SUPERFICIES
, or Surface, in Geometry, the outside or exterior face of any body. This is considered as having the two dimensions of length and breadth only, but no thickness; and therefore it makes no part of the substance or solid content or matter of the body.
The terms or bounds or extremities of a Superficies, are lines; and Superficies may be considered as generated by the motions of lines.
Superficies are either rectilinear, curvilinear, plane, concave, or convex. A
Rectilinear Superficies, is that which is bounded by right lines.
Curvilinear Superficies, is bounded by curve lines.
Plane Superficies is that which has no inequality in it, nor risings, nor sinkings, but lies evenly and straight throughout, so that a right line may wholly coincide with it in all parts and directions.
Convex Superficies, is that which is curved and rises outwards.
Concave Superficies, is curved and sinks inward.
The measure or quantity of a Surface, is called the area of it. And the finding of this measure or area, is sometimes called the quadrature of it, meaning the reducing it to an equal square, or to a certain number of smaller squares. For all plane figures, and the Surfaces of all bodies, are measured by squares; as square inches, or square feet, or square yards, &c; that is, squares whose sides are inches, or feet, or yards, &c. Our least superficial measure is the square inch, and other squares are taken from it according to the proportion in the following Table of superficial or square measure.
| 144 | square inches | = 1 | square foot |
| 9 | square feet | = 1 | square yard |
| 30 1/4 | square yards | = 1 | square pole |
| 16 | square poles | = 1 | square chain |
| 10 | square chains | = 1 | acre |
| 640 | acres | = 1 | square mile. |
The Superficial measure of all bodies and figures depends entirely on that of a rectangle; and this is found by drawing or multiplying the length by the breadth of | it; as is proved from plane geometry only, in my Mensuration, pt. 2, sect. 1, prob. 1. From the area of the rectangle we obtain that of any oblique parallelogram, which, by geometry, is equal to a rectangle of equal base and altitude; thence a triangle, which is the half of such a parallelogram or rectangle; and hence, by composition, we obtain the Superficies of all other figures whatever, as these may be considered as made up of triangles only.
Beside this way of deriving the Superficies of all figures, which is the most simple and natural, as proceeding on common geometry alone, there are certain other methods; such as the methods of exhaustions, of fluxions, &c. See these articles in their places, as also QUADRATURES.
Line of Superficies, a line usually found on the sector, and Gunter's scale. The description and use of which, see under Sector and Gunter's Scale.
SUPERPARTICULAR Proportion, or Ratio, is that in which the greater term exceeds the less by unit or 1. As the ratio of 1 to 2, or 2 to 3, or 3 to 4, &c.
SUPERPARTIENT Proportion, or Ratio, is when the greater term contains the less term, once, and leaves some number greater than 1 remaining. As the ratio of 3 to 5, which is equal to that of 1 to 1 2/3; of 7 to 10, which is equal to that of 1 to 1 3/7; &c.
