INDEX OF TECHNICAL TERMS1algorisme,33/12;algorym,augrym,3/3; the art of computing, using the so-called Arabic numerals.The word in its various forms is derived from the Arabical-Khowarazmi(i.e. the native of Khwarazm (Khiva)). This was the surname of Ja’far Mohammad ben Musa, who wrote a treatise early in the 9th century (see p. xiv).The formalgorithmis also found, being suggested by a supposed derivation from the Greekἀριθμός(number).antery,24/11; to move figures to the right of the position in which they are first written. This operation is performed repeatedly upon the multiplier in multiplication, and upon certain figures which arise in the process of root extraction.anterioracioun,50/5; the operation of moving figures to the right.article,34/23;articul,5/31;articuls,9/36,29/7,8; a number divisible by ten without remainder.cast,8/12; to add one number to another.‘Addition is acastingtogether of two numbers into one number,’8/10.cifre,4/1; the name of the figure 0. The word is derived from the Arabicsifr= empty, nothing. Hencezero.A cipher is the symbol of the absence of number or of zero quantity. It may be used alone or in conjunction with digits or other ciphers, and in the latter case, according to the position which it occupies relative to the other figures, indicates the absence of units, or tens, or hundreds, etc. The great superiority of the Arabic to all other systems of notation resides in the employment of this symbol. When the cipher is not used, the place value of digits has to be indicated by writing them in assigned rows or columns. Ciphers, however, may be interpolated amongst the significant figures used, and as they sufficiently indicate the positions of the empty rows or columns, the latter need not be indicated in any other way. The practical performance of calculations is thus enormously facilitated (seep. xvi).componede,33/24;composyt,5/35; with reference to numbers, one compounded of a multiple of ten and a digit.conuertide= conversely,46/29,47/9.cubicede,50/13;to be c., to have its cube root found.cubike nombre,47/8; a number formed by multiplying a given number twice by itself,e.g.27 = 3 × 3 × 3. Now called simply a cube.decuple,22/12; the product of a number by ten. Tenfold.departys= divides,5/29.digit,5/30;digitalle,33/24; a number less than ten, represented by one of the nine Arabic numerals.dimydicion,7/23; the operation of dividing a number by two. Halving.duccioun, multiplication,43/9.duplacion,7/23,14/15; the operation of multiplying a number by two. Doubling.i-mediet= halved,19/23.intercise= broken,46/2; intercise Progression is the name given to either of the Progressions 1, 3, 5, 7, etc.; 2, 4, 6, 8, etc., in which the common difference is 2.lede into, multiply by,47/18.lyneal nombre,46/14; a number such as that which expresses the measure of the length of a line, and therefore is notnecessarilythe product of two or more numbers (videSuperficial, Solid). This appears to be the meaning of the phrase as used inThe Art of Nombryng. It is possible that the numbers so designated are the prime numbers, that is, numbers not divisible by any other number except themselves and unity, but it is not clear that this limitation is intended.mediacioun,16/36,38/16; dividing by two (see alsodimydicion).medlede nombre,34/1; a number formed of a multiple of ten and a digit (videcomponede, composyt).medye,17/8, to halve;mediete, halved,17/30;ymedit,20/9.naturelle progressioun,45/22; the series of numbers 1, 2, 3, etc.produccioun, multiplication,50/11.quadrat nombre,46/12; a number formed by multiplying a given number by itself,e.g.9 = 3 × 3, a square.rote,7/25;roote,47/11; root. The roots of squares and cubes are the numbers from which the squares and cubes are derived by multiplication into themselves.significatyf, significant,5/14; The significant figures of a number are, strictly speaking, those other than zero,e.g.in 3 6 5 0 4 0 0, the significant figures are 3, 6, 5, 4. Modern usage, however, regards all figures between the two extreme significant figures as significant, even when some are zero. Thus, in the above example, 3 6 5 0 4 are considered significant.solide nombre,46/37; a number which is the product of three other numbers,e.g.66 = 11 × 2 × 3.superficial nombre,46/18; a number which is the product of two other numbers,e.g.6 = 2 × 3.ternary, consisting of three digits,51/7.vnder double, a digit which has been doubled,48/3.vnder-trebille, a digit which has been trebled,49/28;vnder-triplat,49/39.w, a symbol used to denote half a unit,17/33.
algorisme,33/12;algorym,augrym,3/3; the art of computing, using the so-called Arabic numerals.
