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# Piece: https://leibnizlegible.com/api/records/25255/text
# Catalogue record: 25255 — Inventio communis Mensurae, eique connexa sublatio literae ope duarum aequationum
# Incipit: Regulam divisionis hanc peculari Scheda invenimus
# Date: 1693
# Other printings: Knobloch: Beginn der Determinantentheorie, 1980, S. 289-294
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=25255&katnr=56695
# Work: https://leibnizlegible.com/work/00068007
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 10
# Folios: Bl. 6–7 (from the shelfmark LH 35, 4, 10 Bl. 6-7): 4 pages, canvases 11–14, page ids 00068007:0011 to 00068007:0014
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068007&page=11
# Lines: 229 recognised on 2 of 4 pages, mean confidence 0.85
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 6r — 00068007:0011
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 7v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068007/jpgs/default/00000011.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 120 lines, status machine
Regulam
Inventio communis Mensurae, eique connexa
sublatio literae ope duarum aequationum.
 aotigationem communis mensurae
 investigationita communis mensurae
Quod fit perdicisiones replicatas
sit dividendus 10 + IIX + 12 X + 13 X + 14 X + 15 X3 + 16X
Divisor 20+ 21X + 22 X +23 X
Zetens sntus
Operatio 30+ 3IX+32 X + 33. X3+ 34 X +35 X + 36X
Quetielis p 3B ro
Residuus 30+3IX + 32X
Quotiens purus 33 +haX + 35 X H6X, : 16
Vel ad huc altius asfurgendo
s
ex operationis
1. 16.23 = 36. 23
15. 23= 35. 23 +26. 22
14.23 = 39. 23+25. 22+3621
13. 23 = 33. 23+34. 22+3
d. 5=
32. 23
2
Sit dividendus: 10 + uX + 12X + 13X +14X + 15 X + 16X +17X + 18X + 19X
Divisor 20t uX FuX + 13XXtX , 6X 
Residuus 30 + 3IX +32X +33X +GAX 135N + 36X +37X7
36. 20
10.26 = 30. 2B + 31. 27 +32. 26+33. 25+34. 29+35. 2) + 36. 22 +37, 21 +38. 20
11. 28= 31. 28 + 32. 23 +33. 26+34. 25 +35. 29. + 35. 27 +37. 28 + 38. 21 + 39. 20
12. 28 = 32. 28+ 13. 28+ 34, 26+35. 25+ 36. 22+ 37. 2+ 38. 2a + 39, 21
13. 28 = 33. 28+ 39. 27+35. 26+ 36. 25+37. 24 +38. 9+ 39. 29
24. +39). 23
tio= 14.  = 3 28 + 35. 27 + 36. 26+37135+3
15. 18 = 25, 28+ 36. 2 + 37. 26+38, 25+3929
16. 2 = 36. 2 + 37, 37 + 3Y. 26+39. 25
19. 8- 39. 2
9. 26
jam rursus it
prins chisor sensemu dividendus 20+ UX tuX LXtRHSX +isx Z 27X +18X
prifisitus sen seundus divisor 30+3IXLZIXY3X B ,35XS +3BX + 37X
secundus Residuus 40 LAXtAIE +4IR tAnX HASX + 4bX
20. 37 = 40. 37+41.36 +42. 35+43. 34+49. 33+45.32 + 96. 31 + 47. 30
1. 37 = 41. 37+43. 36+ 43. 35 + 44. 39Y 45. 33 +4b. 3st + 47. 31 +48. 30
12. 37 = 42. 37 + 13. 3br 47. 3 + 45. 34 + 96. 33 + 47. 31 + 48. 31
24. 27 a 44 27+45. 36+ 4b. 3
f. 3) = 45 43
6
8. 11
.= 4  3  ab 3b
28. 37= 18
. 34+48. B
47. 35+48. 3
45. 35
Et tertiavice
primus ralituus sen digsni sen snus Dividendus 30 + 31X132X +35X +aX + 18X +36X 137X
3tius Residuus SOtSIX FSix H SSXHsX +SIX 
30.46=50. 46+51. 45+5244+53, 93+ 54. 42+ 55. 41 +5640
31. 46 = 51. 46 +52. 45 +53. 49 +54. 48+ 55. 42 + 5b. 41 +57. 40
32. ab = 52. 46 + 53. 95+54. 44 +55 11+ 5b. 42 + 57. 41
33. 4b = 53. 96 + 54. 45+ 55, 49 +36. 13+ 57. 42
2 46 = 14. 46 + 55. 4 156. 44 +57. 8
35. 46 = 55.
