Literature analysis for language learners: Euclidis Elementa by

Euclidis Elementa by : Difficulty Assessment for Swedish Learners

How difficult is Euclidis Elementa for Swedish learners? We have performed multiple tests on its full text (freely available here) of approximately 42,574, crunched all the numbers for you and present the results below.

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Difficulty Assessment Summary

We have estimated Euclidis Elementa to have a difficulty score of 63. Here're its scores:

Measure Score
easy difficult (1 - 100)
Overall Difficulty 63% 63
Vocabulary Difficulty 89% 89
Grammatical Difficulty 38% 38

Vocabulary Difficulty: Breakdown

89%

Vocabulary difficulty: 89%

This score has been calculated based on frequency vocabulary (the top most frequently used words in Swedish). It combines various measures of Euclidis Elementa's text analyzed in terms of frequency vocabulary: a plain vocabulary score, frequency-weighted vocabulary score, banded frequency vocabulary scores based on vocabulary of the text falling in the top 1,000 or 2,000 most frequent words, etc. Here's a further breakdown of how often the top most frequently used words in Swedish appear in the full text of Euclidis Elementa:

Vocabulary difficulty breakdown for Euclidis Elementa: a test for Swedish top frequency vocabulary

We have also calculated the following approximate data on the vocabulary in Euclidis Elementa:

Measure Score
Measure Score
Number of words 42,574
Number of unique words 4,183
Number of recognized words for names/places/other entities 1,465
Number of very rare non-entity words 6,694
Number of sentences 8,123
Average number of words/sentence 5

There is some research suggesting that that you need to know about 98% of a text's vocabulary in order to be able to infer the meaning of unknown words when reading. If true, this means that you would need to know around 4,099 words (where all the forms of the word are still counted as unique words) in Swedish to be able to read Euclidis Elementa without a dictionary and fully understand it.

Grammatical Difficulty: Breakdown

38%

Grammatical difficulty: 38%

Here is the further grammatical comparison on this text. You can find an explanation of all these scores below.

Measure Score
Measure Score
Automated Readability Index 1
Coleman-Liau Index 3
Type/Token Ratio (TTR) 0.0982525
Root type/Token Ratio (RTTR) 0.0000023078
Corrected type/Token Ratio (CTTR) 0.0000011539
MTLD Index 40
HDD Index 63
Yule's I Index 69
Lexical Diversity Index (MTLD + HD-D + Yule's I) 57

The type-token ratio (TTR) of Euclidis Elementa is 0.0982525. The TTR is the most basic measure of lexical diversity. To calculate it, we divide the number of unique words by the number of words in the text. For example, for this text, the number of unique words is 4,183, while the number of words is 42,574, so the TTR is 4,183 / 42,574 = 0.0982525. However, the TTR is a very crude measure, as it is extremely dependent on text length. The longer the text, the lower the TTR is usually going to be, since common words tend to often repeat. Especially since the number of words in this text is more than 1,000, the TTR is not likely to give an accurate measure.

The root type-token ratio (RTTR) and corrected type-token ratio (CTTR) are measures which were suggested by researchers to partially address the problem of TTR's variance on text length. In the RTTR, the number of unique words is divided by a square of the number of words (therefore, 4,183 / (42,574 * 42,574) = 0.0000023078), while in CTTR, it is divided by a square of the number of words, multiplied twice 4,183 / 2 * (42,574 * 42,574) = 0.0000011539). However, these measures are not as easily readable, and also there is a growing body of research asserting that CTTR and RTTR do not effectively address the problems of text length. Therefore, while we do provide the full text's TTR, RTTR and CTTR on this page, these fiqures do not form part of our final calculations.

The Automated Readability Index (ARI) is one readability measure that has been developed by researchers over the years. The formula for calculating the ARI is as follows:
Formula for calculating the Automated Readability Index

The ARI should compute a reading level approximately corresponding to the reader's grade level (assuming the reader undertakes formal education). Thus, for example, a value of 1 is kindergarten level, while a value of 12 or 13 is the last year of school, and 14 is a sophomore at college. The current ARI of this text is 1, making it understandable for 1-grade students at their expected level of education.

