NUMBERS. 



the 3d, 5th, 7th power, the double of 

 that exponent is the divisor that has the 

 property required. 



Determinate number, is that referred 

 to some given unit, us a ternary or three : 

 whereas an indeterminate one, is that 

 referred to unity in general, and is call- 

 ed quantity. Homogcneal numbers, are 

 those referred to the same unit : as those 

 referred to different units are termed 

 heterogeneal. Whole numbers are other- 

 wise called integers. Rational number, 

 is one commensurable with unity ; as a 

 number, incommensurable with unity, is 

 termed irrational, or a surd. See SURD. 

 In the same manner a rational whole 

 number is that whereof unity is an aliquot 

 part; a rational broken number, that 

 equal to some aliquot part of unity ; and 

 a rational mixed number, that consisting 

 of a whole number and a broken one. 

 Even number, that which may be divided 

 into two equal parts without any fraction, 

 as 6, 12, Stc. The sum, difference, and 

 product of any number of even numbers, 

 is always an even number. An evely 

 even number, is that which may be mea- 

 sured, or divided, without any remainder, 

 by another even number, as 4 by 2. An 

 unevenly even number, when a number 

 may be equally divided by an uneven 

 number, as 20 by 5. Uneven number, 

 that which exceeds an even number, at 

 least by unity, or which cannot be divid- 

 ed into two equal parts, as 3, 5, &c. The 

 sum or difference of two uneven num- 

 bers make an even number ; but the fac- 

 tum of two uneven ones make an uneven 

 number. If an even number be added to 

 an uneven one, or if the one be subtract- 

 ed from the other, in the former case the 

 sum, in the latter the difference, is an un- 

 even number ; but the factum of an even 

 and uneven number is even. The sum 

 of any even number of uneven numbers 

 is an even number ; and the sum of any 

 uneven number of uneven numbers is an 

 uneven number. Primitive, or prime 

 numbers, are those only divisible by uni- 

 ty, as 5, 7, &c. And prime numbers 

 among themselves, are those which have 

 no common measure besides unity, as 12 

 and 19. Perfect number, that whose ali- 



quot parts added together make the 

 whole number, as 6, 28 ; the aliquot parts 

 of 6 being 3, 2, and 1, =E 6 ; and those of 

 28 being 14, 7, 4, 2, 1, = 28. Imperfect 

 numbers, those whose aliquot parts, add- 

 ed together, make either more or less 

 than the whole. And these are distin- 

 guished into abundant and defective ; an 

 instance in the former case is 12, whose 

 aliquot parts 6, 4, 3, 2, 1, make 16; and 

 in the latter case 16, whose aliquot parts 

 8, 4, 2, and 1, make but 15. Plain num- 

 ber, that arising from the multiplication 

 of two numbers, as 6, which i.s the pro- 

 duct of 3 by 2 ; and these numbers are 

 called the sides of the plane. Square 

 number, is the product of any number 

 multiplied by itself: thus 4, which is the 

 factum of 2 by 2, is a square number. 

 Every square number added to its root 

 makes an even number. Polygonal, or 

 polygonous numbers, the sums of arith- 

 metical progressions beginning with 

 unity : these, where the common differ- 

 ence is 1, are called triangular numbers ; 

 where 2, square numbers ; where 3, pen- 

 tagonal numbers; where 4, hexagonal 

 numbers ; where 5, heptagonal numbers, 

 &c. See POLYGONAL. Pyramidal num- 

 bers : the sums of polygonous numbers, 

 collected after the same manner as the 

 polygons themselves, and not gathered 

 out of arithmetical progressions, are call- 

 ed first pyramidal numbers : the sums of 

 the first pyramidals are called second py- 

 ramidals, &c. If they arise out of trian- 

 gular numbers, they are called triangular 

 pyramidal numbers; if out of pentagons, 

 first pentagonal pyramidals. From the 

 manner of summing up polygonal num- 

 bers, it is easy to conceive how the 

 prime pyramidal numbers are found, viz. 

 (a 2) n3 -f 3 w 1 (a 5) n 

 - g - ' expresses all 



the prime pyramidals. 



NUMBER of direction, in chronology, 

 some one of the 35 numbers between 

 the Easter limits, or between the earliest 

 and latest day on which it can fall ; i. c. 

 between the 22d of March and the 25lh of 

 April. Thus, if Easter Sunday fall as in 

 the first line below, the number of direc- 

 tion will be as on the lower line. 



March. April. 



Easter-day 22, 23, 24, 25, 26, 27, 28, 29, 30, 31. 1, 2, 3, &c. 



Number of direction 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, &c. 



and so on, till the number of direction 

 and the sum will be so many days in 

 March for the Easter-day ; if the* sum 

 exceed 31, the excess will be the day 

 of April. To find the number of direc- 



tion : enter the following table with the 

 dominical letter on the left hand, and the 

 golden number at top ; then where the 

 columns meet is the number of direction 

 for that year, 