+56. 45+ 57. 44
16. 46 = 5b. 46 +57. 45
3. 9b = 57. 4b
et quarta vice
Edgresitu en 3tiusomtaseu atque dividendlis40 +AIX tAX 143X 1 AX L4X bX
50 + SI X +5IX +53X+54X 155X
60+61X +62 4 63 X  6qX 1
90. 55 = 60. 55 +61. 54 + G653t (2. 52 169. 51 +65: 50
41. 55 = 1. 55+62. 54+653+64. 52 +65. 51 +66. 50
G2. 55 = 62. 35+ 63. 34 +6)53+65. 51 +06. s
42. 55 = 61. 55 +5454+ 45. 53+ 46. 51
44055 = 64. 35 +5. 54 +66. 53
4c. 55 = 45. 53 + (b. 54
Et ita pergendum est ad huc vicibus quatuor; et ita omnino instituendae sunt operationes
46. 5 = 66. si 
seu divisiones octo. Quia regulariter seu generubler, residuns est uno gradu inferio.
divisore, ideo ut residuus ultimus sit gradus nullius, seu ut litera sit sublata
oportet divistones fieri 8. Nam primus est gradus ymi secundus gratus sexti etc. ergo
octavus est gradus nullius. Tot ergo opas est divisionibus, quot graduum est divisor
In aequationibus duabus ejusdem literae, sem peus reperiri potest communis divisor, cujuscunque gradus;
imo plures. Itaque hiac eadem Methodo datis duabus aequationibus ejusdem literae
possumus tertiam lavenire ejusdem literae inferiorem fe ambabus, quae sit dat gradus;
adem et valorem literae, qui est comndi aequasio infima literam continens. Data una
aequatione licet invenire ab huc aliam per inversionem turarum, pro X substituendo y = L
idem est calculus; tartum ex nutis primis fiuut novissim et, pene primis, penultimae ete
oguit
a
jam
se imiem ducartur, sed inveninntur ordti
ita  lalrus s asi catmt abat sa aqeatires qua se sratutum si inalicatione
Quotieas hic negligitur,
quia non pertinet
ad replicatas
divisiones
qua-
nes
 ssse 2y resitussenHius Divisor 40+ 41X + 42X +43X + 44X 145X + 4bX
atus Residuus
3tiis residussenatus Divisor
HIC potius scripsi 10 + IX+ nX etc
ut residum divisore mutato in
in dividendum, residuoque in divisorem
novum idem temper literarum
progressus se notarum servetur
continuatis licet replicationibus
Etsi Residuus non contineat
notas omnes sui ordinis, nempe 37, 38
tamen concurrunt ea ad reliquarum
ejusdem ordinis inventionem, quippe
ingredientes operationem anteceda
nec ad inventionem residui;
nam constituunt quotientem
ste
cujus inventioni infa
Pior est inventio
ui Etsi
igitur ipso quotiente non utamm
tanec utiuur ejus ingredientibus.

## Folio 6v — 00068007:0012
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 7r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068007/jpgs/default/00000012.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 109 lines, status machine
Octava seu ultima vicestabit sic
90 + 91 X
10d pe. 8091 = 100. 91 + 101 . 90 seu 90.91 = 100.91 + 81 90. 9 = 92.90
o. B1. 91 = 109,91 + 102. 90  _son 81. 95 = 101. 91 4 82. 90. 
nes 8+ 91 = 102.9
Residuns
valor ea
septima seu penultima Vice:) 91. 101 = 81. 91 - 82.90
Dividendus 70 + 71X +72 X +73X
divisor
80 + 81 x +B2X
90+ 91X
70. B2- 9u.88 1 91. 8
Aequa 70. 82= 90. 82 + 91. 81 +92. 80
tio- 71. 82 = 91. 82 + 92. 81 + 93. 80
nes 72. 81~ 92. 82 + 93. 81
73, 82
investigatio valorum,
ce
 93 = 73. Ex 2e15 fit  92. 92 = 72. 92 - 73. 81
Ex I5 fit 71. 82= 91. 82 + 12. 81. 82- 73. 812+ 73. 80. 82 sen 8E. 91 = 71. 85- 72. 81. 82+ G. 8.
