+ _plus_, or _more_, is the sign of real existence of the quantity it
stands before, and is called an affirmative or positive sign. It is also
the mark of addition: thus, _a_+_b_, or 6+9, implies that _a_ is to be
added to _b_, or 6 added to 9.
− _minus_, or _less_, before a single quantity, is the sign of negation,
or negative existence, showing the quantity to which it is prefixed to be
less than nothing. But between quantities it is the sign of subtraction:
thus, _a_−_b_, or 8−4, implies _b_ subtracted from _a_, or 8 after 4 has
been subtracted.
= _equal_. The sign of equality, though Des Cartes and some others use
this mark, ∝: thus, _a_=_b_ signifies that _a_ is equal to _b_. Others
use the mark = to denote identity of ratios.
× _into_ or _with_. The sign of multiplication, showing that the
quantities on each side the same are to be multiplied by one another:
as, _a_×_b_ is to be read, _a_ multiplied into _b_; 4×8, the product
of 4 multiplied into 8. Wolfius and others use a dot between the two
factors: thus, 7·4 signifies the product of 7 and 4. In algebra the sign
is commonly omitted, and the two quantities put together: thus, _bd_
expresses the product of _b_ and _d_. When one or both of the factors are
compounded of several letters, they are distinguished by a line drawn
over them: thus, the factum of _a_+_b_-_c_ into _d_ is written, _d_ ×
_a̅_+̅_b̅__-̅c̅_. Others distinguish the compound factors by including
them in parentheses: thus, (_a_+_b_-_c_)_d_.
÷ _by_. The sign of division: thus, _a_÷_b_ denotes the quantity _a_ to
be divided by _b_. Wolfius makes the sign of division two dots; 12:4
denotes the quotient of 12 divided by 4 = 3.
> or ⫍ are signs of majority: thus, _a_>_b_ expresses that _a_ is greater
than _b_.
< or ⫎ are signs of minority,—when we would denote that _a_ is less than
_b_.
∞ is the character of similitude used by Wolfius, Leibnitz, and others.
It is used in other authors for the difference between two quantities
when it is unknown which is the greater of the two.
∷ _so is_. The mark of geometrical proportion disjunct, and is usually
placed between two pair of equal ratios: as, 3∶6∷4∶8 shows that 3 is to 6
as 4 is to 8.
∶ or ∴ is an arithmetical equal proportion: as, 7.3∶13.9; _i. e._ 7 is
more than 3, as 13 is more than 9.
⬜ quadrate, or regular quadrangle,—viz. ⬜AB=⬜BC; _i. e._ the quadrangle
upon the line AB is equal to the quadrangle upon the line BC.
△ triangle: as, △ABC=△ADC.
∠ an angle: as, ∠ABC=∠ADC.
⟂ perpendicular: as, AB⟂BC.
▭ rectangled parallelogram, or the product of two lines.
∥ the character of parallelism.
⧧ want of parallelism.
≚ equiangular, or similar.
⫨ equilateral.
▱ rhomboid.
◠ concentrix.
○ circle.
∟ right angle.
∫ integration, (_summa_ or sum).
° denotes a degree: thus, 45° implies 45 degrees.
´ a minute: thus, 50´ is 50 minutes; ´´, ´´´, ´´´´, denote seconds,
thirds, and fourths; and the same characters are used where the
progressions are by tens, as it is here by sixties.
∺ the mark of geometrical proportion continued, implies the ratio to be
still carried on without interruption: as, 2, 4, 8, 16, 32, 64 ∺ are in
the same uninterrupted proportion.
√ When used without a figure above it, indicates the square root, and is
called the radical sign. Any other root is expressed by the index figure
placed above the sign. √16 is the square root of 16, ∛27 the cube root of
27, &c.
≅ difference equal.
∹ the difference, or excess.
Q or q, a square.