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Trismegistos 64346 = LDAB 5568 = michigan.apis.2701



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Canonical URI: http://papyri.info/dclp/64346

DCLP/LDAB Data [xml]

Title Mathematical text: a table of parts
Principal Edition 95951. Giuseppina Azzarello, "SB XX 15071 + P.Mich. III 146: The American journey of a parted "Table of Parts"," ArchPF, 65 (2019), pp. 52-98. https://doi.org/10.1515/apf-2019-0004
Partial Edition
  • - 61068. P.J. Sijpesteijn, "Varia papyrologica II.," ZPE, 81 (1990), pp. 245-251. http://www.jstor.org/stable/20187265
  • - 3559. John Garrett Winter, Michigan Papyri. Volume III. Papyri in the University of Michigan Collection: Miscellaneous Papyri., (Ann Arbor 1936). 146
  • - 14993. Hans-Albert Rupprecht and Joachim Hengstl eds., Sammelbuch Griechischer Urkunden aus Ägypten. Zwanzigster Band (Nr. 14069-15202)., (Wiesbaden 1997). 15071
Catalog(s) MP3 02312.350
Fragments Princeton, University Library Garrett deposit 9556; Ann Arbor, Michigan University, Library P. 621
Support Material papyrus
Date 200 - 399
More from the period between 200 CE and 399 CE
Origin Fundort: Egypt; Schreibort: Egypt
More from Fundort: Egypt; Schreibort: Egypt
Form and Layout papyrus sheet? (columns: 2, pagination: 0)
Genre mathematics; division table
Culture science
Images quod.lib.umich.edu/.../x-2701
Print Illustrations ZPE 81 (1990), pl. 8 b; A. Verhoogt, Discarded, discovered, collected. The University of Michigan papyrus collection (2017), p. 88-89
Availability © Digital Corpus of Literary Papyri. This work is licensed under a Creative Commons Attribution 3.0 License .

Trismegistos: 64346 [source]

Publications ZPE 81 (1990), p. 246 no. 2 (Sijpesteijn, Pieter Johannes; 1990) = SB 20 15071 (Rupprecht, Hans-Albert; 1997)
Inv. no. Princeton, University Library Garrett deposit 9556
Date AD 200 - 399
Language Greek
Provenance Egypt[found & written]

Catalog Record: michigan.apis.2701 [xml]

Title Table of Fractions
Author Unknown
Summary Table of fractions, beginning with the last part of the sevenths and ending with the eighteenths (a heading "nineteenths" follows, but the table was never filled in). Accents distinguishing fractions from integers were added afterwards, with a few mistakes.
Citations Robbins FE, CP 18, 328-333, 1923 Robbins FE, PMich III, 146, 1936
Inv. Id P.Mich.inv. 621
Support/Dimensions 1 papyrus ; About 106.75 x 9.2 cm
Condition Broken (or cut) off on the left
Lines Col. I - 12;;col. II - 15;;col. III - 15;;col. IV - 14;;col. V - 14;;col. VI - 14;;col. VII - 15;;col. VIII - 15;;col. IX - 12;;col. X - 13;;col. XI - 14;;col. XII - 15;;col. XIII - 16;;col. XIV - 16;;col. XV - 16;;col. XVI - 15;;col. XVII - 14;;col. XVIII - 13;;col. XIX - 1
Recto/Verso Source of description: Recto
Hands Clear, uniform hand (Robbins)
Origin Unknown
More from Unknown
Language Greek
Date IVth century A.D.
More from the period between 300 CE and 399 CE
Note (general) Location: Ann Arbor
Note (general) Pub. status: Recto; Verso is blank
Subjects Greek literature.; Mathematics, Greek.; Mathematics, Ancient--Study and teaching.; Fractions.; Literary: Mathematical; Papyrus
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License Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 License.

