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Liste des mots-clefs ponctuels

Pour toute correction, suggestion ou demande, contacter :
alain.herreman@univ-rennes.fr

To group keywords related to the same Book, we have sometimes included extended aspects.

Book I

Definitions

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I Déf. 15 : avec/sans

Text having Definition I.15 and having or not having the phrase "until the circumference of the circle" (“πρὸς τὴν τοῦ κύκλου περιφέρειαν”) omitted by Grynée in the definition of a circle.

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I Déf. seg. cercle : 1/3

The definition of a segment of a circle is given in Book I or exclusively in Book III.

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I Déf. seg. cercle+ : Stand/Gn/sans

Stand: Complete version of the definition of a circle segment: A circle segment is the figure contained by both a line and an arc of a circle, larger or smaller than a semicircle.

Gn: Abbreviated version of the definition of a circle segment: A circle segment is the figure contained by both a line and an arc of a circle.

sans: Does not have the definition of a circle segment in Book I.

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I Déf. parallélogramme : avec/sans

With or without the definition of a parallelogram.

Keyword specific to printed editions.

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I Déf. compléments : avec/sans

With or without the definition of complementary parallelograms.

Keyword specific to printed editions.

Demandes

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D+NC=n

The total number of Demands and Common Notions is n (n=9, 14, 15, 16, 17, 23, 24, 36, 48).

For manuscripts, without distinction between text and margin.

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Dn-NCm

n Demandes and m Common Notions ((n, m)=(3,12), (3,13), (3, 14), (3, 20), (4, 20), (4, 44), (5, 4), (5, 9), (5, 10), (6, 9),  (6, 12), (6, 30).

For manuscripts, without distinction between text and margin.

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D4 Clavius : +/-

With or without the Demand added by Clavius:

“Item quacunque magnitudine data, sumi posse aliam magnitudinem vel maiorem, vel minorem”.

Keyword specific to printed editions.

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D5=D/NC

The parallel postulate is a Demand or a Common Notion. 

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D6=D/NC/sans

The principle "Two lines do not enclose an area" is a Demand, a Common Notion, or not present.

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D6 inf./ind.

For texts in Greek, the principle "Two lines do not enclose an area" is in the infinitive or indicative form.

Keyword specific to manuscripts.

Common Notions

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NC droites concourantes : avec/sans

Edition with or without the Common Notion on intersecting lines which, when extended, intersect.

Keyword specific to printed editions.

*

NC droites seg. commun : avec/sans

Edition with or without the Common Notion on the impossibility of two lines having a common segment.

Keyword specific to printed editions.

*

Espace entre droites : D/NC

The principle "Two lines do not enclose an area" is a Demande or a Common Notion.

NC espace entre droites n°x

Numéro du principe “Deux droites ne contiennent pas une aire” (qu’il soit une Demande ou une Notion commune).

Keyword specific to printed editions.

Propositions

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I.11 : I.2/I.3/indét.

The construction of I.11 uses I.2 or I.3 or provides no indication.

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I.15 Por. : avec/sans

Existence or non-existence of a Porism at I.15, without distinguishing variations in wording and its position in the text or margin.

I.18-19/19-18

Order of I.18 and I.19

I.45 : avec/sans

Avec ou sans le problème I.45 demandant la construction d'un parallélogramme dans un angle donné.

Book II

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II.8 : tronqué/complet/autre

With or without the assertion "Or BD is equal to BC" just before the instantiated conclusion preceding the general conclusion. Another possible case for a different proof.

II.14 : triangle/général

Formulation of II.14 for triangles or general formulation for rectilinear figures..

Book III

III.11 dém. : I.20/III.7

The proof of III.11 uses either I.20 or III.7.

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III.12 cercles tangents : 1/2

Propositions III.12 and III.13 regarding externally and internally tangent circles are stated as one proposition or as two separate propositions.