The word in its various forms is derived from the Arabical-Khowarazmi(i.e. the native of Khwarazm (Khiva)). This was the surname of Ja’far Mohammad ben Musa, who wrote a treatise early in the 9th century (see p. xiv).
The formalgorithmis also found, being suggested by a supposed derivation from the Greekἀριθμός(number).
antery,24/11; to move figures to the right of the position in which they are first written. This operation is performed repeatedly upon the multiplier in multiplication, and upon certain figures which arise in the process of root extraction.
anterioracioun,50/5; the operation of moving figures to the right.
article,34/23;articul,5/31;articuls,9/36,29/7,8; a number divisible by ten without remainder.
cast,8/12; to add one number to another.
‘Addition is acastingtogether of two numbers into one number,’8/10.
cifre,4/1; the name of the figure 0. The word is derived from the Arabicsifr= empty, nothing. Hencezero.
A cipher is the symbol of the absence of number or of zero quantity. It may be used alone or in conjunction with digits or other ciphers, and in the latter case, according to the position which it occupies relative to the other figures, indicates the absence of units, or tens, or hundreds, etc. The great superiority of the Arabic to all other systems of notation resides in the employment of this symbol. When the cipher is not used, the place value of digits has to be indicated by writing them in assigned rows or columns. Ciphers, however, may be interpolated amongst the significant figures used, and as they sufficiently indicate the positions of the empty rows or columns, the latter need not be indicated in any other way. The practical performance of calculations is thus enormously facilitated (seep. xvi).
componede,33/24;composyt,5/35; with reference to numbers, one compounded of a multiple of ten and a digit.
conuertide= conversely,46/29,47/9.
cubicede,50/13;to be c., to have its cube root found.
cubike nombre,47/8; a number formed by multiplying a given number twice by itself,e.g.27 = 3 × 3 × 3. Now called simply a cube.
decuple,22/12; the product of a number by ten. Tenfold.
departys= divides,5/29.
digit,5/30;digitalle,33/24; a number less than ten, represented by one of the nine Arabic numerals.
dimydicion,7/23; the operation of dividing a number by two. Halving.
duccioun, multiplication,43/9.
duplacion,7/23,14/15; the operation of multiplying a number by two. Doubling.
i-mediet= halved,19/23.
intercise= broken,46/2; intercise Progression is the name given to either of the Progressions 1, 3, 5, 7, etc.; 2, 4, 6, 8, etc., in which the common difference is 2.
lede into, multiply by,47/18.
lyneal nombre,46/14; a number such as that which expresses the measure of the length of a line, and therefore is notnecessarilythe product of two or more numbers (videSuperficial, Solid). This appears to be the meaning of the phrase as used inThe Art of Nombryng. It is possible that the numbers so designated are the prime numbers, that is, numbers not divisible by any other number except themselves and unity, but it is not clear that this limitation is intended.
mediacioun,16/36,38/16; dividing by two (see alsodimydicion).
medlede nombre,34/1; a number formed of a multiple of ten and a digit (videcomponede, composyt).
medye,17/8, to halve;mediete, halved,17/30;ymedit,20/9.
naturelle progressioun,45/22; the series of numbers 1, 2, 3, etc.
produccioun, multiplication,50/11.
quadrat nombre,46/12; a number formed by multiplying a given number by itself,e.g.9 = 3 × 3, a square.
rote,7/25;roote,47/11; root. The roots of squares and cubes are the numbers from which the squares and cubes are derived by multiplication into themselves.
significatyf, significant,5/14; The significant figures of a number are, strictly speaking, those other than zero,e.g.in 3 6 5 0 4 0 0, the significant figures are 3, 6, 5, 4. Modern usage, however, regards all figures between the two extreme significant figures as significant, even when some are zero. Thus, in the above example, 3 6 5 0 4 are considered significant.
solide nombre,46/37; a number which is the product of three other numbers,e.g.66 = 11 × 2 × 3.
superficial nombre,46/18; a number which is the product of two other numbers,e.g.6 = 2 × 3.
ternary, consisting of three digits,51/7.
vnder double, a digit which has been doubled,48/3.
vnder-trebille, a digit which has been trebled,49/28;vnder-triplat,49/39.
w, a symbol used to denote half a unit,17/33.
