Algorithms; Arithmetic -- Early works to 1900; Mathematics -- History
Expone þis v{er}se. A cifre tokens noȝt, bot he makes þe fig{ure} to
betoken þat comes aft{ur} hym mor{e} þan he schuld & he wer{e} away, as
þus 1φ. her{e} þe fig{ure} of on{e} tokens ten, & yf þe cifre wer{e}
away[{1}] & no fig{ure} by-for{e} hym he schuld token bot on{e}, for
þan he sch{ul}d stonde in þe first place. ¶ And þe cifre tokens nothyng
hym selfe. for al þe nomb{ur} of þe ylke too fig{ure}s is bot ten.
¶ Questio. Why says he þat a cifre makys a fig{ure} to signifye (tyf)
mor{e} &c. ¶ I speke for þis worde significatyf, ffor sothe it may happe
aft{ur} a cifre schuld come a-noþ{ur} cifre, as þus 2φφ. And ȝet þe
secunde cifre shuld token neu{er} þe mor{e} excep he schuld kepe þe
ord{er} of þe place. and a cifre is no fig{ure} significatyf.
+¶ Q{ua}m p{re}cedentes plus ulti{m}a significabit+ /
[Sidenote: The last figure means more than all the others,
since it is of the highest value.]
Expone þis v{er}se þus. Þe last figu{re} schal token mor{e} þan all{e}
þe oþ{er} afor{e}, thouȝt þ{ere} wer{e} a hundryth thousant figures
afor{e}, as þus, 16798. Þe last fig{ure} þat is 1. betokens ten
thousant. And all{e} þe oþ{er} fig{ure}s b{e}n bot betoken{e} bot sex
thousant seuyn{e} h{u}ndryth nynty & 8. ¶ And ten thousant is mor{e} þen
all{e} þat nomb{ur}, {er}go þe last figu{re} tokens mor{e} þan all þe
nomb{ur} afor{e}.
[Headnote: The Three Kinds of Numbers]
[*leaf 138a]
¶ Post p{re}dicta scias breuit{er} q{uod} tres num{er}or{um}
Distincte species sunt; nam quidam digiti sunt;
Articuli quidam; quidam q{uoque} compositi sunt.
¶ Capit{ulu}m 2^m de t{ri}plice divisione nu{mer}or{um}.
[Sidenote: Digits. Articles. Composites.]
¶ The auctor of þis tretis dep{ar}tys þis worde a nomb{ur} into 3
p{ar}tes. Some nomb{ur} is called digit{us} latine, a digit in englys.
So{m}me nomb{ur} is called articul{us} latine. An Articul in englys.
Some nomb{ur} is called a composyt in englys. ¶ Expone þis v{er}se. know
þ{o}u aft{ur} þe forsayd rewles þ{a}t I sayd afore, þat þ{ere} ben thre
spices of nomb{ur}. Oon{e} is a digit, Anoþ{er} is an Articul, & þe
toþ{er} a Composyt. v{er}sus.
[Headnote: Digits, Articles, and Composites.]
¶ Sunt digiti num{er}i qui cit{ra} denariu{m} s{u}nt.
[Sidenote: What are digits.]
¶ Her{e} he telles qwat is a digit, Expone v{er}su{s} sic. Nomb{ur}s
digitus ben{e} all{e} nomb{ur}s þat ben w{i}t{h}-inne ten, as nyne,
8. 7. 6. 5. 4. 3. 2. 1.
¶ Articupli decupli degito{rum}; compositi s{u}nt
Illi qui constant ex articulis degitisq{ue}.
[Sidenote: What are articles.]
¶ Her{e} he telles what is a composyt and what is an{e} articul. Expone
sic v{er}sus. ¶ Articulis ben[{2}] all{e} þ{a}t may be deuidyt into
nomb{urs} of ten & nothyng{e} leue ou{er}, as twenty, thretty, fourty,
a hundryth, a thousand, & such oþ{er}, ffor twenty may be dep{ar}tyt
in-to 2 nomb{ur}s of ten, fforty in to four{e} nomb{ur}s of ten, & so
forth.
[Sidenote: What numbers are composites.]
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