III.13 dém. : III.2/III.12/I.20

The contradiction in the demonstration of the case of the exterior circle is obtained using III.2 or III.12 or I.20.

*

III.37 : avec/sans

With or without proposition III.37.

Book IV

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IV.16 ajout : avec/sans

With or without the addition to IV.16.

Book V

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V scholie : avec/sans tronquée

Text with or without the Vatican preliminary scholium in Book V, possibly truncated.

Definitions

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V Déf. prop. : identité/similitude

Definition of added proportion (ἀναλογία) formulated with "identity" ("identity of ratios") or "similarity" ("similarity of ratios").

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V Déf. prop. : sans

Does not have the added definition of a proportion.

*

V Déf. prop. n°n

The number of the added definition of a proportion is not specified.

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V Déf. 5 : <,=,>/>,=,</=,>,</>,<,=

The order of the relations considered in the definition of being in the same ratio is not specified.

Propositions

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V #props+ : n

Number of additional propositions in Book V.

Keyword specific to printed editions.

Book VI

Definitions

VI Défs : 1-5/1, 2, 5, 3, 4/ 1-4+5 marge/1, 2, 4, 3, 5/1, 2, 5, 4, 3/1-10

Distribution of definitions in Book VI:

  • 1-5;  
  • 1, 2, 5, 3, 4, 1-4+5 margin ;
  • 1, 2, 4, 3, 5 ;
  • 1, 2, 5, 4, 3.
  • 1, 3, 4

*

VI Déf. rapport composé : avec/sans

With or without the definition of a compound ratio.

*

VI Déf. parall. par défaut : avec/sans

With or without the definition of a parallelogram by default.

Keyword specific to printed editions.

*

VI Déf. parall. par défaut+ : +/-

With or without the addition to the definition of a parallelogram by default.

Keyword specific to printed editions.

Propositions

VI #props : n

Number of propositions in Book VI.

*

VI.33 ajout : avec/sans

With or without the Theonine addition.

*

VI.33 ajout : marge/texte

With the Theonine addition in the margin or within the text.

Keyword specific to manuscripts.

Book VII

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VII : avec/sans

With or without Book VII.

Keyword specific to printed editions.

Demandes and Commune Notions

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VII #demandes : n

Number of Demandes in Book VII.

Keyword specific to printed editions and certain medieval versions.

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VII #NC : n

Number of Common Notions in Book VII.

Keyword specific to printed editions and certain medieval versions..

Definitions

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VII Déf. impairement pair : avec/sans

With the definition of an odd-even number.

VII Déf. nombres proport. n° n

The definition number of numbers in proportion is not available.

Keyword specific to printed editions.

VII Déf. nombre parfait n° n

"Definition number of a perfect number."

Keyword specific to printed editions.

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VII Déf. nombre parfait : avec/sans

Version with or without the definition of a perfect number.

Keyword specific to printed editions and certain medieval versions.

*

VII Déf. nombre parfait last/not last

The definition of a perfect number is or is not the last definition.

Mot-clef propre aux imprimés et aux versions médiévales.

VII Déf. mesurer par : avec/sans

With or without the definition of measuring by.

Mot-clef propre aux imprimés et à certaines versions médiévales.

VII Déf. raison double, triple : avec/sans

With or without the definition of a double, triple, etc., ratio.

Mot-clef propre aux imprimés et à certaines versions médiévales.

VII Déf. racines proportion : avec/sans

With or without the definition of two numbers as the roots of a proportion.

Mot-clef propre aux imprimés et à certaines versions médiévales.

VII Déf. racines proportion n°

Definition number of the roots of a proportion.

Keyword specific to printed editions.

Propositions

VII.3 ajout

With or without Grynée's formulation:

Keyword specific to printed editions.

*

VII.20vulgo : avec/sans

With or without VII.20vulgo: if three numbers are in proportion, the product of the extremes is equal to the square of the mean and recipr.

