lar falls within or without, by the Affection of the given Angles.

Here they feem to have spoken as tho' the Quæfitum was always determined, and never ambiguous; for they have here determined whether the Perpendicular falls within or without, and thereby whether they are to take the Sum or the Difference of the Vertical Angles or Bases for the fought Angle or Side.

But notwithstanding thefe imaginary Determinations, I affirm, that the Quæfitum here, as in the two Cafes laft mentioned, is fometimes ambiguous, and fometimes not; and that too, whether the Perpendicular falls within, or whether it falls without. See my Solutions of these two Cafes in Page 323,

The Determination of the 3d Cafe of Oblique Plane Triangles, fee in Page 325.

SAM. CUNN.

EUCLID's

ELEMENTS.

BOOK I.

I.

DEFINITIONS.

Α'

POINT, is that which hath no Parts, or Magnitude.

II. A Line is Length, without Breadth. III. The Ends (or Bounds) of a Line, are Points.

IV. A Right Line, is that which lieth evenly between its Points.

V. A Superficies, is that which hath only Length and Breadth.

VI. The Bounds of a Superficies are Lines.

VII. A Plane Superficies, is that which lieth evenly between its Lines.

VIII. A Plane Angle, is the Inclination of two Lines to one another in the fame Plane, which touch each other, but do not both lie in the fame Right Line. IX. If the Lines containing the Angle be Right ones, then the Angle is call'd a Right-lin'd Angle.

X. When

X. When a Right Line, standing on another Right Line, makes Angles on either Side thereof, equal between themselves, each of thefe equal Angles is a Right one, and that Right Line which stands upon the other, is call'd a Perpendicular to that whereon it stands.

XI. An Obtufe Angle, is that which is greater than a Right one.

XII. An Acute Angle is that which is less than a Right one.

XIII. A Term (or Bound) is that which is the Extreme of any Thing

XIV. A Figure is that which is contained under one, or more Terms.

XV. A Circle, is a plain Figure, contained under one Line, called the Circumference; to which all Right Lines, drawn from a certain Point within the Figure, are equal.

XVI. And that Point is called the Center of the Circle.

XVII. A Diameter of a Circle, is a Right Line drawn through the Center, and terminated on both Sides by the Circumference, and divides the Circle into two equal Parts.

XVIII. A Semicircle, is a Figure contain❜d under a Diameter, and that Part of the Circumference of a Circle, cut off by that Diameter.

XIX. A Segment of a Circle, is a Figure contain'd under a Right Line, and Part of the Circumference of the Circle [which is cut off by that Right Line.]

XX. Right-lin❜d Figures, are fuch as are contain'd under Right Lines.

XXI. Three-fided Figures are fuch as are contain’d under three Lines.

XXII. Four-fided Figures, are fuch as are contain'd under four. XXIII. Many-fided Figures, are thofe that are contained under more than four Right Lines.

XXIV. Three