× _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. C or c, a cube. QQ, the ratio of a square number to a square number.