*

VII.22vulgo : avec/sans

With or without VII.22vulgo: if there are three numbers and others equal to them in multitude, taken two by two in the same ratio, and the proportion is disturbed, they will also be in the same ratio with equality of rank.

Book VIII

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VIII.5 ajout : avec/sans

With or without the addition in the construction of VIII.5 concerning composite ratios of ratios followed by a fully lettered second diorism, unlike the first ("Dico igitur ut A ad B, ita esse G ad K" Commandino 1572, p. 103).

Book IX

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IX.19 : 2/3/4 cas

Demonstration of IX.19 in 2, 3, or 4 cases.

Keyword specific to manuscripts.

IX infinité premiers n°n

The proposition number on the existence of an infinity of prime numbers either follows the two problems related to the third and fourth proportional numbers, either 14 or 20.

IX impair par impair n°n

The proposition number on the product of an odd number by an odd number is not specified.

Book X

*

X : avec/sans

Has Book X.

Definitions

X.i #Défs : n

The number of definitions in the first group of definitions in Book X is not specified.

*

X.i ajout proph. : avec/sans

With or without the addition of "prophetic" (related to the existence of commensurable and incommensurable lines).

X.i ajout proph. in déf./comm.

The addition "prophetic" is either integrated into a definition or is a commentary.

Keyword specific to manuscripts.

X.i ajout proph. n°n

Number of the definition containing the "prophetic" addition.

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X Déf.i.1 : grandeurs/quantités

The definition X.i.1 relates to magnitudes or quantities.

Keyword specific to printed editions.

X Déf.i.2a aires/superficies/espaces/surface/aires-superficies/espaces-superficies/indét.

The definition of power-commensurable lines relates to measurements by areas, surfaces, spaces, a surface, areas and surfaces, spaces and surfaces, indeterminate.

Keyword specific to printed editions.

X Déf.i.4 : aires

The definitions given in 4 are related to areas, surfaces, figures, surfaces, indeterminate quantities.

Keyword specific to printed editions.

*

X Déf.i.4 ajout Z : avec/sans

With or without the addition of the definition of irrational areas added by Zamberti (i.e., commensurable to irrational areas).

Keyword specific to printed editions.

Demande and Common Notions

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X : Dn-NCm

There are n Demands and m Common Notions in Book X.

Keyword specific to printed editions.

*

X Ax. Archimède : avec/sans

Avec ou sans l'axiome d'Archimède (Axiom of Archimedes).

Mot-clef propre aux  imprimés.

*

X Ax. Archimède : D/NC

Keyword specific to printed editions.

Propositions

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X.10-11/X.11-10

Propositions X.10 and X.11 are in the order X.10-11 or X.11-10.

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X.13 vulgo : avec/sans lemme/proposition/indét.

Presence or absence of X.13 vulgo and indication of the attributed textual unit or if it is indeterminate.

X.21aliter : avec/sans

lemme/scholie

With or without X.21aliter, inserted before X.21 (Lemma) or after (scholium).

*

X.23 Por.++ : avec/sans

With or without the addition to the addition to the Porism at X.23 (EHS III, 218.1-13).

X.29 n°n

Numéro du problème X.29

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Scholie X.71 : avec/sans texte/marge

Text with or without the Vatican scholium No. 352 at X.71, either in the margin or in the text.

Keyword specific to manuscripts.

*

X.105aliter : 105/fin Livre X

The alternative proofs for X.105-106 are inserted either after them or at the end of Book X.

Book XI

Definitions

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XI Déf. 5 : avec/sans

With or without Definition XI.5 (inclination of a line to a plane).

Propositions

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XI.13 plan donné : avec/sans

With or without the mention of "given plane" in the statement of Proposition XI.13.

Book XIII

Propositions

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XIII analyse-synthèse : avec/sans groupé/séparé

With or without the definitions of analysis and synthesis, plus the proofs for XIII.1-5, grouped (after XIII.5) or separated.