FRANCO MELETTI S. J. 
PROPORTION BETWEEN NUMBER OF WORDS 
AND NUMBER OF FORMS IN THE WORKS 
OF THE "INDEX THOMISTICUS" 
1. THE PROBLEM 
At the conclusion of his long work of elaboration of the Index 
Thomisticus (the concordance of all the works of St. Thomas Aquinas), 
Father ROBERTO BUSA s.j. proposed the following problem to me: 
For each of the 179 elaborated works, we know the exact number 
of words and the exact number of graphic forms. Obviously, from this 
data it also results that the ratio between the number of forms and 
the number of words decreases with an increasing number of words. 
Does a formula exist that will compare two works of different length 
so that one can affirm that one work has comparatively more forms 
than another? For instance, the work with the code number 017-QDI 
contains 10,238 words and 1,471 forms. Does this work have compara- 
tively more or less forms than work 012-QDV which has 114,991 
words and 9,016 forms? 
Father Busa asked me for the pure quantitative data. He also told 
me that he would not interpret or evaluate this data in terms of" lexical 
wealth" as he doubts that anything can be concluded in this regard on 
the basis of this data alone. Indeed, he believes that lexical wealth must 
be measured on the basis of a much wider range of parameters. 
2. THE ANSWER 
Following the process reported below, a relation between the num- 
ber of words (W) and the number of graphic forms (F) has been found: 
it results that this relationship can be expressed with a straight line on 
a bi-logarithmic diagram: 
(i) log F= log A + B' 1o~(W/10,000) 
90 PRANCO MELETTI S. J. 
where log A and B are two constants which characterize the linear 
function. Therefore the function F =f(W) is expressed by a general- 
ized parabola: 
(2) F= A. (W/lo,ooo)" 
The values of A and B are the following for the set of the works 
of the entire Index Thomisticus Corpus and for the various groups of 
works according to the subdivisions indicated below: 
TABLE 1. 
A B 
Index Thomisticus Corpus (n, 179) 2197 0.685 
Thomistic Works (n. 118) 2163 0.660 
Parathomistic Works (n. 61) 2301 0.777 
T~a3LE 2. Thomlstlc Works 
A B 
Proper Works (n. 49) 2114 0.628 
Commentaries (n. 27) 2015 0.702 
Stenographic Reports (n. 24) 2604 0.655 
Works of" Dubious Authent. (n. 18) 1901 0.663 
3. GRAPHIC AND CALCULUS PROCEDURE 
To establish first of all whether a relationship exists between the 
values of W and F in the works of the Index Thomisticus Corpus, the 
points corresponding to couples IV, F are traced on a bi-logarithmic 
diagram, that is with scales log Wand log F. The choice of the logarithmic 
scales was suggested directly by the distribution of the values of W 
and F arranged in increasing order. These values on a logarithmic scale 
would result well distributed along the entire W and F interval. 
From the diagram log W- log F it immediately appeared clear that 
a straight line could well approximate the distribution of the points 
all over the W interval, from minimal to maximal values (see figure 1). 
PROPORTION BETWEEN WORDS AND FORMS " INDEX THOMISTICUS " 91 
I00,000 
10~000 
1,000 
100 
| - j • | , 
100 
..o2..2. ;e • 
~4+~ + • " 
.1-, f', ...... k 1,000 10,000 100,000 
Fig. 1. Words-Forms Diagram 
0 Thomistic Works (n. 118) 
+ Parathomistic Works (n. 61) 
Q Whole Thomistic Corpus 
S 
.s .S 
,I. 1,000,000 10,000,000 
W 
Therefore the relationship between log W and log F is linear as express- 
ed in (1) and the function F=f(W) is as expressed in (2). 
The expression (2) has been preferred to the expression F = A" W B, 
because in (2) the constant A has a significant value, that is the number 
of forms corresponding to 10,000 words, mean value in the interval 
of log W. It is evident that the expressions (1) and (2) are valid only 
within the intervals of the respective works. For lower values of W 
the function F =f(W) obviously links with the straight line F = W, 
which is valid for very short texts. 
The constants log A and B of (1) were computed by least-squares 
polynomial approximation on the logarithmic diagram. 
The complete results of the computations are reported in Tables 3 
92 rl~NCO MELETTI S. J. 
and 4, for the entire Index Thomisticus Corpus; for two major divisions 
of the Corpus: Thomistic Works and Parathomistic Works (works of 
other authors included in the Corpus); for four divisions of Thomistic 
works: Proper Works (OPERA PROPRIA), Commentaries (COM- 
MENTARIA: Aristotle's, Bible's, etc.), Stenographic reports (REPOR- 
TATIONES), works of dubious authenticity (OPERA DUBIAE 
AUTHENTICITATIS). 