The Coleman Liau Index (CLI) is a similar index designed by Meri Coleman and T. L. Liau, and it is supposed to compute the grade level of the reader (thus, for example, sophomore level material would be around grade 14, or year 14 of formal education, while kindergarten / primary school level material would be close to grade 1 in the CLI). The CLI is usually slightly higher than the ARI. The CLI is computed with this formula:
Formula for calculating the Coleman-Liau Readability Index

It is notable that other indexes exist, such as the Flesch-Kincaid Reading Ease, Gunning-Fog Score, and others, but we have chosen not to include them, since, contrary to the ARI and CLI, such other indexes are based on a syllable count and therefore arguably only work for English and not Swedish.

We compute a further compound lexical diversity index, which should range from 1 to a 100 (with the standard deviation being around 10, and its average value being around 50) - it is 57 in the present case. The compound lexical diversity index consists of the following indexes, averaged out (and also provided in the table above):

  • the Measure of Textual Lexical Diversity (MTLD) index - a measure which is based on computing the TTR for increasingly larger parts of the text until the TTR drops below a certain threshold point (around 0.7 in our case) - in which case, the TTR is reset, and the overall counter is increased; the counter is at the end divided by the number of words in text; as a result, the MTLD does not significantly vary by text length;
  • the Yule's I index (based on Yule's K characteristic inverted) - an index based on the work of the statistician G.U. Yule, who published his index of Frequency Vocabulary in his paper "The statistical study of literary vocabulary"; Yule's I takes into account the number of words in the text, and a compound summed measure of word frequency;
  • the Hypergeometric Distribution D (HD-D) index (based on vocd) - an index which assesses the contribution of each word to the diversity of the text; to calculate such contributions, a hypergeometric distribution is used to compute probabilities of each word appearing in word samples extracted from the text; then such distributions are divided by sample sizes and added up;

Our overall measure of grammatical diversity is based on a combination of the compound lexical diversity index (which includes the MTLD, Yule's I and HD-D indexes), the ARI and CLI, all normalized and given certain weight. The score should normally range from 1 to 100. In this case, the score is 38.

Other Information about Euclidis Elementa by

We provide you a sample of the text below, however, the full text of the Euclidis Elementa is also available free of charge on our website.

Sample of text:

fot = 1000 kub. tum , l kub. famn = 216 kub fot = 27 kub. al nar; o. s. v. Theorem. Rymden af ett prisma är lika stor med producten af dess bas och höjd, Elfte Boken. 211 l:o Hvar och en parallelepiped är lika stor med en rätvinklig parallelepiped, som har lika stor bas, och samma höjd; men denna sednare parallelepipedens rymd är lika stor med producten af hans bas och höjd; derföre måste äfven den förres rymd vara lika stor med producten af hans bas och höjd. 2:o Hvart och ett trekantigt prisma är half-parten af en parallelepiped, som har samma höjd, men dubbelt så stor bas; således är rymden af ett trekantigt prisma lika stor med producten af dess höjd och parallelepipedens halfva, d. v. s. det trekantiga prismats hela bas. 3:o Hvart och ett mångkantigt prisma kan delas i ...

