Cowie's Printer's Pocket-Book and Manual/Mathematical, Algebraical, and Geometrical Characters
MATHEMATICAL, ALGEBRAICAL, AND GEOMETRICAL
CHARACTERS.
+ 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, shewing the quantity to which it is prefixed to be less than nothing. But between quantities it is the sign of substraction; thus, a − b, or 8 − 4, implies b substracted from a, or 8 after 4 has been substracted.
= equal. The sign of equality, though Des Cartes and some others use this mark ; thus, a = b signifies that a is equal to b. Wolfius and some others use the mark = for the identity of ratios.
× into, or with. The sign of multiplication, shewing 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 make the sign of multiplication 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, b d 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 wrote d × a + b − c. Leibnitz, Wolfius, and others, distinguish the compound factors, by including them in a parenthesis 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; thus, 12 : 4 denotes the quotient of 12 divided by 4 = 3. If either the divisor or dividend, or both be composed of several letters; for example, a + b ÷ c, instead of writing the quotient like a fraction.
involution. The character of involution.
υν evolution. The character of evolution, or the extracting of roots.
⦢ 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, while 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, shews 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.
□ Quadrat, or regular quadrangle as follows, □ 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.
≚ equiangular, or similar.
equilateral.
∟ right angle.
° 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.
√ irrationality. The character of a surd root, and shews, according to the index of the power that is set over it, or after it, that the square, cube, or other root, is extracted, or to be extracted; thus, √16, or √²16, or √(2) 16, is the square root of 16, ∛25, the cube root of 25, &c.
—: the differences, or excess.
Q or q, a square.
C or c, a cube.
QQ, the ratio of a square number to a square number.