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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 10
# Folio 6r, page id 00068007:0011
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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.