d Figures, that is, a Square, U L A T E S. bat a Right Line may be drawn iny one point to another. Right Line may be continued dids. a Circle may be described about with апу Distance. lar falls within or without, by the Affection of the given Angles. Here they seem to have spoken as tho' the Quæsitum 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 these imaginary Determinations, 1 affirm, that the Quæfitum here, as in the two Cases last mentioned, is sometimes ambiguous, and sometimes 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 Case of Oblique Plane Triangles, see in Page 325. SA M. CUNN. E U, C L I D's ELEMENTS Β Ο Ο Κ Ι. DEFINITIONS. "A 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 be tween 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 even Ly between its Lines: VIJI. 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 same Right Line. IX. If the Lines containing the Angle be Right ones, then the Angle is callod 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 these equal Angles is a Right one, and that Right Line which stands upon the other, is called a Perpendicular to that whereon it stands. XI. An Obtuse Angle, is that which is greater than a Right one. XII. Ăn Acute Angle is that which is less than a Right one. XIII. A Term (or Bound) is that which is the Ex treme 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 such as are contain'd under Right Lines. XXI. Three-sided Figures are such as are contain'd under tbree Lines. XXII. Four-sided Figures, are such as are contain'd under four. XXIII. Many-sided Figures, are those that are contained under more than four Right Lines. XXIV. Three |