D I V

D I V»

•S the Linejc^ cso'stiU lessen upwards,J

never become nothing ..be&yse u° L^Qtn 4 to any part of d a though never Q * _ ,, jtan possibly ever coincide with the upper

Sce also the Learned ,Mr. Kofi's 4thA? 3 ms, read in the University of QxWh

7 Andfhat'the Parts of Solid Bodies are almost.

tthmtely small, and that they ave capable

m g divided wonderful minutely the ri«thews by these Instances. c (malU

u APiece of Silver Wire was draw t0

dut the Weight of but a Gram would retlfoot or 314 Inches in length; an ec . ua tInch can easily he divided tnto ^ ^f «ts, one Grain of this Wive be divvd d^64^0 Parts. And siisee this Div £iCY0t *ly to the Surface of the Wire, us ^hdcy may.

easily he conceived to consist of seianymchPans. „ wa8

a- One of the Oval Cases ot Sl u lk " V !^a^d ,00

Yar? ° UC a Length that much excecdcd i

Yards, and yec weighe d but two Grams anbab > lo that each Cylindrical Gram ot

above 50 inclics; and then

redded to a Square, and us 8'des <uvmaiter vV>.» - ■ -

«cer the ^ “ square, anu us onther e h e , mann er before-mencioned, Ar. so tharhe fuppec. 0 , 0 divisions in an Inch: If Parallel Line9visions' t | Co ^ drawn through thole lubeile di-tw 0 ]U:i|.' e drea will be divided into no less than

4. If of little Squares.

h°ve t0 'i U hippose the Silver Wire mentioned a-fultlun> o^Btit with Gold sand allow for thewhich 6 V ra ms °f Gold to an Ounce of Silver,?dll find a B !^ ore than is commonly used ) you^irejj a Ounce of Gold may cover as much

5 . By difr? acl11015 5 1 Miles in length.

* enn,i v solving one Grain of Crude Copper in

deep B| u r °p 0nujn of Spirit of Sal Armoniack ..good 0 C .our was produced, and after this adduteh ntu Y of distill’d Water was pur to it, to

soain vires' f° a & that the Blue Colour did still re-tire > "hie

.iqy' Dn *he comparing the Weight of

P io “ ulc ; and

ved, it w hh the Grain of Copper first dissol-parii ne found, that Grain was capable of im-Colour to above 513630 times

" s fiulk a ’ Cns,b se

if y were to be divided by i, the Quotient t 4 willbe much bigger than the Dividend ? r , because as1 . : : t 4 • -<■. (i. e.) as one is to the Divisor: :

lo is the Qubrtenc to the Dividend, but 1 is great-er than v or '., wherefore -{4 must also be greaterthan y.

DIVISION in Species Or Algebra, is in generalthe reducing the Dividend and Divisor to the formot a Fraction, which Fraction k the Quotient.Thus if ab were to be divided by cd, it must be

placed thus, » and that traction is the Quoti-

ent; though somethooie to write it thus, cd)ab ,or ab~cd. which last Mark -j- is the commonCharacter for Division,

Par the performing the Wor^ of Division Algebra 1-- calty observe these Ruses.

iso. Ruse: Whet* the Dividend is equal to theDivisor, the Quotient is Unity, and must beplaced in the Quotient, because every thingcontains it self once. > ■

id. Rule, When the Quotient is express’d Fracti-on-ways (as in Simple Division) it the sem*Letters are found equally repeated in everyMember of the Numerator and Denominator,cast away those Letters, and the Remainder

is the Qtjorient > thus, ^pifi and--** so,&c.

3 d. Rule, When there are any Co-efficients, di-vide rlK'm as in Common’ Arichmetiek, and.to the Quotients annex the Quantities ex-press’d by Letters, thus, 1 5 a.

4th. Rule. The general way ot' Division of Com*

’ pound Quantities is like the ordinary way in- Common Arichmeckk, respect being had tothe Rules of Algebraick Addition, Subduftion,and Multiplication , as also, that like Signsgive -f-> and unlike — in the Quotient; ra-king care to divide every part of the Divi-dend by its corresponding Divisor (/. <?.) thatwhose Letters shew dt of the same kindwith the other) to prevent a Fraction whichwould otherwise arise;thus, it-s b) a a -j~ a b~-~-c <7——c b so—< ,a a-\-a b

'°f Li

‘quor,

IIn go r In krneral, signifies the distribu-

’"u i 8o ||i Cln g of a n y Whole into its proper Parts,p Compendium ot Subfiratiion , for theas 1 here ar ° !so an Y times contain’d in the Dividend, a ^ins> . y ' s * in the Quotients so that sob-

■»«“ '7 -

. ^r'seom the D»«>'

, ." n S continually the D»«s° r ' c b time, thei' n < a ud accounting an XJmte for ea

of tliole Units is the to be di-

», the Number or U?ai J which you

v ‘ded a called the Dividend ; tha U thatthe Divisor ; and the tbc gue-

lbe dividend contains the Divisor is , { the

r r t0t ^. And sometimes the

Reason ot which see under that w® 1 . j- ot , ; so is

t ,‘ na H Division, as one is to the *■ - c though

- e ^hsotient to the Dividend ; wh a pwaysso wsioi € slumbers the Quotient mu must

U {> than the Dividend, yet in Fraft^

aW s he greaW> Ouotsent is

thus, let 36 be divided by 4, toe ^ ^e.his than 36. because, since 1. A : • 9 *

'"L lest than - ■ - - "

. • t , « , , u , AU, 4 uv*

• 9 must also b e j c | S than 36; but

That the same Reason for like Signs giving apositive and unlike a negative Quotient, must hoJ|lin Division as well as in Multiplication ; is clear fromconsidering the Nature of Division, (which is onlyresolving the thing into its Parts) therefore sinceevery Dividend is nothing else but the Product ofthe Divisor and Quotient multiplied bv each other,the Quotient must consist of (uch Signs whichcould produce the Dividend; therefore, if the Di-vidend be divided by a Quantity that hath a simi-lar Sign with it, the Quotient most be positive ;it by a Quantity having a dissimilar Sign, it mustbe Negative.

It may be a General Rule in Compound Divi-sion in A'ksebra. always to place such a ; Letter inthe Quotient, as will, when multiplied into theDivisor, produce the Dividend ; for that is al-ways a Rectangle under the Divisor and the Quq-tienc.

H h

A. t