est
Exaeq.1 tt
5t
ve Et ex 4, p. s, 6, 8, fit 20. B2 = 9082 + 71. 81- 72. 81. 52 +73. 8]
Hatum vatorum a
33. 50818
+72. 80. 82 - 73. 50. 81. 82
Hi valores praeter altimum
realrs Valores
B = 23
ex praecedentibus, promotis literis
transcribi possunt. Ponelio haoecest:
inpruantur sinistre anguntur unitate; quia
p
92. 92 = 72. 82 - 73.81
8591 = 71. 81- 72. 8182 +73. 81. 81
- 73. 80. 82
8290 = 70. 82- 71. 81. 82+12. 81. 82 -73. 81
- 72. 80. 82 +273. 80.51. 82
sexta seu antepenultima vice
dividendus 60 +6IX+ 62 X +63 X2+64X
divisor
70+71X + 72X +I3X
Residuus So+BIXEBIX e
.60, 73 = 80. 73 + 81. 7 2+82. 71+ 83. 70
51. 73= 81. 73+ 82. 72 +83.71 + 84. 7
62. 93(282. 75+ 83. 72+84. 71
63. 736183. 75+ 84 22
64. 73 = 84. 75
Ex aeg. 1. fit 84 = 64 ex aeq. 2 perbfit 63. B = 83. B + 64. 72 seu 473. 83 = 68. 63. 73. 67. 72
investigatio valorum
e ex Ex aeq. 4. 758) = 61. 73 - 62. 82. 73 +62, 72. 7 = 4. 43
-63. 71. 13 +269. 71. X. 13
Tandem ex 2p. 5 8050. 23 = 80. 72+61. 73. 72 ek + 62.75. 71 etc. + 63.73. 33270
per valarem penulluu calculi
praecedentis vel per 6, 3140
per 9, f10. I. seu 73380 = 60. 73( -61. 72. 733 162. 72.75 63. 12.73 + 64. 72
seu 13. 80 =60. 3  - 61 .12. 73+52. 12. 75 - 6318. 17 164. 72
84 = 64
-62.71. 132 ., 1. 7275- 364 21.72. 73
63. 20.75 +64. 71.75
Valones ergo
Valores ergo
73. 83 = 63. 73 -64. 72
73. 82 = 62. 75 - 63. 72. 73 +64. 72. 72
-64. 71. 73
+63. 71.72. 13 2. 64. 71.71.13
= 62.71. 157 +6371.72.73 -64. 71. 72. 13
73.91 = 61. 73 - 62. 72.75 +63. 72.73 - 64.72
+64. 21. 73
- 63. 71. 73 +2.69. )1. 72. 73
- - 63. 70. 5
jn eadem vatorum serie, cujus vis vuboris termiri
multiplicati per eandem, hoc loco 13. insunt
sequenti. sed sequens aliquid preterea habet.
79.80 =60.13- 61. 72. 75+62. 7775 - 63, 75.93 464. 75
- 62. 71753 42. 63. 71. 72.73 3.64. 71. 72.73
- 63, 70. 737 +64. 712. 731
Valores hujus calculi sumuntur ex Tabula explicationum  ipsarum notarum
possitulio cambinalone 20; 21; 22; 28, etc per B. 21 - 11. 20;110. 2E - 12. 20; 10. 23 - 13, 20; 10. 24- 14. 20 ete.
sed Motatis taatum ciphris sinstris, quae in Tabula ab initio versus magis composita semper manent
eedem  et nesemt nempe _1 et 2. Hic vero sunt modo 9 et 8, modo 8 et7, modo y et b, etc.
q conferntur
ita ut grespende at ipsi 1, et 8 ipsi 2. vel B ipsi 1, et 7 ipsi 2; et ita porro.
quae adscutsimus ad Tabulam divisionum. Nam quotientes et Residuit sinatatis tantum dicto modo
stendimus autem optersum autem est ibi, quomod
imen sine Tabula, et calculo extemporanpa ratione possint
esti .  e  buloe tas coincidgu
ser ad rabulam, qvoluodo ex secitu. me
Etus esihysa asdnitor seu BVu Dividetdus 30 + 8IX + B2 X
Inghesiduns sevu Divisor
8ru Reliduus
sic fit in datis
Nempe exterie valorum praecedentium tantur
alorssequentis demed uttimo si dextrae cidirae
Nodu st omnes
combinatione cone–
incutes ex
A6
non adest 6l. 21.tB
la
baci io
+calculo
i
alores implicit
Seu calulo ntracto
95. 100 = 80. 91 - 81. 90,91 +82. 90
Et cob 100 quaeruntur 100, et 102

## Folio 7r — 00068007:0013
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6v); this page is its right half.
# No recognised text on this page (recognized).

## Folio 7v — 00068007:0014
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6r); this page is its left half.
# No recognised text on this page (recognized).