Introduction

Transcribing this text for papyri.info required a number of departures from the critical edition of Azzarello 2019, principally as regards the handling of the small oblique strokes (or ‘ticks’) that accompany whole numbers and fractions on papyri. Where Azzarello’s text supplements these (if they are missing), and expunges them (if they were added superfluously), papyri.info is unable to render these ‘ticks’ within angled or curly brackets. The text transcribed here, therefore, is that of the papyrus: where a tick is present on the papyrus – even in error – it is encoded; when one is absent it is not, even if the number is a fraction and would normally be expected to include one. The exception to this practice is where ticks are marked on the papyrus beside each digit in a double or triple-digit fraction (e.g., col. i.4 where λ´ ε´ = 1/35): in such cases, papyri.info can only render a single tick even if two appear on the papyrus (λε´ instead of λ´ ε´). The commentary notes other curiosities involving ticks.

The first two columns are preserved by SB 20 15071; the rest are on P.Mich. 3 146.

DCLP transcription: 64346 [xml]

column i
[Ἕβδο]μα̣´(*)
[τῆς] α̣ τὸ ζ´ ζ´(*)
[τὸ] ζ´ ω´ ν´ζ´ ζ´(*)
[τῶν] β̣ δ´ κη´(*)
5[τῶν] γ̣ γ´ ιε´ λε´(*)
[τῶν] δ̣ 𐅵´ ι̣δ´(*)
[τῶν ε] 𐅷̣´ κ̣α´(*)
[τῶν ϛ 𐅵 γ´ μβ´]
[τῶν ζ] α
10[τῶν η] α̣´ ζ´
[τῶν θ] α´ δ´ κη´
[τῶν ι] α´ γ´ ιε´ λε´(*)
[τῶν κ β] 𐅵̣´ γ̣´ μ̣β̣´
[τῶν λ δ δ´ κη´] column ii
15[τ]ῶ̣ν̣ μ ε´ 𐅷̣´ κ̣α̣´
