The Earliest Arithmetics in English

Algorithms; Arithmetic -- Early works to 1900; Mathematics -- History

where I haue expressed y^e same su{m}me 198 l’i. 19 s. 11 d’. But here
you se the pe{n}nes stande toward y^e ryght hande, and the other
encreasynge orderly towarde the lefte hande. Agayne you maye se, that
auditours wyll make 2 lynes (yea and more) for pennes, shyllynges, {and}
all other valewes, yf theyr summes extende therto. Also you se, that
they set one counter at the ryght ende of eche rowe, whiche so set there
standeth for 5 of that roume: and on [*132a] the lefte corner of the
rowe it sta{n}deth for 10, of y^e same row. But now yf you wold adde
other subtracte after any of both those sortes, yf you marke y^e order
of y^t other feate which I taught you, you may easely do the same here
without moch teachynge: for in Additio{n} you must fyrst set downe one
su{m}me and to the same set the other orderly, and lyke maner yf you
haue many: but in Subtraction you must sette downe fyrst the greatest
summe, and from it must you abate that other euery denominatio{n} from
his dewe place.

_S._ I do not doubte but with a lytell practise I shall attayne these
bothe: but how shall I multiply and diuide after these fourmes?

_M._ You can not duely do none of both by these sortes, therfore in
suche case, you must resort to your other artes.

_S._ Syr, yet I se not by these sortes how to expresse hu{n}dreddes,
yf they excede one hundred, nother yet thousandes.

_M._ They that vse such accomptes that it excede 200 [*132b] in one
summe, they sette no 5 at the lefte hande of the scores of poundes, but
they set all the hundredes in an other farther rowe {and} 500 at the
lefte hand therof, and the thousandes they set in a farther rowe yet,
{and} at the lefte syde therof they sette the 5000, and in the space
ouer they sette the 10000, and in a hygher rowe 20000, whiche all I haue
expressed in this exa{m}ple,

      o o o o
       o
  o   o o
  o   o o o
      o o o
  o   o o o o
        o
      o o
        o
      o o o
               o o
               o

which is 97869 l’i. 12 s. 9 d’ ob. q. for I had not told you before
where, nother how you shuld set downe farthynges, which (as you se here)
must be set in a voyde space sydelynge beneth the pennes: for q one
counter: for ob. 2 counters: for ob. q. 3 counters: {and} more there can
not be, for 4 farthynges [*133a] do make 1 d’. which must be set in his
dewe place.

    [Headnote: Auditors’ Casting Counters.]

And yf you desyre y^e same summe after audytors maner, lo here it is.

           o o        o               o   o       o
  o o o   o o     o o o   o o o   o o o   o o   o o o
  o                               o                      o o
                                                         o

Public-domain text, read in full here on John Shaqi.

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History

The Earliest Arithmetics in English

Algorithms; Arithmetic -- Early works to 1900; Mathematics -- History

where I haue expressed y^e same su{m}me 198 l’i. 19 s. 11 d’. But here
you se the pe{n}nes stande toward y^e ryght hande, and the other
encreasynge orderly towarde the lefte hande. Agayne you maye se, that
auditours wyll make 2 lynes (yea and more) for pennes, shyllynges, {and}
all other valewes, yf theyr summes extende therto. Also you se, that
they set one counter at the ryght ende of eche rowe, whiche so set there
standeth for 5 of that roume: and on [*132a] the lefte corner of the
rowe it sta{n}deth for 10, of y^e same row. But now yf you wold adde
other subtracte after any of both those sortes, yf you marke y^e order
of y^t other feate which I taught you, you may easely do the same here
without moch teachynge: for in Additio{n} you must fyrst set downe one
su{m}me and to the same set the other orderly, and lyke maner yf you
haue many: but in Subtraction you must sette downe fyrst the greatest
summe, and from it must you abate that other euery denominatio{n} from
his dewe place.

_S._ I do not doubte but with a lytell practise I shall attayne these
bothe: but how shall I multiply and diuide after these fourmes?

_M._ You can not duely do none of both by these sortes, therfore in
suche case, you must resort to your other artes.

_S._ Syr, yet I se not by these sortes how to expresse hu{n}dreddes,
yf they excede one hundred, nother yet thousandes.

_M._ They that vse such accomptes that it excede 200 [*132b] in one
summe, they sette no 5 at the lefte hande of the scores of poundes, but
they set all the hundredes in an other farther rowe {and} 500 at the
lefte hand therof, and the thousandes they set in a farther rowe yet,
{and} at the lefte syde therof they sette the 5000, and in the space
ouer they sette the 10000, and in a hygher rowe 20000, whiche all I haue
expressed in this exa{m}ple,

      o o o o
       o
  o   o o
  o   o o o
      o o o
  o   o o o o
        o
      o o
        o
      o o o
               o o
               o

which is 97869 l’i. 12 s. 9 d’ ob. q. for I had not told you before
where, nother how you shuld set downe farthynges, which (as you se here)
must be set in a voyde space sydelynge beneth the pennes: for q one
counter: for ob. 2 counters: for ob. q. 3 counters: {and} more there can
not be, for 4 farthynges [*133a] do make 1 d’. which must be set in his
dewe place.

    [Headnote: Auditors’ Casting Counters.]

And yf you desyre y^e same summe after audytors maner, lo here it is.

           o o        o               o   o       o
  o o o   o o     o o o   o o o   o o o   o o   o o o
  o                               o                      o o
                                                         o

Public-domain text, read in full here on John Shaqi.

The Earliest Arithmetics in English

The Earliest Arithmetics in English

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