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XIII. - The Three Angles of every Triangle are equal to a Semi-circle, or 180°; the two Acute Angles of every Right-angled Triangle are equal to 90°. -

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Sides or Angles given, are marked with a Dash; but, when required, with a Cypher.

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Degrees are always marked with a Cypher over them, (") and Mi. nutes with a Dash. (')

XVI.

Three Letters denote an Angle ; the Middle one shews the Angular Point, and the other two the Sides that inclose it.

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• * - s An Angle More Multiplication Equal to * - - - Division - - - - - - - - - --> Less Triangle | stands for A Sine : - . . . . . . - Sine Complement or Co-Sine Tangent - Tangent Complement or Co-Tangent Secant Sec. C. Secant Complement or Co-Secant Co. AI. i Complement Arithmetic - - | is to, or to the . . . . .J Uso is as thus, 2 .. 4:: 3.. 6 That is, as 2 is to 4, so is 3 to 6.

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To draw a Line parallel to a given Line AB, at any given Dflance, as C.

TAKE with a pair of Compasses the D. C nearest Distance between the given / X x 2. Point C and the Line A B. . A —# With that Distance and one Foot of the Compasses, any where in the Line A B, draw (on that Side where the Point Clieth) the Arch D, from the Point C draw a Line to touch the Arch D, and it is done; for the Line CD is parallel to the Line A B, as was required.

P R O B L E M II.
To bised or divide a given Line into two equal Parts.

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To ere? a Perpendicular at the end of a given Line, as A G.

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- - - - i J * From a Point as at C, to let fall a Perpendicular on the Line A B.

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At Asín the Line A B, to make a Right SL
Angle, erect the Perpendicular A C, and -
it is done ; for the Angle B A C is a Right
Angle containing 90 Degrees. Or, des-
cribe an Arch from B to C, with the Chord
of 60°, and set off 90° from B to C, and it
is done.

To make an Angle equal to any given Number of Degrees.

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In like Manner an Angle may be made, which shall contain any Number of Degrees required.

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The Anglo and Hypothenus of a Right-Angled Triangle given, to find either of the Legs.

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The Angles and one Leg of a Right-Macled T; - - gled Triangle being given, to find the Hypothenus, and other £. g given,

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Draw the Base B C equal to 274, upon Berect the Perpendicular BA; from C draw the Line CA, making an Angle with BC of 33° 15' to cut the Line BA in A, and it is done; for A C being measured on the same Scale that B C was, will be 327.6 Miles, and BA 179.6 Miles, as was required.

P R O B 'L E M VIII. The Hypothens, and one Leggiven, to find the Angles and other Log.

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P R O B L E M IX.
The Legs given to find the Angles and Hypothenus.

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