τῶν ν ζ´ ζ´
τῶν ξ η´ 𐅵´ ιδ´
τῶ̣ν ο ι̣´
τῶ̣ν π ια´ γ´ ι̣ε´ λε´(*)
20τῶν ϙ ιβ´ 𐅵´ γ´ μβ´
τ̣ῶν(*) ρ ιδ´ δ´ κη´
τῶ̣ν̣ σ̣ κη 𐅵̣ ιδ´
τῶ̣ν τ̣ μβ´ 𐅵̣ γ´ μβ´
τῶν̣ υ νζ´ ζ´
25τῶν φ οα´ γ´ ιε´ λ[ε]´(*)
τῶν χ πε´ 𐅷´ κα´
τῶν̣ ψ ρ´
[τῶν] ω ριδ´ δ´ κη´
[τῶν] Ϡ ρκη 𐅵 ιδ column iii
30[τῶν Ἀ] ρ´ μ´ β´ 𐅵´ γ´ μβ´
[τῶν 'Β] σ´ π´ ε´ 𐅷´ κα´
[τῶν 'Γ] υ´ κ´ η´ 𐅵´ ιδ´
[τῶν 'Δ] φ´ ο´ α´ γ´ ιε´ λε´
[τῶν 'Ε] ψ´ ι´ δ´ δ´ κη´
35[τῶν 'Ϛ] ω´ ν´ ζ´ ζ´
[τῶν 'Ζ] Ἀ´
[τῶν 'Η] Ἀ´ ρ´ μ´ β´ 𐅵´ γ´ μβ´
[τῶν 'Θ] Ἀ´ σ´ π´ ε´ 𐅷´ κα´
[τῶν μ(υριάς) \α/´] Ἀ´ υ´ κ´ η´ 𐅵´ ιδ´
40[—]
[Ὄ]γδα(*)´
[τῆς] α̣ τὸ η´ η´
[τὸ] η̣´ ψ´ ν´ column iv
τῶν β δ´
45τῶν γ δ´ η´
τῶν δ 𐅵´
τῶν ε 𐅵´ η´
τῶν ϛ 𐅵´ δ´
τῶν ζ 𐅵´ δ´ η´
50τῶν η α
τῶν θ α´ η´
τῶν ι α´ δ´
τῶν κ β´ 𐅵´
τῶν λ γ´ 𐅵´ δ´
55τῶν μ ε´
τῶν ν ϛ´ δ´
τῶν ξ ζ 𐅵´
τῶν ο η´ 𐅵´ δ´ column v
τῶν π ι
60τῶν ϙ ι´ α´ δ´
τῶν ρ ι´ β´ 𐅵´
τῶν σ κ´ ε´
τῶν τ λ´ ζ´ 𐅵´
τῶν υ ν´
65τῶν φ ξ´ β´ 𐅵´
τῶ[ν] χ ο´ ε´
τῶν ψ π´ ζ´ 𐅵´
τῶν ω ρ´
τῶν Ϡ ρ´ ι´ β´ <𐅵´>
70τῶν Ἀ ρ´ κ´ ε´
τῶν 'Β σ´ ν´
τῶν 'Γ τ´ ο´ ε´
τῶν 'Δ φ´ column vi
τῶν Ἐ χ´ κ´ ε´
75τῶν 'Ϛ ψ´ ν´
τῶν 'Ζ ω´ ο´ ε´
τῶν Ἠ Ἀ
τῶν 'Θ Ἀ ρ´ κ´ ε´
τῶν μ(υριάς) \α/´ Ἀσ´ ν´
80—
Ἔνατα
τῆς α τὸ θ´ θ´
τὸ θ´ χξϛ 𐅷
τῶν β ϛ´ ιη´
85τῶν γ γ´
τῶν δ γ´ θ´
τῶν ε 𐅵´ ιη´
τῶν ϛ 𐅷 column vii
τῶν ζ 𐅷´ θ´
90τῶν η 𐅵 γ´ ιη´
τῶν θ α´
τῶν ι α´ θ´
τῶν κ β´ ϛ´ ιη´
τῶν λ γ´ γ´
95τῶν μ δ´ γ´ θ´
τῶν ν ε´ 𐅵´ ιη´
τῶν ξ ϛ´ 𐅷´
τῶν ο ζ´ 𐅷´ θ´
τῶν π η´ 𐅵´ γ´ ιη´
100τῶν ϙ ι´
τῶν ρ ι´ α´ θ´
τῶν σ κ´ β´ ϛ´ ιη´ column viii
τῶν τ λ´ γ´ γ´
τῶν υ μ´ δ´ γ´ θ´
105τῶν φ ν´ ε´ 𐅵´ ιη´
