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+ Increased by.
Diminished by. X Multiplied by. • Divided by.
Since, or seeing that. .. Hence, or therefore.
: Indicates the quotient of one divided by the other of the quantities it connects, called sometimes the ratio of the quantities.
:: Indicates an equality of ratios, and connects equal ratios in a proportion. Thus, a :b::c: d indicates that a = b= • d; or it may be read, a is to b as c is to d.
( ) Brackets indicate that the operations embraced by them shall first be performed, and the result treated as a single factor in the remaining processes required by a formula. Thus, (a X b) = (a + b) requires that the product of a and 0 shall be divided by their sum.
A2. A small secondary figure annexed thus to an expression is called its exponent. It requires the principal to which it is attached to be used as many times in continued multiplication as there are units in the exponent. Thus, A? = A X A; A3 = A X A X A, which is called the cube, or third power, of A.
✓ This is called the square root sign: it signifies that the square root of the quantity covered by it is to be taken.
Ý If preceded by a small secondary figure, called the index, as in the marginal figure, it indicates that the cube root of the quantity covered by it shall be taken; and so on.
Ñ If the index be fractional, as in the marginal figure, it requires that the square root of the third power of the quantity covered shall be taken. B. M. Bench-mark : any fixed reference point for the level,
as outcropping ledge, water-table of building, or other permanent object. Usually a blunt conical seat for the rod, hewn on a buttressed tree-base, having a small nail sometimes.driven flush in the top of it, and a blaze opposite, on which the elevation is marked with kiel.
T. P. Turning-point: usually marked O in the field-book.
P. I. Point of intersection : as of tangents, which are to be connected by a curve.
A. D. Apex distance : i.e., the distance from the P. I. 10 the point where a curve merges in the tangent.
P. C. Point of curve : the stake-mark at the beginning cf à curve.
P. T. Point of tangent: the stake-mark at the end of a
P. C. C. Point of compound curvature: the stake-mark where a curve merges in another of different curvature, turning in the same direction.
P. R. C. Point of reverse curvature: the stake-mark where a curve merges in another turning in the opposite direction.
B. S. Backsight, in transit work; or the reading of the roc to ascertain the instrument height in levelling.
F. S. Foresight, in transit work; or the reading of the rod to ascertain elevations in levelling.
H. I. Height of instruinent : elevation of the level above the datum or zero plane.
H. W. High water.
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