In Tables 3 and 4 the following values are reported: 
the constants log A, A, B, 
the log F RMS deviation, that is, the RMS deviation between 
the true values of log F and the mean values of log F computed by (1), 
the max. upper deviation, that is the ratio (Ft,,JF,~,~),~,, for 
values F~,~, > F,,,,,=, 
the max. lower deviation, that is the ratio (F~,,,/F,~,,~),~I,, for 
values F~,., < Fm,,~. 
TABL~ 3. 
Index Thomisticus Corpus 
Thomistic Works 
Parathomistic Works 
log A 
3.3417 
3.3351 
3.3620 
A2--~- L log F RMS deviation 
0.126 = log 1.34 
0.660 0.116 = log 1.30 
2~- 0.-~ 0.126=1ogl.34 
max. \[ max. 
upper i lower devia- devia- 
tion Ilion 
2il/2.0___*_* 
1.83 11/1.73 
17--  
TABLE 4. Thomistic Works 
Proper Works 
Commentaries 
Stenographic Reports 
Works of Dubious 
Authenticity 
log A ! A 
3.--Sgd12-i-ff 
3.3042 2015 
3.4156 2604 
3.2790 1901 
B 
0. f 
0.702 t 
--\[. 
0.655 
0.663 
log F RMS 
deviation 
0.093 = log 1.24 
0.154 = log 1.43 
0.045 = log 1.11 
0.121 = log 1.32 
max. 
upper devia- 
tion 
1.60 
1.73 
1.13 
1.80 
max. 
lower 
devia- 
tion 
1/1.64 
1/1.83 
1/1.45 
111.34 
PROPORTION BETWEEN WORDS AND FORMS " INDEX THOMISTICUS " 93 
4. NOTES, RESERVATIONS AND COMMENTS 
The values of the constants A and B with reference to four divi- 
sions of 118 Thomistic works (Tables 2 and 4) present not significant 
differences, which are included in the random variations. On the other 
hand, the constants A and B of the Thomistic works compared with 
those of the Parathomistic works (Table 1 and 3) present significant 
differences, using the Student-Fisher's test (see Figure 2). 
10,000 
1,000 
100 
100 
I I 
,,"2 
, 1 ..... I I .... 
1,000 10,000 100,000 
Fig. 2. Words-Forms Mean Diagram 
with limits of RMS error. 
Thomistic Works 
Parathomistic Works 
1,000,000 
W 
In Table 4 one can notice that among the Thomistic works the 
Stenographic reports (REPOtLTATIONES), which are distinct from 
the truly dictated works (these are among the proper works), present 
a RMS deviation of F which is about half of that of the other groups 
of Thomistic works; is this a significant fact? 
The straight-line behaviour of the function F =f(W) on the log- 
arithmic diagram is seen along the whole interval of W, from the 
94 FRANCO MELETTI S. J. 
minimum of about W = 200 up to a maximum of about 600,000 words, 
without showing a tendency to flatten with regard to the W axis. 
However the sum of the words of the entire Thomistic Corpus (W = 
10,600,085) presents a number of graphic forms F = 132,125 which 
is lower than the mean (extrapolated) value computed by the expres- 
sion (1); but this point does not much exceed the double of the RMS 
deviation (see figure 1). 
5. LIST OF THE WORKS OF THE CORPUS OF THE INDEX THOMISTICUS 
Serial number, abbreviation, tide, number of words, number of 
graphic forms are reported for every work. 
