If the Lines incline to each other, the Angle made is lefs than a Right Angle, and is faid to be cute, as the Angle C.

If one of the Lines fall backward, the Angle is greater than a Right Angle, and faid to be Óbtufe, as the Angle D.

Obruse Angle

A Line going from one Corner of a Figure to the other is called a Diagonal, as A B.

If a Line bends round regularly returning into itself, it is called a Periphery, or Circumference; and all the Space within is called the Circle. The Point in the Middle is called the Center, as at C.

If a Line paffes exactly across the Middle of a Circle, from one Part of the Circumference to the Part oppofite, dividing it into two equal Parts, it is called a Diameter, as A B.

Diameter

A Right Line paffing acrofs a Circle in any Part, except it be exactly in the Middle, divides it into two unequal Parts, which Parts are called Segments of a Circle. Such Line is called a Chord, as C D, and the Part of the Circumference lying between is called an Arch, as CRD.

A Right Line being drawn from the Middle or Center of a Circle to any Part of the Circumference, is called a Radius or Semi-diameter, as C R.

Ifa Line bends or coils round like the Spring of a Watch, it is called an Helix or Spiral Line, as B."

B

A Right Line falling perpendicularly upon the End of the Diameter, fo as juft to touch the Arch of a Circle, is called a Tangent, as BC in the Figure below.

Geometrical Arioms.

Axioms are Propofitions which contain felf-evide Truths: The Principal are these that follow:

Ariom I.

The Whole is greater than any of its Parts.

Ariom 2.

All the Parts taken together are equal to the Whole.

Axiom 3.

Two Things that are equal to a third, are equal betw themselves.

Ariom 4.

If two equal Things are equally increased, or diminish they ftill continue to be equal.

Ariom 5.

If two equal Things are increased or diminished unequa they will become unequal.

Axiom 6.

From Nothing, Nothing can arife; nor hath it a Properties or Dimenfions of Length, Breadth, or Thi ness.

All thefe Truths hold good, not only in Numbers, alfo in Lines, Superficies, and Solids.

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Geometrical Problems.

Def. Problems in Practical Geometry are Propofitions wherein fome Operation or Conftruction is required or propofed to be done; as to divide Lines, Angles; erect or fall Perpendiculars, &c. ·

Problem 1.

To divide the Right Line A B into two equal Parts.

Conftruction. Firft open the Compaffes to more than Half the Length of the given Line; with that Wideness, fetting one Foot in A, defcribe the Arch bc; then fet one Foot in B, and defcribe the Arch de, interfecting the former in the Points C and D. Laftly, through the Points C and D draw the Right Line CD, and it will divide the given Line A B into two equal Parts, which was required.

Parts.

This Problem is useful in dividing Measures into small equal