1.This Index has been kindly prepared by Professor J. B. Dale, of King’s College, University of London, and the best thanks of the Society are due to him for his valuable contribution.
GLOSSARYWords whose first appearance is earlier than the page cited in the Glossary are identified in supplementary notes, and both occurrences are marked in the main text.ablacioun, taking away,36/21addyst, haddest,10/37agregacioun, addition,45/22. (First example in N.E.D., 1547.)a-ȝenenes, against,23/10allgate, always,8/39als, as,22/24and, if,29/8;&,4/27;& yf,20/7a-nendes, towards,23/15aproprede, appropriated,34/27apwereth, appears,61/8a-risyȝt, arises,14/24a-rowe, in a row,29/10arsemetrike, arithmetic,33/1ayene, again,45/15bagle, crozier,67/12bordure= ordure, row,43/30borro,inf.borrow,11/38;imp. s.borowe,12/20;pp.borwed,12/15;borred,12/19boue, above,42/34caputule, chapter,7/26certayn, assuredly,18/34clepede, called,47/7competently, conveniently,35/8compt, count,47/29contynes, contains,21/12;pp.contenythe,38/39craft, art,3/4distingue, divide,51/5egalle, equal,45/21excep, except,5/16exclusede, excluded,34/37excressent, resulting,35/16exeant, resulting,43/26expone, expound,3/23ferye= ferþe, fourth,70/12figure= figures,5/1for-by, past,12/11fors; no f., no matter,22/24forseth, matters,53/30forye= forþe, forth,71/8fyftye= fyftþe, fifth,70/16grewe, Greek,33/13haluendel, half,16/16;haldel,19/4;pl.haluedels,16/16hayst, hast,17/3, 32hast, haste,22/25heer, higher,9/35here, their,7/26here-a-fore, heretofore,13/7heyth, was called,3/5hole, whole,4/39;holle,17/1;hoole, of three dimensions,46/15holdyþe, holds good,30/5how be it that, although,44/4lede= lete, let,8/37lene, lend,12/39lest, least,43/27lest= left,71/9leue, leave,6/5;pr. 3 s.leues, remains,11/19;First used in10/40leus,11/28;pp.laft, left,19/24lewder, more ignorant,3/3lust, desirest to,45/13lyȝt, easy,15/31lymytes, limits,34/18;lynes,34/12;lynees,34/17;Lat. limes,pl.limites.maystery, achievement;no m., no achievement, i.e. easy,19/10me,indef. pron.one,42/1First used in34/16mo, more,9/16moder= more (Lat. majorem),43/22most, must,30/3First used in3/12multipliede,to be m.= multiplying,40/9mynvtes, the sixty parts into which a unit is divided,38/25myse-wroȝt, mis-wrought,14/11nether, nor,34/25nex, next,19/9noȝt, nought,5/7First used in4/8note, not,30/5oo, one,42/20;o,42/21First used in34/27(oo);33/22(o)omest, uppermost, higher,35/26;omyst,35/28omwhile, sometimes,45/31First used in39/17on, one,8/29opyne, plain,47/8or, before,13/25or= þe oþer, the other,28/34ordure, order,34/9;row,43/1Word form is “order”other, or,33/13,43/26;Note also “one other other” in35/24other . . . or, either . . . or,38/37First used in37/5ouerer, upper,42/15ouer-hippede, passed over,43/19recte, directly,27/20First used in26/31remayner, remainder,56/28representithe, represented,39/14resteth, remains,63/29First used in57/29rewarde, regard,48/6rew, row,4/8rewle, row,4/20,7/12;rewele,4/18;rewles, rules,5/33s.