A) 
001 1SN 
002 2SN 
003 3SN 
004 4SN 
005 SCG 
006 ADL 
007 ST1 
008 ST2 
009 ST3 
010 ST4 
011 QDV 
012 QDV 
013 QDP 
014 QDM 
015 QDS 
016 QDA 
017 QDI 
018 QDV¢ 
019 QDL 
020 OCE 
021 OCG 
022 OSF 
023 OTS 
024 O2D 
025 OCI 
026 OAP 
027 OCtL 
028 OCA 
029 OEE 
030 OPN 
031 OPC 
032 OPX 
OPERA THOMISTICA (Thomistic works) 
1 - OPERA PROI'mA (Proper works) W: from 351 to 597821 
In I Sententiarum 268965 12266 
In 11 Sententiarum 296309 16610 
In m Sententiarum 334431 17504 
In IV Sententiarum 597821 28109 
Summa contra Gentiles 325820 18406 
Autographi deleta 70763 7543 
Summae Theologiae Prima Pars 364483 16906 
Summae Theologiae Prima Secundae 358954 19603 
Summae Theologiae Secunda Secundae 513890 28013 
Summae Theologiae Tertia Pars 336106 21557 
Qu. Disp. de Veritate x-xxu A. 11 Co. 287123 13864 
Qu. Disp. de Veritate xxn A. 11 tLA-Finis 114991 9016 
Qu. Disp. de Potentia 184562 10860 
Qu. Disp. de Malo 180464 12319 
Qu. Disp. de Spirit. Creaturis 35279 4002 
Qu. Disp. de Anima 59920 5190 
Qu. Disp. de Unione Verbi 10238 1471 
Qu. Disp. de Virtutibus 80073 7475 
Quodlibeta I-xx 134153 13209 
Contra Errores Graecorum 16602 2947 
De tkationibus Fidei 9446 2558 
De Forma Absolutionis 3698 1227 
De Substantiis Separatis 21615 3701 
Super Decretalem 7420 1965 
Contra Impugnantes etc. 66708 10375 
De Perfectione Spiritualis Vitae 23626 5224 
Contra Doctrinam 1Letrahentium etc. 19402 5136 
De Unitate Intellectus 14452 2407 
De Ente et Essentia 7318 1255 
De Principiis Naturae 4335 761 
De Motu Cordis 1729 586 
De Mixtione Elementorum 961 376 
W: from 183 to 597821 
PROPORTION BETWEEN WORDS AND FORMS " INDEX THOMISTICUS " 95 
033 OPO De Occultis Operibus Naturae 1917 702 
034 OCM De Aeternitate Mundi 2188 692 
035 OTP. De Sortibus 5203 1863 
036 OTE De Judiciis Astrorum 351 231 
037 OP-.I De P.egimine Judaeorum 1660 788 
038 OP.P De P.egimine Principum 13504 4069 
039 OTT Compendium Theologiae 69896 8371 
040 OSS De Articulis Fidei etc. 6478 2105 
041 OPW De Emptione et Venditione 546 309 
042 OS1 tkesponsio ad Lect. Venetum de art. 30 2147 813 
043 OS2 P.esponsio ad Lect. Venetum de art. 36 3877 1254 
044 OS3 t(esponsio ad Lect. Vercell. de art. 42 3719 1339 
045 OS4 R.esponsio ad Lect. Vercell. de art. 108 8077 1575 
046 OS5 Responsio ad Lect. Bisuntinum 773 422 
047 OS6 Responsio ad Bernardum 754 388 
048 OTC Principium Biblicum 2496 1015 
049 OTD Breve Principium 1271 656 
2 - COMMENTARIA (Commentaries) W: ~om 6596 to 269016 
050 CCM In Libros de Caelo et Mundo 108691 7622 
051 CGC In Libros de Gener. et Corrupt. 21979 2677 
052 CPY In Libros Physicorum 197747 8955 
053 CTC Sententia Libri Ethicorum 199955 12836 
054 CTE Tabula Libri Ethicorum 31905 4951 
055 CPO Sententia Libri Politicorum 56192 6751 
056 CPA In Libros Posteriorum Analyticorum 86684 5538 
057 CME In Libros Metereologicorum 34673 4562 
058 CPE In Libros Perihermeneias 31750 3276 
059 CAN In Libros de Anima II et m 66800 5620 
060 CSS In Libros de Sensu et Sensato 33118 4291 
061 CMt( In Libros de Memoria et Reminiscentia 10629 2044 
062 CMP In Libros Metaphysicorum 260960 11624 
063 CDC In Librum de Causis 29665 3435 
064 CBT In Librum Boethii de Trinitate 41502 5483 
065 CBH In Librum Boethii de Hebdomadibus 6596 1336 
066 CDN In Dionysii de Divinis Nominibus 96689 9245 
067 CIO In Job 115239 16212 
068 CIS In Isaiam 100331 15232 
069 CPH In Hieremiam 58473 10921 
070 CTH In Threnos Hieremiae 12147 3782 
071 CMT Catena Aurea in Matthaeum 269016 29390 
072 CMC Catena Aurea in Marcum 78115 14510 
073 CLC Catena Aurea in Lucam 191638 27765 
074 CJO Catena Aurea in Johannem 175419 19643 
075 CR.O Super Ep. ad t(omanos 131357 13499 
076 C1C Super Iad Cot. I-vii L. 2 38215 6383 
3 - aEPOaTArION~S (Stenographic Reports) 
