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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°. -
Sides or Angles given, are marked with a Dash; but, when required, with a Cypher.
Degrees are always marked with a Cypher over them, (") and Mi. nutes with a Dash. (')
Three Letters denote an Angle ; the Middle one shews the Angular Point, and the other two the Sides that inclose it.
• * - 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.
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 ere? a Perpendicular at the end of a given Line, as A G.
- - - - i J * From a Point as at C, to let fall a Perpendicular on the Line A B.
At Asín the Line A B, to make a Right SL
To make an Angle equal to any given Number of Degrees.
In like Manner an Angle may be made, which shall contain any Number of Degrees required.
The Anglo and Hypothenus of a Right-Angled Triangle given, to find either of the Legs.
The Angles and one Leg of a Right-Macled T; - - gled Triangle being given, to find the Hypothenus, and other £. g given,
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.
P R O B L E M IX.