τῶν χ ξ´ ϛ´ 𐅷´
τῶν ψ ο´ ζ´ 𐅷´ θ´
τῶν ω π´ η´ 𐅵´ γ´ ιη´
τῶν Ϡ ρ´
110τῶν Ἀ ρ´ ι´ α´ θ´
τῶν 'Β σ´ κ´ β´ ϛ´ ιη´
τῶν 'Γ τ´ λ´ γ´ γ´
τῶν 'Δ υ´ μ´ δ´ γ´ θ´
τῶν Ἐ φ´ ν´ ε´ 𐅵 ιη´
115τῶν 'Ϛ χ´ ξ´ ϛ´ 𐅷´
τῶν 'Ζ ψ´ ο´ ζ´ 𐅷´ θ´ column ix
τῶν Ἠ ω´ π´ η´ 𐅵´ γ´ ιη´
τῶν 'Θ Ἀ´
τῶν μ(υριάς) \α/´ Ἀ´ ρ´ ι´ α´ θ´
120—
Δέκατα´
τῆς α τὸ ι´ ι´
τὸ ι χ´
τῶν β ε´
125τῶν γ ε´ ι´
τῶν δ γ´ ιε´
τῶν ε 𐅵
τῶν ϛ 𐅵 {  ̣´} <ι´>
τῶν ζ 𐅵 ε´
130τῶν η 𐅷 ι´ λ´
τῶν θ 𐅵 γ´ ιε´
τῶν ι α column x
τῶν(*) κ β
τῶν λ γ
135τῶν μ δ
τῶν ν ε
τῶν ξ ϛ
τῶν ο ζ
τῶν π η
140τῶν ϙ θ
τῶν ρ ι
τῶν σ κ
τῶν τ λ
τῶν υ μ
145τῶν φ ν
τῶν χ ξ
τῶν ψ ο column xi
τῶν ω π
τῶν Ϡ ϙ
150τῶν Ἀ ρ
τῶν 'Β σ
τῶν 'Γ τ
τῶν 'Δ υ
τῶν Ἐ φ
155τῶν 'Ϛ χ
τῶν 'Ζ ψ
τῶν Ἠ ω
τῶν 'Θ Ϡ
τῶν μ(υριάς) \α/ τῶν Ἀ
160— column xii
[ἑνδέ]κͅατα
τῆς α τὸ ια´ ια´
τὸ ια φ´ μ´ ε´ γ´ ια´ λγ´
τῶν β ϛ´ ξϛ´
165τῶν γ δ´ μδ´
τῶν δ γ´ λγ´
τῶν ε´ γ´ ια´ λγ´
τῶν ϛ 𐅵 κβ´
τῶν ζ 𐅵 ια´ κβ´
170τῶν η 𐅷´ κβ´ ξϛ´
τῶν θ 𐅵 δ´ κβ´ μδ´
τῶν ι 𐅵 γ´ κβ´ λγ´
τῶν ια α
— column xiii
175Δωδέκατα
τῆς α τὸ ιβ ιβ
τὸ ιβ φ
τῶν β ϛ´
τῶν γ δ´
180τῶν δ γ´
τῶν ε γ´ ιβ
τῶν ϛ 𐅵
τῶν ζ 𐅵 ιβ
τῶν η 𐅷
185τῶν θ 𐅷 ιβ̣
τῶν ι 𐅵 γ´
τῶν ια 𐅵 γ´ ιβ´
τῶν ιβ α´
— column xiv
190τρ̣ε̣ι̣σ̣κ̣αι̣δέκατα
τῆς α τὸ ιγ´ ιγ´
τὸ ιγ υ´ ξ´ α´ 𐅵 κϛ´
τῶν β ζ´ ϙα´
τῶ̣ν̣ γ ϛ´ κϛ´ λθ´
195τῶ̣ν̣ δ δ´ κϛ´ νβ´
τῶν ε γ´ κϛ οη
τῶν ϛ γ´ ιγ´ κϛ´ οη´
τῶν ζ 𐅵 κϛ´
τῶν η 𐅵 ιγ´ κϛ´ {οη´}
200τῶν θ 𐅷´ λθ´
τῶν ι 𐅷 ιγ λθ
τῶν ια 𐅵 γ´ οη´
τῶν ιβ 𐅵 γ ιγ {κϛ´} οη
τ̣ῶ̣ν̣ ιγ α
205<—> column xv
Τεσσαρ̣εσκαιδέκατα
τῆς α τὸ ιδ´ ιδ´
τὸ ιδ υ´ κ´ η´ 𐅵´ ιδ´
τῶν β ζ´