= scilicet,3/8sentens, meaning,14/29signifye(tyf),5/13. The last three letters are added above the line, evidently because of the word ‘significatyf’ in l. 14. But the ‘Solucio,’ which contained the word, has been omitted.sithen, since,33/8some, sum, result,40/17, 32First used in36/21sowne, pronounce,6/29singillatim, singly,7/25spices, species, kinds,34/4First used in5/34spyl, waste,14/26styde, stead,18/20subtrahe, subtract,48/12;pp.subtrayd,13/21sythes, times,21/16taȝt, taught,16/36take,pp.taken;t. fro, starting from,45/22taward, toward,23/34thouȝt, though,5/20trebille, multiply by three,49/26twene, two,8/11First used in4/23þow, though,25/15þowȝt, thought;be þ., mentally,28/4þus= þis, this,20/33vny, unite,45/10wel, wilt,14/31wete, wit,15/16;wyte, know,8/38;pr. 2 s.wost,12/38wex, become,50/18where, whether,29/12wher-thurghe, whence,49/15worch, work,8/19;First used in7/35wrich,8/35;wyrch,6/19;imp. s.worch,15/9;First used in9/6pp.y-wroth,13/24write, written,29/19;First used in4/5y-write,16/1wryrchynge= wyrchynge, working,30/4wt, with,55/8y-broth, brought,21/18ychon, each one,29/10ydo, done, added,9/6First used in8/37ylke, same,5/12y-lyech, alike,22/23y-myȝt, been able,12/2y-nowȝt, enough,15/31;ynovȝt,18/34yove, given,45/33yt, that,52/8y-write,v.write.y-wroth,v.worch.
Words whose first appearance is earlier than the page cited in the Glossary are identified in supplementary notes, and both occurrences are marked in the main text.
ablacioun, taking away,36/21
addyst, haddest,10/37
agregacioun, addition,45/22. (First example in N.E.D., 1547.)
a-ȝenenes, against,23/10
allgate, always,8/39
als, as,22/24
and, if,29/8;
&,4/27;
& yf,20/7
a-nendes, towards,23/15
aproprede, appropriated,34/27
apwereth, appears,61/8
a-risyȝt, arises,14/24
a-rowe, in a row,29/10
arsemetrike, arithmetic,33/1
ayene, again,45/15
bagle, crozier,67/12
bordure= ordure, row,43/30
borro,inf.borrow,11/38;
imp. s.borowe,12/20;
pp.borwed,12/15;
borred,12/19
boue, above,42/34
caputule, chapter,7/26
certayn, assuredly,18/34
clepede, called,47/7
competently, conveniently,35/8
compt, count,47/29
contynes, contains,21/12;
pp.contenythe,38/39
craft, art,3/4
distingue, divide,51/5
egalle, equal,45/21
excep, except,5/16
exclusede, excluded,34/37
excressent, resulting,35/16
exeant, resulting,43/26
expone, expound,3/23
ferye= ferþe, fourth,70/12
figure= figures,5/1
for-by, past,12/11
fors; no f., no matter,22/24
forseth, matters,53/30
forye= forþe, forth,71/8
fyftye= fyftþe, fifth,70/16
grewe, Greek,33/13
haluendel, half,16/16;
haldel,19/4;
pl.haluedels,16/16
hayst, hast,17/3, 32
hast, haste,22/25
heer, higher,9/35
here, their,7/26
here-a-fore, heretofore,13/7
heyth, was called,3/5
hole, whole,4/39;
holle,17/1;
hoole, of three dimensions,46/15
holdyþe, holds good,30/5
how be it that, although,44/4
lede= lete, let,8/37
lene, lend,12/39
lest, least,43/27
lest= left,71/9
leue, leave,6/5;
pr. 3 s.leues, remains,11/19;First used in10/40
leus,11/28;
pp.laft, left,19/24
lewder, more ignorant,3/3
lust, desirest to,45/13
lyȝt, easy,15/31
lymytes, limits,34/18;
lynes,34/12;
lynees,34/17;
Lat. limes,pl.limites.