077 R.QD Quodlibetum x.u 
078 RAN In Aristotelis de Anima L. I 
079 R.SV In Symbolum Apostolorum 
W: from 1668 to 320019 
8300 2194 
23798 3164 
15582 3674 
96 I~RANCO MELETTI S. J. 
080 RSU In Orationem Dominicam 8254 2304 
081 R.ST In Salutationem Angelicam 1668 709 
082 RAC De Duobus Praeceptis Charitatis 16437 4061 
083 tkSB. Sermones 35371 6733 
084 R.PS In Psalmos 193568 18876 
085 ILEM Super Evangelium Matthaei 233176 20597 
086 tkEl Super Evangelium Johannis 320019 22144 
087 I~IL l~.eportationes Ineditae Leoninae 34363 5818 
088 R.1C Super Iad Cor. xr-xvI 54098 7896 
089 R2C Super II ad Cot. 65409 8542 
090 kGL Super ad Galatas 48078 7173 
091 I~.EP Super ad Eph. 48331 7350 
092 ILPL Super ad Philip. 18068 3941 
093 RCL Super ad Coloss. 19190 4170 
094 R1T Super ad Thess. x 12341 3148 
095 B.2T Super ad Thess. a 8456 2346 
096 t~T1 Super ad Thim. I 27755 5589 
097 tkT2 Super ad Thim. n 16816 3981 
098 RTT Super ad Titum 12484 3306 
099 B.PM Super ad Philemonem 3082 1182 
100 R.HE Super ad Hebraeos 100965 11787 
4 -- DUBIAE AUTHENTICITATI$ (Works of dubious authenticity) 
W: from 183 to 17509 
101 DTX De Secreto 795 344 
102 DTI De Natura Verbi Intellectus 2912 689 
103 DP5 De Instantibus 4622 992 
104 DPM De Nat. Materiae et Dimens. Int. 9030 1536 
105 DP9 De Principio Individuationis 1511 511 
106 DPA De Natura Accidentis 1925 553 
107 DPG De Natura Generis 17509 2310 
108 DP4 De Quatuor Oppositis 6842 1206 
109 DP3 De Fallaciis 9820 1621 
110 DPP De Propositionibus Modalibus 753 255 
111 DAS Epistola de Modo Studendi 183 142 
112 DSG Officiumde Festo Corporis Christi 2144 1123 
113 DSR Sermones 6249 2503 
114 DSP Piae Preces 2050 1139 
115 DP2 De Concordantiis Suiipsius 7290 1793 
116 DOA Utrum in Creaturis sit Ordo Agendi 457 217 
117 DIA Qu. de Immortalitate Animae 4883 1199 
118 DLV Utrum A1. de Libro Vitae Deleri possit 2302 593 
\]3) OPERA PAR&THOMISTICA (Works of other authors included in the L T. Corpus) 
W: from 555 to 191110 
Author: Haimo Altissiodorensis O..S.B. t850 c. 
119 XCC In Canticum Exp. I-Salomon Inspiratus 26958 6468 
Author: Richardus de Wedinghausen O. Praem. t 1180 c. 
120 XEM Expositio Missae 3087 1073 
Author: Adamus de Buckfield t 1285 
121 XSV In de Somno et Vigilia 6955 1385 
PROPORTION BETWEEN WORDS AND FORMS " INDEX TFIOMISTICUS " 97 
122 XSM In de Somniis 
123 XDS In de Divinatione per Somnum 
Author: Aegidius de Lessinia O.P. t 1278 c. 
124 XTU De Usurls in Commtmi 
Author: Aegidius de l~oma O.S.A. t 1316 
125 XC2 In Canticum Exp. n- In Principio 
Author: Albertus Magnus O.P. t 1280 
126 XDP De Pulchro et Bono 
127 XPZ De Fato 
Author: Aldobrandinus de Cavalcantibus O.P. t 1279 
128 XAW Sermones pro Dominicis etc. 
Author: Aldobrandinus de Toscanella O.P. t 1292 
129 XSU Insertum in Opusc. in Pater 
Author: Guillelmus Peraldus O.P. t 1271 c. 
