GEOMETRY. 
angle. 11. When more than 90 degrees, it 
is called an obtuse angle. 12. A term, or 
bound, implies the extreme of any thing. 
13. A figure is contained under one or more 
bounds. 14. A circle is a plain figure, 
contained in one line, called the' circum- 
ference, every where equally distant from a 
certain point within it. 15. That equidis- 
tant point within the circle is called its 
centre. 16. A line passing from one side 
to the other of a circle, ami through its cen- 
tre, is the greatest line it can contain, and 
is called its diameter. 17. The diameter 
divides the circle into two equal and similar 
parts, called semicircles. 18. When a line 
shorter than the diameter is drawn from one 
point to another on the circumference of a 
circle, it is called a chord. 19. The part of 
the circle so cut olf or divided by such line 
or chord is called an arc or segment. 20. 
Figures contained under right lines are cal- 
led right-lined figures. 21. A figure having 
three sides is called a triangle. 22. If all 
the sides of a triangle are of the same length, 
it is called an equilateral triangle. 23. If 
all the sides and angles are unequal, it is 
called a scalene triangle. 24. If two of the 
sides are of equal length, it is called an isos- 
celes, or equi-crural triangle. 25. If con- 
taining a right angle, it is called a right- 
angled triangle. 26. The long-side sub- 
tending, and opposite to, the right angle is 
called the hypothenuse. 27. When the two 
shortest sides of a triangle stand at a greater 
angle than 90 degrees, the figure is said to 
be “ obtuse ;” and when all the angles are 
acute, it is called an acute-angled triangle. 
28. When two lines preserve an equal dis- 
tance from each other in every part, they 
are said to be parallel. 29. Parallel lines 
may be either straight or curved, but can 
never meet. 30. A figure having four 
equal sides, and all the angles equal, is 
a square. 31. But if its opposite angles 
only be equal respectively, the figure will 
then be a rhombus, or lozenge. 32. When 
all the sides of a figure are right lines, and 
that the opposite sides are parallel and 
equal, it is called a parallelogram. 33. If 
the opposite sides are equal, the others be- 
ing unequal, the figure is called a rhom- 
boides. 34. Four-sided figures, unequal in all 
respects, are called trapezia. 35. Figures 
having more than four sides are called poly- 
gons, and are thus distinguished : with five 
sides, it is called a pentagon ; with six, an 
hexagon; with seven, an heptagon; with 
eight, an octagon ; with nine, an enneagon ; 
with ten, a decagon ; with eleven, an ende- 
cagon ; with twelve, a dodecagon. 36. A 
solid has length, breadth, and thickness. 
37. A pyramid is a solid standing on a base, 
of any number of sides, all of which con- 
verge from the base to the same point or 
summit. 38. When standing on a triangu- 
lar base, it is called a triangular pyramid ; 
on four, a square pyramid ; on five, a pen- 
tagonal ; and thus in conformity with the 
figure of its base. 39. Every side of a py- 
ramid is a triangle. 40. A cone is found 
by the revolution of a triangle on its apex, 
or summit, and a point situated in the cen- 
tre of its base ; therefore a cone (like a su- 
gar-loaf) has a base, but no sides, 41. A 
prism is a figure contained under planes, 
whereof the two opposite are equal, similar, 
and parallel; and all the sides parallelo- 
grams. 42. A sphere is a solid figure, ge- 
nerated by the revolution of a circle on its 
diameter, which is then called the axis. 
43. A cube is a solid formed of six equal 
and mutually parallel sides, all of which are 
squares. 44. A tetrahedron is a solid con- 
tained under four equal, equilateral triangles. 
45. A dodecahedron is a solid contained 
under twelve equal, equilateral, and equian- 
gular pentagons. 46. An icosahedron is a 
solid contained under twenty equal, equila- 
teral triangles. ) 47. A parallelopipedon is 
a figure considered under six quadrilateral 
figures or planes, whereof those opposite are 
respectively parallel. 48. Figures, or bo- 
dies, are said to be equal when their bulks 
are the same ; and similar, when they are 
alike in form, though not equal. 49. There- 
fore similar figures or bodies are to each 
other in proportion to their respective areas 
or bulks. 50. The line or space on which 
a figure stands is called its base ; its altitude 
is determined by a line drawn parallel to 
its base, and touching its vertex, or highest 
part. 51. A right-lined figure is said to be 
inscribed within another, when all its pro- 
jecting angles are touched thereby. 52. The' 
figure surrounding or enveloping another is 
said to be described around, or on it. 53. 
When a line touches a circle, and proceeds 
without cutting it, such line is called a tan- 
gent. 54. Any portion, less than a semi- 
circle, taken out from a circle by two lines, 
or radii, proceeding from the centre, is cal- 
led a sector. 
Certain axioms are likewise proper to 
be carried in mind ; viz. 1. That things equal 
to one and the same thing are equal to one 
another. 2. If to equal things (or numbers) 
we add equal things, (or numbers) the whole 
will be equal. 3. If from equal things we 
