taken in the Compafles to describe a Circle, as A C.

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Note. The Radius, generally used in describing Circles, is < 60°, (taken from the Line of Chords) the Circumference of which ( will contain 360°, the Number of equal Parts or Degrees that all « Circles are supposed to be divided into ; and each of these De

grees are divided into 60 equal Parts, called Minutes, &c. • All Angles are measured by an Arch of this Circle, described upon the Angular Point as a Centre, with the Chord of 60°, as

above, and the Angle is faid to be greater or less, according to the • Number of Degrees contained between the Legs; but the Sides or * Legs are measured by a Scale of equal Parts.'

The Diameter is twice its Radius, joined into one Right Line drawn through the Centre, which divides the Circle into two equal Parts called Semi-circles.

A Quadrant is half a Semi-circle.

A Chord Line is a Right Line that cuts the Circle in two un. equal Parts called Segments.

A Sector is a Figure included between two Radius's, and is less than a Quadrant.

All Plan Triangles are Figures comprehended under three Right Lines, and are distinguished into three Sorts ; viz. A Right-angled Triangle, an Obtufe-angled Triangle, and an Acute-angled Triangle.

A Right-angled Triangle is that which hath one

C of its Legs perpendicular to the other, and is equal to a Quadrant or 90°; as B AC; the longest Side of which is called the Hypothenuse, as B C, and the other two Sides are called Legs.



E An Obtuse-angled Triangle is that which hath one of its Angles greater than a Right Angle, as E DF.




An Acute-angled Triangle is that which hath all its Angles less than a Right Angle, G as G HI.

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