Arithmetic, Part 1 · Section 1 – Section 2

Arithmetic · Part 1 · Section 1 – Section 2

p. 1Numeration.

NUmeration is accounted the firſt part of Arithmetick, and it is to know how to read a Summe of figures expreſſed in writing; or to write down any Summe to be expreſſed.

To the doing of which there are four things neceſſary.

Firſt, to know their number, which is Nine.

Secondly, their ſhapes, which are 1 2 3 4 5 6 7 8 9. Of which the firſt toward the left hand ever ſignifieth One, the ſecond Two, &c.

Thirdly, to know the value of their places.

Laſtly, How their proper ſignification i… altered thereby.

The value of their places is thus, When two, three, or more figures ſtand in one Summe, tha… is, without any Point, Line or Comma betwixt p. 2them, as 321, that place next the right hand where the figure 1 ſtandeth, is called the place of Unity, or Unities, and the figure 1 ſtandeth in that place onelyonly for one, and the figure 2 when it is found in that firſt place, ſtands only for two; and the like of the reſt.

But in the Summe 321, above expreſſed, the figure 2 is in the ſecond place, and every place conteines the value of that place before towards the right hand ten times; and therefore the figure 2 doth not ſignifie two, but (in this ſecond place) ten times two, that is Twenty. And ſo the figure 3 if it had been in that place had ſignified ten times three, that is Thirty; but being here in the third place it ſignifies ten times thirty, that is Three hundred. And ſo the whole Summe 321, is to be read, Three hundred twenty and one.

Fourthly, It is hereby ſeen, how their proper ſignifications, which were Three, Two and One, are altered by being thus placed, and the Sum, which otherwiſe had been but Six, is Three hundred twenty one, as before.

In like ſort, if their had been more places, as ſeven, the value is quite through increaſed ten times by being a place behinde towards the left hand; as in the Summe 1̇111̇111̇, The figure 1 in the ſecond place ſtands for ten times one (that is ten,) in the third for ten times ten (which is one hundred,) in the fourth for ten hundred, (which is called one thouſand,) in the fifth for ten thouſand, in the ſixth for ten p. 3times ten thouſand (which is one hundred thouſand) in the laſt (here the ſeventh) place for ten hundred thouſand, which is called a Milion: and ſo on, if there were more places, obſerving the ſame order.

Now to read this readily, make a prick over the place of Unity, another over the third from it, and over every third ſtill towards the left hand, for ſo thoſe points will be over the places of Unites, Thouſands, and Milions; and ſo beginning at the laſt, that is, at the left hand, read one Milion, and becauſe the three following towards the right ſignifie properly one hundred and eleven, but the prick belonging to them is in the place of thouſands, call them one hundred and eleven thouſand, and three remaining being under the point over Unity, ſignifie onelyonly one hundred and eleven; and all three points read together in one ſumme is, One Milion, one hundred and eleven Thouſand, one hundred and eleven.

In like manner, if this number 73598624 were given to be read (according to former directions) make a prick over every third figure, beginning with the firſt figure towards the right hand (which is the place of Unity) and then will your number ſtand thus.

73̇598̇624̇

Then for the ready reading thereof (becauſe the third prick ſignifieth Millions) call all the figures towards the left hand, ſtanding from that prick, Milions, which in this example are 7 and 3, p. 4ſo then this number conteins 73 Millions, 598 Thouſand, 624 which in words at length we read Seventy three Millions, five hundred ninety eight thouſand, ſix hundred twenty four.

Let thus much ſuffice concerning the planing of large numbers, for the ready reading of them, only take theſe foure Tables following, for illuſtration of what hath been hitherto delivered in words, the very ſight whereof is better then a whole Chapter of information.

The firſt Table is thus to be read] One in the firſt place ſignifies One. One in the ſecond place ſignifies Ten. One in the third place ſignifies a hundred, &c. as in the Table.

The third Table is only certain rowes of figures ſet together and orderly diſpoſed, having the ſignification or reading of the ſame numbers in words at length to them annexed, and is only inſerted for the better ſatisfaction of ſuch as ſhall doubt whether they perfectly underſtand what hath been before taught.

The fourth Table is much like the ſecond, only it conſiſteth but of one number and extends p. 5three places farther then the greateſt number in the ſecond Table doth: viz. to twelve places which figures are thus to be read. 736 Millions of Millions, 842 Millions, 708 Thouſand, 645.

(1 Table)

(2 Table)

p. 6(3 Table)

(4 Table)

p. 7Addition.

ADdition is the collecting or gathering together of two or more ſums, either of one or of diverſe denominations, into one ſum, which is called the (Aggregate) (Total) or Groſſe ſum.)

In addition of numbers of one denomination, the order is to ſet the numbers to be added one directly under the other, that is to ſay Unites under Unites, Tens under Tens, Hundreds under Hundreds, &c.

The Rule.

Having placed your numbers to be added in due order, one under another, draw a line under them, and begin at the lowermoſt figure towards your right hand, and adde that to the next figure above, and the ſumme of them to the next figure above that, proceeding in this order till you have added the whole line together, which when you have done, conſider how many tens are contained in that line, and for every ten keep one Ʋnite in your mind, to be added to the next row, but if there be any odde digits, you muſt ſet them beneath the ſtroake, juſt under the line you added together, having thus p. 8finiſhed the addition of one line proceed to the next, and from thence to the third, and ſo forward, be there never ſo many. The Examples following will make this plain,

Example 1.

Let the numbers given to be added together be 7832, 5609, 376, 8547, having thus placed them in order one under another as in the Margine is done, draw a line under them, then begin your addition, at the lowermoſt figure towards your right hand, ſaying, 7 and 6 is 13, and 9 is 22, and 2 is 24 now becauſe in 24, there is two tens, and 4 remaining, I place the 4 under the line, and carry the two zens to the next row, ſaying, 2 which I carryed and 4 makes 6, and 7 makes 13, and 3 makes 16, in which row there is but one ten conteined and 6 remaining, which 6 I ſet under the line, and carry the ten to the next row of hundreds, ſaying, 1 that I carryed and 5 makes 6, and 3 makes 9, and 6 makes 15, and 8 makes 23, in which 23, ten is conteined two times, and 3 remaining, the three I place under the line, and carry the two tens to the next row, ſaying 2 which I carryed and 8 makes 10, and 5 makes 15, and 7 makes 22, in which ten is conteined two times, and 2 remaining, which 2 I ſet under the line, and becauſe there is never another p. 9row to be added (to which I ſhould carry the two tens) I therefore ſet it down alſo under the line towards the left hand, as you ſee done in the margine, ſo the total or groſſe ſum of theſe numbers being added together is 22364.

Example, 2.

A man hath in his Orchard 136 Apple trees, 76 Pear trees, 107 Cherry trees, and 36 Plum trees, and he deſires readily to know how many trees he hath in all, place your uumbers one under another as in the margine, and then begin to adde them together, at your right hand, ſaying, 6 and 7, make 13, and 6 make 19, and 6 make 25, place 5 under the line, and carry 2 to the next row, ſaying 2 and 3 is 5, and 7 is 12, and 3 is 15, place 5 under the line, and carry 1 to the next row, ſaying 1 and 1 is 2, and 1 is 3 which 3 I ſet under the line, and becauſe there was no tens conteined in that line therefore the totall is 355, and ſo many Trees are in the Orchard.

Other Examples for Practice. …