130 XRE De Eruditione Principum 
Author: Guillelmus Wheatley t post 1317 
131 XBC In Boethii de Consol. Philos. 
132 XBD In Boethii de Scholarium Disc. 
Author: Helvicus Theutonicus O.P. t 1300 
133 XAO De Dilectione Dei et Proximi 
Author: Hugo de S. Caro O.P. t 1263 
134 XIA Super Apocalypsim I-Vidit Jacob 
Author: Jacobus de Benevento O.P. t 1260/70 
135 XTA De Adventu etc. Antichristi 
136 XTP De Praeambulis ad Judicium etc. 
Author: Joharmis Michaelis O.F.M. t 1320 c. 
137 XDA In Danielem 
138 XMB In Libros Machabaeorum 
Author: Leonardus Pistoriensis O.P. t 1280 c. 
139 XTZ De Praescientia et Praedesfinatione 
Author: Nicolaus de Cotrone t 1260 c. 
140 XFT Liber de Fide Trinitatis 
Author: Nicolaus de Gorran O.P. t 1295 
141 XEC In 7 Epistolas Canonicas 
Author: Petrus de Alvernia t 1304 
142 XCM In de Caelo et Mundo Continuatio 
143 XPO In Politicorum Continuatio 
Author: Petrus de Scala O.P. t 1295 
144 XLM Inserta in Lectura super Matthaeum 
Author: Petrus Johalmis Olivi O.F.M. t 1298 
145 XGN PostiUa in Librum Geneseos 
Author: Petrus de Tarantasia t 1295 (Nic. de Gorran) 
146 X1C Postilla in I ad Corinthios 
Author: Ptolomaeus de Lucca O.P. t 1237 
147 XRP De Regimine Principum Continuatio 
Author: Thomas de Sutton O.P. t 1315 c. 
148 XPF De Pluralitate Formarum 
Author: Matthaeus de Cracovia t 1410 
149 XSC De Modo Cortfitendi et Pur. Consc. 
Author: Vincentius de Castronovo O.P. t 1506 
150 XQP Insertum in Qu. Disp. de Potentia 
151 XQW Insertum in Qu. Disp. de Virtutibus 
4437 999 
2396 718 
21951 3713 
31238 5601 
9154 1604 
5759 1832 
86141 12653 
565 325 
75552 14301 
116573 17726 
56040 13710 
44831 8935 
182105 21074 
12527 3417 
16420 4420 
55605 10720 
31242 7065 
9204 2225 
27730 5013 
89395 13333 
29267 3091 
150392 11332 
14066 3953 
128398 19714 
23711 4865 
44545 9268 
15078 2453 
11922 3658 
11962 2089 
1951 609 
98 FRANCO MELETTI S. J. 
Author: Card. Caietanus O.P. "l" 1533 
152 XPE In Perihermeneias Continuatio 
Unknown Authors: 
153 XGC In de Gener. et Corrupt. Continuatio 
154 XME In Meteorologicorum Continuatio 
155 XPT De Tempore 
156 XP6 De Natura Loci 
157 XPI De Intellectu e Intelligibili 
158 XP8 De Potentiis Animae 
159 XPS De Natura Syllogismorum 
160 XPL De Totius Logicae Aristotelicae Summa 
161 XPV De Inventione Medii 
162 XPU De Universalibus I 
163 XU2 De Universalibus 
164 XSA De Vener. Sacramento Altaris 
165 XSE De Sacramento Eucharistiae 
166 XTH De Humanitate J.C.D.N. 
167 XTM De Divinis Moribus 
168 XTB De Beatitudine 
169 XSO De Officio Sacerdotis 
170 XAV De Vitiis et Virtutibus 
171 X2A Expositio II super Apocalypsim-Vox Domini 
172 XPB De Motoribus Corporum Caelestium 
173 XSIL Sermo: Intravit l~ex 
174 XSX Offlcium de Festo S. Augustini 
175 XPD De Demonstratione 
176 XNB Qu. de Natura Beatitudinis 
177 XUN De Universalibus 
178 XAM De Arte Musica 
179 XM2 Ars Musyce 
30203 3380 
31602 3462 
39760 5333 
5240 931 
2880 679 
1620 497 
6300 1584 
2863 689 
55779 4500 
555 151 
3272 794 
2688 653 
37820 7806 
7285 2150 
44809 8917 
4850 2037 
13743 3847 
9248 2755 
4666 2086 
191110 19079 
2283 743 
1583 707 
1581 960 
891 248 
1371 476 
6456 1062 
1866 762 
5024 1766 