maystery, achievement;
no m., no achievement, i.e. easy,19/10
me,indef. pron.one,42/1First used in34/16
mo, more,9/16
moder= more (Lat. majorem),43/22
most, must,30/3First used in3/12
multipliede,to be m.= multiplying,40/9
mynvtes, the sixty parts into which a unit is divided,38/25
myse-wroȝt, mis-wrought,14/11
nether, nor,34/25
nex, next,19/9
noȝt, nought,5/7First used in4/8
note, not,30/5
oo, one,42/20;o,42/21First used in34/27(oo);33/22(o)
omest, uppermost, higher,35/26;
omyst,35/28
omwhile, sometimes,45/31First used in39/17
on, one,8/29
opyne, plain,47/8
or, before,13/25
or= þe oþer, the other,28/34
ordure, order,34/9;
row,43/1Word form is “order”
other, or,33/13,43/26;Note also “one other other” in35/24
other . . . or, either . . . or,38/37First used in37/5
ouerer, upper,42/15
ouer-hippede, passed over,43/19
recte, directly,27/20First used in26/31
remayner, remainder,56/28
representithe, represented,39/14
resteth, remains,63/29First used in57/29
rewarde, regard,48/6
rew, row,4/8
rewle, row,4/20,7/12;
rewele,4/18;
rewles, rules,5/33
s.= scilicet,3/8
sentens, meaning,14/29
signifye(tyf),5/13. The last three letters are added above the line, evidently because of the word ‘significatyf’ in l. 14. But the ‘Solucio,’ which contained the word, has been omitted.
sithen, since,33/8
some, sum, result,40/17, 32First used in36/21
sowne, pronounce,6/29
singillatim, singly,7/25
spices, species, kinds,34/4First used in5/34
spyl, waste,14/26
styde, stead,18/20
subtrahe, subtract,48/12;
pp.subtrayd,13/21
sythes, times,21/16
taȝt, taught,16/36
take,pp.taken;
t. fro, starting from,45/22
taward, toward,23/34
thouȝt, though,5/20
trebille, multiply by three,49/26
twene, two,8/11First used in4/23
þow, though,25/15
þowȝt, thought;
be þ., mentally,28/4
þus= þis, this,20/33
vny, unite,45/10
wel, wilt,14/31
wete, wit,15/16;
wyte, know,8/38;
pr. 2 s.wost,12/38
wex, become,50/18
where, whether,29/12
wher-thurghe, whence,49/15
worch, work,8/19;First used in7/35
wrich,8/35;
wyrch,6/19;
imp. s.worch,15/9;First used in9/6
pp.y-wroth,13/24
write, written,29/19;First used in4/5
y-write,16/1
wryrchynge= wyrchynge, working,30/4
wt, with,55/8
y-broth, brought,21/18
ychon, each one,29/10
ydo, done, added,9/6First used in8/37
ylke, same,5/12
y-lyech, alike,22/23
y-myȝt, been able,12/2
y-nowȝt, enough,15/31;
ynovȝt,18/34
yove, given,45/33
yt, that,52/8
y-write,v.write.
y-wroth,v.worch.
MARGINAL NOTESHeadnoteshave been moved to the beginning of the appropriate paragraph. Headnotes were omitted from the two Appendixes, as sidenotes give the same information.Line Numbersare cited in the Index and Glossary. They have been omitted from the e-text except in the one verse selection (App. II,Carmen de Algorismo). Instead, the Index and Glossary are linked directly to each word.Numbered Notes:Numbered sidenotes show page or leaf numbers from the original MSS. In the e-text, sidenote numbers have been replaced with simple asterisks.Footnotes give textual information such as variant readings. They have been numbered sequentially within each title.Sidenotesgiving a running synopsis of the text have been kept as close as possible to their original format and location.
Headnoteshave been moved to the beginning of the appropriate paragraph. Headnotes were omitted from the two Appendixes, as sidenotes give the same information.
Line Numbersare cited in the Index and Glossary. They have been omitted from the e-text except in the one verse selection (App. II,Carmen de Algorismo). Instead, the Index and Glossary are linked directly to each word.
Numbered Notes:
Numbered sidenotes show page or leaf numbers from the original MSS. In the e-text, sidenote numbers have been replaced with simple asterisks.
Footnotes give textual information such as variant readings. They have been numbered sequentially within each title.
Sidenotesgiving a running synopsis of the text have been kept as close as possible to their original format and location.