Letters are used to shorten or simplify a formula. Supposing we wish to express length × breadth × depth, we may put the initial letters only, thus, l × b × d, or, as is usual when algebraical symbols are employed, leave out the sign × between the factors, and write the formula lbd.
When division is to be expressed in simple form, the divisor is written under the dividend; thus (x + y) ÷ z = (x + y) / z
° ’ ” are signs used to express certain angles in degrees, minutes, and seconds; thus 25 degrees 4 minutes 21 seconds would be expressed 25° 4’ 21”.
√ This sign is called the radical sign, and placed before a quantity indicates that some root of it is to be taken, and a small figure placed over the sign, called the exponent of the root, shows what root is to be extracted.
Thus ²√ a or √ a means the square root of a
∛ a ” cube ”
∜ a ” fourth ”
ρ This sign is used to denote the force of gravity at any given latitude.
π The Greek letter pi is invariably used to denote 3·14159, that is, the ratio borne by the diameter of a circle to its circumference.
When the figure 2 is affixed to any number, as diameter² or 12², the number is to be squared, as 12 × 12 = 144, the square; and with ³ affixed, the number is to be cubed—i.e., multiplied twice by itself, as 6³ = 6 × 6 × 6 = 316, the cube of 6.