210τῶν γ ζ´ ιδ´
τῶν δ δ´ κη
τῶν ε δ´ ιδ´ κη´
τῶν ϛ γ´ ιε´ λε´
τῶν ζ 𐅵
215τῶν η 𐅵 ιδ´
τῶν θ 𐅵´ ζ´(*)
τῶν ι 𐅷´ κα´
τῶν ια 𐅷´ ιδ´ κη´(*)
τῶν ιβ 𐅵 γ´ μβ´
220τῶν ιγ 𐅵´ γ´ ιδ´ μβ´
τῶν ιδ α
— column xvi
Πεντεκαιδέκατα
τῆς α τὸ ιε´ ιε´
225τὸ ιε υ´
τῶν β ι´ λ´
τῶν γ ε´
τῶν δ ε´ ιε´
τῶν ε γ´
230τῶν ϛ γ´ ιε´
τῶν ζ γ´ ι λ
τῶν η 𐅵 λ´
τῶν θ 𐅵 ι
τῶν ι 𐅵 {γ´} <ϛ´>
235τῶν ια 𐅵´ {γ´} <ϛ´> ιε´
τῶν ιβ 𐅷 ι λ
τῶν ιγ 𐅵 γ´ λ´
τῶν ιδ 𐅵 γ´ ι´ column xvii
τῶν ιε α
240<—>
ἑκκαιδέκατα´
τῆς α τὸ ιϛ´ ιϛ´
τὸ ιϛ τοε
τῶν β η´
245τῶν γ η´ ιϛ´
τῶν δ δ´
τῶν ε δ´ ιϛ´
τῶν ϛ δ´ η´
τῶν ζ δ´ η´ ιϛ´
250τῶν η 𐅵
τῶν θ 𐅵´ ιϛ´
τῶν ι 𐅵´ η´
τῶν ια 𐅵´ η´ ιϛ´
τῶν ιβ 𐅵´ δ´
255τῶν ιγ 𐅵´ δ´ ιϛ´ column xviii
τῶν ιδ 𐅵´ δ´ η´
τῶν ιε 𐅵´ δ´ η´ ιϛ´
τῶν ιϛ α´
—
260 ἑπτακαιδέκατα
τῆς α τὸ ιζ ιζ
τὸ [ι]ζ τ´ ν´ β´ 𐅵´ γ´ ιζ´ λδ´ να´
τῶ[ν] β̣ ιβ´ να´ ξη´
τῶ[ν γ] ιβ´ ιζ´ να´ ξη´
265τῶ[ν δ] ιβ´ ιε´ ιζ´{λδ´ να´} <ξη´ πε´>
τ[ῶν] ε δ´ λδ´ ξη´
τῶ̣ν̣ ϛ´ γ´ να´
τῶ̣ν̣ ζ γ´ ιζ´ να´
τῶν η γ´ ιε´ ιζ´ πε´
270τῶ̣ν θ 𐅵´ λδ´
τῶ̣ν ι 𐅵´ ιζ´ λδ´ column xix
τῶν ια 𐅵 ιβ´ {ιζ´} λδ´ να´ [ξ]η̣´
τῶν ιβ 𐅵 ιβ´ ιζ´ λδ´ να´ ξη´
τῶν ιγ 𐅵´ δ´ ξη´
275τῶν ιδ 𐅵´ δ´ ιζ´ ξη´
τῶν ιε 𐅵´ δ´ ιζ´ λδ´ ξη´(*)
τῶν ιϛ 𐅵 γ´ ιζ´ λδ´ να´
τῶν ιζ α
—
280 ὀκτωκαιδέκατα
τῆς α´ τὸ ιη´ ιη´
τὸ ιη τ´ λ´ γ´ γ´
τῶν β θ´
τῶν γ θ´ ιη´
285τῶν δ ϛ´ ιη´
τῶν ε ϛ´ θ´ column xx
τῶν ϛ γ´
τῶν ζ γ´ ιη´
τῶν η γ´ θ´
290τῶν θ 𐅵
τῶν ι 𐅵 ιη´
τῶν ια 𐅵 θ´
τῶν ιβ 𐅷´
τῶν ιγ 𐅷 ιη
295τῶν ιδ 𐅷 θ
τῶν ιε 𐅵 γ´
τῶν ιϛ 𐅵´ γ´ ιη´
τῶν ιζ 𐅵´ γ´ θ´
τῶν ιη α´
300— column xxi
ἐννεακαιδέκατα
⁦ vac. ? ⁩