Top most frequently used words in Euclidis Elementa by *

Position Word Repetitions Part of all words
Position Word Repetitions Part of all words
1 och 1,519 3.57%
2 är 902 2.12%
3 en 759 1.78%
4 så 736 1.73%
5 som 596 1.4%
6 med 554 1.3%
7 att 548 1.29%
8 den 534 1.25%
9 lika 512 1.2%
10 af 480 1.13%
11 uti 437 1.03%
12 äro 404 0.95%
13 måste 373 0.88%
14 prop 368 0.86%
15 AB 337 0.79%
16 vinkeln 330 0.78%
17 vara 328 0.77%
18 på 297 0.7%
19 stora 288 0.68%
20 till 286 0.67%
21 de 284 0.67%
22 räta 278 0.65%
23 samma 228 0.54%
24 det 225 0.53%
25 man 222 0.52%
26 stor 216 0.51%
27 rät 210 0.49%
28 således 210 0.49%
29 Om 199 0.47%
30 AC 197 0.46%
31 linea 181 0.43%
32 Bevis 181 0.43%
33 båda 175 0.41%
34 Proposition 174 0.41%
35 Boken 171 0.4%
36 tvänne 170 0.4%
37 skall 165 0.39%
38 triangeln 164 0.39%
39 BC 163 0.38%
40 samt 144 0.34%
41 ABC 144 0.34%
42 då 143 0.34%
43 mot 138 0.32%
44 än 134 0.31%
45 eller 133 0.31%
46 CD 128 0.3%
47 plan 125 0.29%
48 bevisas 125 0.29%
49 Theorem 124 0.29%
50 lineen 123 0.29%
51 hvarandra 123 0.29%
52 lineer 123 0.29%
53 AD 123 0.29%
54 genom 119 0.28%
55 pr 116 0.27%
56 större 114 0.27%
57 derföre 113 0.27%
58 vinkel 111 0.26%
59 vinklarne 109 0.26%
60 äfven 105 0.25%
61 EF 102 0.24%
62 ett 101 0.24%
63 BD 99 0.23%
64 men 97 0.23%
65 sätt 96 0.23%
66 parallela 93 0.22%
67 vinkelrät 93 0.22%
68 hvar 92 0.22%
69 emedan 90 0.21%
70 triangel 87 0.2%
71 kan 86 0.2%
72 bevises 85 0.2%
73 från 83 0.19%
74 11 83 0.19%
75 alla 82 0.19%
76 AE 82 0.19%
77 parallel 82 0.19%
78 gifven 81 0.19%
79 vinklar 80 0.19%
80 sidor 79 0.19%
81 axiom 79 0.19%
82 planet 79 0.19%
83 har 79 0.19%
84 Låt 78 0.18%
85 emot 77 0.18%
86 dessa 76 0.18%
87 qvadraten 75 0.18%
88 cirkel 75 0.18%
89 Ty 75 0.18%
90 sida 74 0.17%
91 hafva 74 0.17%
92 alltså 72 0.17%
93 andra 71 0.17%
94 DF 70 0.16%
95 mindre 69 0.16%
96 cirkeln 69 0.16%
97 gifna 69 0.16%
98 punkt 65 0.15%
99 BE 64 0.15%
100 basen 64 0.15%
101 stå 64 0.15%
102 vid 63 0.15%
103 sidan 63 0.15%
104 hela 62 0.15%
105 nu 62 0.15%
106 Problem 62 0.15%
107 icke 60 0.14%
108 sidorna 59 0.14%
109 imellan 59 0.14%
110 ej 58 0.14%
111 midtitu 57 0.13%
112 Sjette 57 0.13%
113 punkten 57 0.13%
114 lineerna 56 0.13%
115 DEF 56 0.13%
116 sin 55 0.13%
117 drag 55 0.13%
118 deras 53 0.12%
119 dubbelt 53 0.12%
120 trianglarna 52 0.12%
121 FG 52 0.12%
122 CE 52 0.12%
123 annan 52 0.12%
124 ena 51 0.12%
125 skulle 51 0.12%
126 blifver 50 0.12%
127 delar 50 0.12%
128 vore 50 0.12%
129 för 50 0.12%
130 denna 50 0.12%
131 CB 49 0.12%
132 förhållande 49 0.12%
133 bas 49 0.12%
134 tum 49 0.12%
135 skära 48 0.11%
136 medelpunkt 48 0.11%
137 CF 47 0.11%
138 vinkelräta 46 0.11%
139 omkring 45 0.11%
140 Elfte 45 0.11%
141 figur 44 0.1%
142 parallelogram 44 0.1%
143 hvilket 43 0.1%
144 hvars 43 0.1%
145 figuren 43 0.1%
146 hvilka 42 0.1%
147 peripheri 42 0.1%
148 DC 42 0.1%
149 tre 42 0.1%
150 hvadan 41 0.1%
151 rectangeln 41 0.1%
152 DB 41 0.1%
153 medelpunkten 40 0.09%
154 ne 39 0.09%

This list excludes punctuation or single-letter words, also some different-case repeats of the same words.

If you think the text would be accessible to you, you can read it on our site (click on the cover to access):

Cover of Euclidis Elementa by

Other resources and languages

If you like this analysis, you should have a look at out our lists of Swedish short stories and Swedish books.

If you like literature as a means to learn languages - please take a look at our project Interlinear Books. We even have a Swedish Interlinear book available for purchase.