CHARACTERS
, are certain marks used by Astronomers, Mathematicians, &c, to denote certain things, whether for the sake of brevity, or perspicuity, in their operations.
| Planets &c. | The twelve Signs or Constellations of the Zodiac. |
| The Sun | Aries, the Ram |
| The Moon | Taurus, the Bull |
| The Earth | Gemini, the Twins |
| Mercury | Cancer, the Crab |
| Venus | Leo, the Lion |
| Mars | Virgo, the Maid |
| Jupiter | Libra, the Balance |
| Saturn | Scorpio, the Scorpion |
| Herschel, or the | Sagittary, the Archer |
| Georgian Planet | Capricorn, the Goat |
| Ascending Node | Aquarius, the Water-bearer |
| Descending Node | Pisces, the Fishes |
| The Aspects, Time, Motion, &c. | |
| Conjunction | ° Degrees |
| Opposition | ′ Minutes or Primes |
| Sextile | ″ Seconds, &c. |
| Quartile | A. M. Ante merid. or m morn. |
| Trine | P. M. Post merid. or a aftern. |
| h, m, s, Hours, min. sec. |
The most common numeral characters, are those called Arabic or Indian, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9, with 0 or cipher for nothing.
The Roman numeral characters are seven, viz, I one, V sive, X ten, L sifty, C a hundred, D or I[C] five hundred, M or D[D] or CI[C] a thousand. Other combinations are as in the following synopsis of the Roman Notation.
| 1 | = | I |
| 2 | = | II: As often as any character is repeated, |
| 3 | = | III so many times its value is repeated. |
| 4 | = | IIII or IV: A less character before a |
| 5 | = | V greater diminishes its value. |
| 6 | = | VI: A less character after a greater in- |
| 7 | = | VII creases its value. |
| 8 | = | VIII |
| 9 | = | IX |
| 10 | = | X |
| 50 | = | L |
| 100 | = | C |
| 500 | = | D or I[C]: For every [C] added, this becomes 10 times as many. |
| 1000 | = | M or CI[C]: For every C and [C], set one at |
| 2000 | = | MM [each end, it becomes 10 times as much. |
| 5000 | = | I[C][C] or ―V: A line over any number in- |
| 6000 | = | ―VI creases it 1000 fold. |
| 10000 | = | ―X or CCI[C][C] |
| 50000 | = | I[C][C][C] |
| 60000 | = | ―LX |
| 100000 | = | ―C or CCCI[C][C][C] |
| 1000000 | = | ―M or CCCCI[C][C][C][C] |
| 2000000 | = | ―MM, &c. |
The Greeks had three ways of expressing numbers. First, The most simple was, for every single letter, according to its place in the alphabet, to denote a number from a 1 to w 24; in which manner the books of Homer's Ilias are distinguished. Secondly, Another way was by dividing the alphabet into (first) 8 units, a 1, b 2, &c; (2nd) 8 tens, i 10, k 20, &c; (3d) 8 hundreds, r 100, s 200, &c: And thousands they expressed by a point or accent under a letter, as a 1000, b 2000, &c. Thirdly, A third way was by six capital letters, thus, I (ia for mia) 1, *p (wente) 5, *d (deka) 10, *h (*heka<*>on) 100, *x (xilia) 1000, *m (mueia|) 10000: and when the letter *p inclosed any of these, except I, it shewed that the inclosed letter was five times its own value, as <06> 50, <07> 500, <08> 5000, <09> 50000.
The Hebrew alphabet was divided into, Nine Units, as 1, 2, &c; Nine Tens, as 10, 20, &c; Nine Hundreds, as 100, 200, &c, 500, 600, 700, 800, 900. Thousands were sometimes expressed by the units prefixed to hundreds, as 1534, &c; and even to tens, as 1070, &c. But more commonly thousands were expressed by the word 1000, 2000; and with the other numerals prefixed to signify the number of thousands, as 3000, &c.
The first letters of the alphabet, a, b, c, &c, denote given quantities; and the last letters z, y, x, &c, denote such as are unknown or sought. Stifelius first used the capitals A, B, C, &c, for the unknown or required quantities. After that, Vieta used the capital vowels A, E, I, O, U, Y for the unknown or required quantities, and the consonants B, C, D, &c, for known or given numbers. Harriot changed Vieta's capitals into the small letters, viz a, e, i, o, u, for unknown, and b, c, d, &c, for known quantities. And Descartes changed Harriot's vowels for the latter letters z, y, x, &c, and the consonants for the leading letters a, b, c, d, &c.