Apparatus


^ i.1. τ̣[ῆς] α´ prev. ed.
^ i.2. τὸ ζ´ ζ´ prev. ed.
^ i.3. [τὸ ζ´ ψήφων] ω´ ν´ ζ´ζ´ prev. ed.
^ i.4. [τῶν β] δ´ κη´ prev. ed.
^ i.5. [τῶν γ] γ´ ια´ λε´ prev. ed.
^ i.6. [τῶν δ ] 𐅵´ ι̣δ´ prev. ed.
^ i.7. [τῶν ε 𐅷´] κ̣α̣´ prev. ed.
^ i.12. [τῶν ι] α´ γ´ ια´ λε´ prev. ed.
^ ii.19. τ̣ῶν π ια´ ια̣´ λε´ prev. ed.
^ ii.21. τῶ̣ν prev. ed.
^ ii.25. φ οα´ γ´ ια´ λ[ε]´ prev. ed.
^ iii.41. l. [Ὄ]γδοα
^ x.133. corr. ex τωβ̣
^ xv.216. corr. ex
^ xv.218. pap. : τῶν ια 𐅷´ ιδ´ κη´ <πδ´> Azzarello
^ xix.276. pap. : 𐅵´ {δ´ ιζ´} <γ´> λδ´ ξη´ <σδ´> Azzarello

Editorial History; All History; (detailed)

Creative Commons License © Duke Databank of Documentary Papyri. This work is licensed under a Creative Commons Attribution 3.0 License.

Notes

  • 26.

    The tick on κα is in a lacuna but has been restored by Azzarello.

  • 43.

    The tick on η is in a lacuna but has been restored by Azzarello.

  • 113.

    The tick on γ is in a lacuna but has been restored by Azzarello.

  • 281.

    The scribe added ticks to both the tau and omicron of the article τό.

APIS Translation (English)

