TEXTS ON MUSIC IN ENGLISH
School of Music
University of Nebraska--Lincoln
Lincoln, NE 68588-0100
(phone:  472-2507; Internet: email@example.com)
Data entry: Peter M. Lefferts
Checked by: Peter Slemon
Approved by: Peter M. Lefferts
Fn and Ft: DEPRPA1C_MDTC516
Title: On the nature of proportions
Source: Dublin, Trinity College, 516, f. 129r-v.
[-f.129r-] Incipiunt proporciones discantis in lingua materna.
For ye schall of your proporcions the mor openly knowynge haue after mynn vnderstondynge schale declare them to youe but for the names therof ben mor conuenyent And mor schortly set in latynn thann they wold be yn englyssche therfor Y schall let the names of thaymm stonde stylle in latyn And as schortly As Y kann declare hemm to you in englysshe
First ye schall al vnderstand that proporcioun ys a comparisoun of II thinges be enchesoun of noumbre other of quantyte lyke other onlyke eyther to other so that proporcioun ys seide in IIo maner wyse that ys equalitatis and Inequalitatis
Proporcioun of aqualyte ys when II euen thingys be lyknede or set togeder in comparisoun as 2 to 2 or 4 to 4 and so proporcion of vn[equ]alyte ys when the mor thinge ys set in compar[i]soun to the lesse other the lesse to the more As 2 to 4. 2. to 3.5. or 5.3. And thus proporcioun of vn[equ]alyte hath 5 spyces or 5 kyndes of proporcioun wich names be thys in generall Multiplex superparciens The first spyce of kynde of vn[equ]alyte ys called multiplex that ys to sey many fold and that is whenn the more Noumbre conteyneth the lesse 2 tymes and then yt is callede dupla in speciall and 2 fold as to 2 to 2 or 4 to 2 6 to 3 and so furth endelesly
Yf the mor noumbre conteynn thryes the lesse then yt is called in speciall Tripla as 3 to 2 6 to 2 9 to 3 And yt be 4 tymes the lesse conteyneth in the more then yt is Quadrupla as X to 2 8 to 2 12 to 3 and so furth Quintupla Sexdupla Sepdupla Ocdupla and so furth vpwarde endelesly As for the other kyndys ze schall vnderstann that ther be II maner partids on ys called Aliquota and another [non] Aliquota Aliquota ys when ony party be any maner multiplicacioun zeldeth hys holde as when betwenn hys hole [-f.129v-] And hem ys proporcio multiplex As an vnite pars Aliquota of euery noumbre For by multiplicacioun of that euery noumbre wexit to other ad vnalite Thys pars Aliquota of euery euen noumbre and thus thys party schall be Named in special after the nowmbre be when he ys multiplied and zeldyth the holde for yf he zilde be multiplicacioun of II then he ys calde altera that ys halfe and he zilde his hole by multiplicacioun of III then he ys calde tercia that ys the IIIde party Exemplum 2 is tercia of 6 and 3 of 9 4 of 12 And yf he zilde his hole by multiplicacioun of 4 then yt is calde quarta As 2 to 4 for 4 times 2 is 8 And yf he zilde his hole by multiplicacioun of 5 then yt is calde quinta of 6 sexta and so furth endelesly Pars non aliquota ys when that party by no maner of multiplicacioun may zelde his hole .28.2. is a party of 5 but he ys non aliquota for howe so euere he be multiplyd he maketh not euene 5 For yf he be take twyes yt maketh 4 and yf he be takenn thryes he passeth and make 6 proporcioun Superparticularis ys when the more nowmebre conteyneth the lesse and moreouer a party of hymm that is Aliquota schall that proporcioun be named [proporcioun be named bis] in speciall as bytwene VI and 4 is proporcio Sesque que altera [in gre del.] sesque in grewe is as mich to sey as totum