Newton denotes the several orders of the fluxions of variable quantities by as many points over the latter letters;
Powers of quantities are denoted by placing the index or exponent after them, towards the upper part; thus a2 is the 2d power, a3 the third power, and an the n power of a. Diophantus marked the powers by their initials, thus dn, kn, ddn, dkn, kkn, &c, for dynamis, cubus, dynamodynamis, &c, or the 2d, 3d, 4th, &c powers; and the same method has been used by several of the early writers, since the introduction of Algebra into Europe: but the first of them, as Paciolus, Cardan, &c, used no mark for powers, but the words themselves. Stifel, and others about his time, used the initials or abbreviations, , [dram], , [dram] [dram], &c, of res or coss, zenzus, cubus, zenzizenzus, &c, barbarous corruptions of the Italian cosa, census, cubo, censi-census, &c. But he used also numeral exponents, both positive and negative, to the general characters or roots A, B, C, &c. Bombelli used a half circle thus <*> as a general character for the unknown or quantity required to be found in any question, and the several powers of it he denoted by figures set above it; thus , are the 1st, 2d, 3d powers of ; which powers he called dignities. Stevinus used a whole circle for the same unknown quantity, with the numeral index within it, and that both integral and fractional; thus ○0, ○1, ○2, ○3, are the 0, 1, 2, 3 powers of the general quantity ○; also ○<*>, ○1/3, ○1/4, he uses as the square root, cubic root, 4th root of the same; and ○2/3, the cube root of the square, and ○3/2, the square root of the cube, and so on. And these fractional exponents were adopted and farther used by his commentator Albert Girard. So that Stevinus ought to be esteemed the first person who rendered general the notation of all powers and roots in the same way, the former by integral, and the latter by fractional exponents. Harriot denoted his powers by a repetition of the letters; thus a, aa, aaa, &c. And Descartes, instead of this, set the numeral index at the upper part of the letters, as at present thus a, a2, a3, &c. Though, I am informed, by such as have seen Harriot's posthumous papers, that he also there makes use of exponents.
The character √ is the sign of radicality, or of a root, being derived from the initial R or r, which was used at first by Paciolus, Cardan, &c. This character √ I first find used by Stifel, in 1544, and by Robert Recorde in 1557. The character √ alone denotes the square root only; but at first they used the initial of the name after it, to denote the several roots: as √q the quadrate or square root, and √c the cubic root. But the numeral indices of the root were prefixed by Albert Girard, exactly the same as they are used at present, viz √2, √3, √, the 2d, 3d, or 4th root.
The character + denotes addition, and a positive quantity. At first the word itself was used, plus, piu, or the initial p. by Paciolus, Cardan, Tartalea, &c. And the character + for addition occurs in Stifelius.
The character - denotes subtraction, and a negative quantity; which also first occurs in the same author Stifelius. Before that, the word minus, mene, or the initial m. was used. Other characters have also been sometimes used by other authors, for addition and subtraction; but they are now no longer in use.
X denotes multiplication, and was introduced by Oughtred.
÷ denoting division, was introduced by Dr. Pell. Division is also denoted like a fraction, thus a/b or 6/3 = 2.
= denotes equality, and was used by Robert Recorde. Descartes uses for the same purpose.
The character :: for proportionality, or equality of ratios, was introduced by Oughtred; as was also the mark <04> for continued proportion. |
> for greater, and [angle] for less, were used by Harriot.
And and were used by Oughtred for the same purposes.
Dr. Pell used for involution, and for evolution.
<01> denotes a general difference between any two quantities, and was introduced by Dr. Wallis.
The Parenthesis ( ), as a vinculum, was invented by Albert Girard, and used in such expressions as these, √<*> (72 + √5120), and B (Bq + Cq), both for universal roots, and multiplication, &c.
The straight-lined vinculum, ―, was used by Victa for the fame purpose; thus ―(A - B) in ―(B + C).
| A Square | [angle] An Angle |
| ▵ A Triangle | A Rightangle |
| A Rectangle | Perpendicular |
| Θ or Θ A Circle | Parallel. |