(Col. I);[Of 1000, the 1/7th =] 142 1/2 1/3 1/42;[Of 2000 =] 285 2/3 1/21;[Of 3000 =] 428 1/2 1/14;[Of 4000 =] 571 1/3 1/15 1/35;[Of 5000 =] 714 1/4 1/28;[Of 6000 =] 827 1/7;[Of 7000 =] 1000;[Of 8000 =] 1142 1/2 1/3 1/42;[Of 9000 =] 1285 2/3 1/21;[Of 10000 =] 1428 1/2 1/14;Eighths:;[Of 1, the 1/8th=] 1/8;[the 1/8th (of 6000) =] 750;;(Col. II);Of 2 =1/4;Of 3 = 1/4 1/8;Of 4 = 1/2;Of 5 = 1/2 1/8;Of 6 = 1/2 1/4;Of 7 = 1/2 1/4 1/8;Of 8 = 1;Of 9 = 1 1/8;Of 10 = 1 1/4;Of 20 = 2 1/2;Of 30 = 3 1/2 1/4;Of 40 = 5;Of 50 = 6 1/4;Of 60 = 7 1/2;Of 70 = 8 1/2 1/4;;(Col. III);Of 80 = 10;Of 90 = 11 1/4;Of 100 = 12 1/2;Of 200 = 25;Of 300 = 37 1/2;Of 400 = 50;Of 500 = 62 1/2;Of 600 = 75;Of 700 = 87 1/2;Of 800 = 100;Of 900 = 112 <1/2>;Of 1000 = 125;Of 2000 = 250;Of 3000 = 375;Of 4000 = 500;;(Col. IV);Of 5000 = 625;Of 6000 = 750;Of 7000 = 875;Of 8000 = 1000;Of 9000 = 1125;Of 10000 = 1250;Ninths:;Of 1, the 1/9th = 1/9;The 1/9th (of 6000) = 666 2/3;Of 2 =1/6 1/18;Of 3 = 1/3;Of 4 = 1/3 1/9;Of 5 = 1/2 1/18;Of 6 = 2/3;;(Col. V);Of 7 = 2/3 1/9;Of 8 = 1/2 1/3 1/18;Of 9 = 1;Of 10 = 1 1/9;Of 20 = 2 1/6 1/18;Of 30 = 3 1/3;Of 40 = 4 1/3 1/9;Of 50 = 5 1/2 1/18;Of 60 = 6 2/3;Of 70 = 7 2/3 1/9;Of 80 = 8 1/2 1/3 1/18;Of 90 = 10;Of 100 = 11 1/9;Of 200 = 22 1/6 1/18;;(Col. VI);Of 300 = 33 1/3;Of 400 = 44 1/3 1/9;Of 500 = 55 1/2 1/18;Of 600 = 66 2/3;Of 700 = 77 2/3 1/9;Of 800 = 88 1/2 1/3 1/18;Of 900 = 100;Of 1000 = 111 1/9;Of 2000 = 222 1/6 1/18;Of 3000 = 333 1/3;Of 4000 = 444 1/3 1/9;Of 5000 = 555 1/2 1/18;Of 6000 = 666 2/3;Of 7000 = 777 2/3 1/9;;(Col. VII);Of 8000 = 888 1/2 1/31/18;Of 9000 =1000;Of 10000 = 1111 1/9;Tenths:;Of 1, the 1/10th = 1/10;The 1/10th (of 6000) = 600;Of 2 =1/5;Of 3 = 1/5 1/10;Of 4 = 1/3 1/15;Of 5 = 1/2;Of 6 = 1/2 1/10;Of 7 = 1/2 1/5;Of 8 = 2/3 1/10 1/30;Of 9 = 1/2 1/3 1/15;Of 10 = 1;;(Col. VIII);Of 20 = 2;Of 30 = 3;Of 40 = 4;Of 50 = 5;Of 60 = 6;Of 70 = 7;Of 80 = 8;Of 90 = 9;Of 100 = 10;Of 200 = 20;Of 300 = 30;Of 400 = 40;Of 500 = 50;Of 600 = 60;Of 700 = 70;;(Col. IX);Of 800 = 80;Of 900 = 90;Of 1000 = 100;Of 2000 = 200;Of 3000 = 300;Of 4000 = 400;Of 5000 = 500;Of 6000 = 600;Of 7000 = 700;Of 8000 = 800;Of 9000 =900;Of 10000 = 1000;;(Col. X);Elevenths:;Of 1, the1/11th = 1/11;The 1/11th (of 6000) = 545 1/3 1/11 1/33;Of 2 =1/6 1/66;Of 3 = 1/4 1/44;Of 4 = 1/3 1/33;Of 5 = 1/3 1/11 1/33;Of 6 = 1/2 1/22;Of 7 = 1/2 1/11 1/22;Of 8 = 2/3 1/22 1/66;Of 9 = 1/2 1/22 1/44;Of 10 = 1/2 1/3 1/22 1/33;Of 11 = 1;;(Col. XI);Twelfths:;Of 1, the 1/12thj = 1/12;The 1/12th (of 6000) = 500;Of 2 =1/6;Of 3 = 1/4;Of 4 = 1/3;Of 5 = 1/3 1/12;Of 6 = 1/2;Of 7 = 1/2 1/12;Of 8 = 2/3;Of 9 = 2/3 1/12;Of 10 = 1/2 1/3;Of 11 = 1/2 1/3 1/12;Of 12 = 1;;(Col. XII);Thirteenths:;Of 1, the 1/13th = 1/13;The 1/13th (of 6000) = 461 1/2 1/26;Of 2 =1/7 1/91;Of 3 = 1/6 1/26 1/39;Of 4 = 1/4 1/26 1/52;Of 5 = 1/3 1/26 1/78;Of 6 = 1/3 1/13 1/26 1/78;Of 7 = 1/2 1/26;Of 8 = 1/2 1/13 1/26 {1/78};Of 9 = 2/3 1/39;Of 10 = 2/3 1/13 1/39;Of 11 = 1/2 1/3 1/78;Of 12 = 1/2 1/3 1/13 {1/26} 1/78;Of 13 = 1;;(Col. XIII);Fourteenths:;Of 1, the 1/14th = 1/14;The 1/14thj (of 6000) = 428 1/2 1/14;Of 2 =1/7;Of 3 = 1/7 1/14;Of 4 = 1/4 1/28;Of 5 = 1/4 1/14 1/28;Of 6 = 1/3 1/15 1/35;Of 7 = 1/2;Of 8 = 1/2 1/14;Of 9 = 1/2 1/7;Of 10 = 2/3 1/21;Of 11 = 2/3 1/14 1/28 <Should be: 1/2 1/4 1/28>;Of 12 = 1/2 1/3 1/142;Of 13 = 1/2 1/3 1/14 1/42;Of 14 = 1;;(Col. XIV);Fifteenths:;Of 1, the 1/15th = 1/15;The 1/15th (of 6000) = 400;Of 2 = 1/10 1/30;Of 3 = 1/5;Of 4 = 1/5 1/15;Of 5 = 1/3;Of 6 = 1/3 1/15;Of 7 = 1/3 1/10 1/30;Of 8 = 1/3 1/5;Of 9 = 1/2 1/10;Of 10 = 1/2 1/3 <Should be: 2/3>;Of 11 = 1/2 1/3 1/15 <Should be: 2/3 1/15>;Of 12 = 2/3 1/10 1/30;Of 13 = 1/2 1/3 1/30;Of 14 = 1/2 1/3 1/10;;(Col. XV);Of 15 = 1;Sixteenths:;Of 1, the 1/16th = 1/16;The 1/16th (of 6000) = 375;Of 2 = 1/8;Of 3 = 1/8 1/16;Of 4 = 1/4;Of 5 = 1/4 1/16;Of 6 = 1/4 1/8;Of 7 = 1/4 1/8 1/16;Of 8 = 1/2;Of 9 = 1/2 1/16;Of 10 = 1/2 1/8;Of 11 = 1/2 1/8 1/16;Of 12 = 2/3 1/14;Of 13 = 1/2 1/4 1/16;;(Col. XVI);Of 14 = 1/2 1/4 1/8;Of 15 = 1/2 1/4 1/8 1/16;Of 16 = 1;Seventeenths:;Of 1, the 1/17th = 1/17;The 1/17th (of 6000) = 352 1/2 1/3 1/17 1/34 1/51;Of 2 = 1/12 1/51 1/68;Of 3 = 1/12 1/17 151 1/68;Of 4 = 1/12 1/15 1/17 1/34 1/51 <Should be: 1/12 1/15 1/17 1/68 1/85>;Of 5 = 1/4 1/34 1/68;Of 6 = 1/3 1/51;Of 7 = 1/3 1/17 1/51;Of 8 = 1/3 1/15 1/17 1/85;Of 9 = 1/2 1/34;Of 10 = 1/2 1/17 1/34;;(Col. XVII);Of 11 = 1/2 1/12 1/17 1/34 1/51 <Should be: 1/2 1/12 1/34 1/51 1/68>;Of 12 = 1/2 1/12 1/17 1/34 1/51 1/78;Of 13 = 1/2 1/4 1/68;Of 14 = 1/2 1/4 1/17 1/68;Of 15 = 1/2 1/17 1/34 1/68 <Should be: 1/2 1/3 1/34 1/51>;Of 16 = 1/2 1/3 1/17 1/34 1/51;Of 17 = 1;Eighteenths:;Of 1, the 1/18th = 1/18;The1/18th (of 6000) = 333 1/3;Of 2 = 1/9;Of 3 = 1/9 1/18;Of 4 = 1/6 1/18;Of 5 = 1/6 1/9;;(Col. XVIII);Of 6 = 1/3;Of 7 = 1/3 1/18;Of 8 = 1/3 1/9;Of 9 = 1/2;Of 10 = 1/2 1/18;Of 11 = 1/2 1/9;Of 12 = 2/3;Of 13 = 2/3 1/18;Of 14 = 2/3 1/9;Of 15 = 1/2 1/3;Of 16 = 1/2 1/3 1/18;Of 17 = 1/2 1/3 1/9;Of 18 = 1;;(Col. XIX);Nineteenths:;;(The rest of the column is left blank)