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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 10
# Folio 3r, page id 00068007:0005
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sublatio literarum
Sublatio literae
10X + 11 = 0
20Xt2I = 0 (+10. 20XF 11. 20 20 vel horffrmat (20
= 10, 20X) - 10. 21
10X +11 = 0 2OX L UIX + n o (YID20X)H1O. IX F1B. 22 LO NL M 30X L IBIX(I
= 10.20 - 11. 20. characteres
ubi notandum aequ. 3 et 4 eo inter se disterre, quod aequationes literae ab initio, sumtue  eodem modo
permutantur res pondentibus a fine. Hinc ex 1 et 3 fit + 10. 1021 X) + 10. 10. 22 =0. 1x 1et 4 111. 1 20X F um21
Generiliter patet cxaeq. 1 et2 oriri aeg. 5. si pro
pro X ( in ag. 2 substituos =H. 10 ex 29. 1.
- 10. 10. 21 ( - 10. 11. 27
+ 10. 1. 20 + 1. H. 20
10X + 1X + 12 =0 20X + 21X + 22 =0  +1, 20X + 12. 20 = 10. 21X + 10. 22
simoliter I. 12X + 1. = i. 4X + 1220 inversibns liferairum. s i  tate  gura
B Ergo 13 - 10. 21 = 12, 21 - 11. 22 similiter 10. 22X + 11. 22 == 12. 20X + 12. 21 inversiore lterarum
Et Unde ha duae aequationes dant unam 5, ut initio in primo calculo 1 et 2 dant unam 4 (vel 3)
Et fit + 11. 20211. 2
10. 215) -13.21
GB) in (21) ( (1) in B.d
C11. 20 = 12. 2
1X L IX +1 =0 20X+ 2IX + 22X + 23 
acqtimo
1. 20X + 12.20X. X 2 19. 21X + 1032X + 10. 23 Et inversione it a 2.
seu 110. 21 X2 + 10. 22X +10. 23 20 IL. 20X + 12. 21X +1 
1. 23 + 1B. 23X X = 12. 22 +12. 2IX + 12. 20X
possunt, ut 1. et 2 
26 quae duce aequatones
fit enim (10) = 10. 21 - 11. 20 (11) = 10. 22 = 12.20 (12 =10. 23.... et anse, aisi quod accedit 12 = 10. 23 carum seu
(20) = 12. 20 (21) = 12. 21 - 10.23 (22) = 12. 22 - 11. 23... consentit priori inversione literrumi chanactus
- 11. 20 - 12. 20
Non est opus nunc scribere actu ipso,  et explicite fiet suo loco
ed Bilot sine  notarum inversione salent
HNTHXA rx et
instituere, ut ipsa notarum inversio sit separatim pro exumine
et depressione. ut: viser enim sit ordinem et simplicililem molius servari hoc tuodo:
V. 10. 21X + 10. 22 =0. Et habemus duas aequationes
+1921. X3 + 10. 2X + 10. 13X + 10 2420
. 20  1220
nempe 2 et 3. e Unde ad tollendam X calculus erit similis calculo quo sustulimus ex
10X L IX+ 12 =0 20X= + 21X + 22=0
aequ. (30 X + 2X + 22 = 0 et (10) X + (1) = 0. tantumque Eratque + b0 19 22 - po ( 21 + (11 (1) 20 = 0
vel si maluissemus, H0X + HX + 12 = 0 et, (2o (1) = 0 fieret 10. (21(2) - 11(20. (21 ) + 12. (20) (20)=0
ubi  (20) = 10. 21 - 11. 20 et (21) = 10. 22 - 12. 20. Sed si in ag. sed si mage in aega substituas
valores (21) et (22), vide oritur aequatio in qua dimensionis uno gradu justo altioris seu diprimibilis,
fit enim 5 otatum cum supra, ubic adhibuimus inversionem aliterarum, fuerit solum
praestatet ergo redire ad modum priorem. Etsi hic constantior futura fuerit progressio
Nam pergento ad 10X +X +2 = et quam  antequam hinc abeamus exponere placet apergendo:
IOX F uX 12 L0 20X + 2IX F 2yC + 23 (10 +10. 21X + 102L X +0. 23 =0. Ubi res redit ad
quatuor notarum
Calculua praecedentem quasi fuiffet ge proter aq. 10. affuiset (20) X + (21) X +(22) =0
=11.20 -12. 20
10X LIXH E =0 20X + 21X + 22X + 23X+ 2420 et HID. 2IX+10. 22X Z 10. 23X + 1024 20
iffet (20) =, 10. 21 - 11. 20 21= 10. 22 - 12. 20
Unde perinde est ac si essent ducae aequationes 10X uX A M = 0 et (20) 1    (2X +(23) = 0. fictqu (20 =-102, -120
et (21) = 10. 22 - 12. 20 et (22) = 10. 23 et (23) = 10. 24
ed placet totam rem repraesentare
sit 10X + 11X + 12 = 0
on rto 1oulouro 102
Et sc eodem etiam modo semper proceditur in infinitam. Sita ubi hoc unum turat quod basis isse progressimis ex eadem lege
ZDX +EIX+ 22 =0 = +10. 5
20X +X+ UXIB=OL
aumo lonido ren iro
Poterimus ergo sic procedere: 10X + 1X + 12 = 0
11. 29, 21.
xGr+14 =0 = 16. 2
ua i ie uua
Et ita porro. Et haec compendiosissima videtu r  iteram ope duarum aequationum tollendi.
aequatio  10X +HX + 12X +0 compinetur cum aliis  ordinie assumtis, procedetu nempe
ondo tantum se per
CoxtEIX, UO=
x+n
ojuntionem jam solatam ex calculo praecedenti,
prodit utique ut ante 10, 213 - 11. 2. 20 +12. 21. 20+ 13, 20.=0
res reducitur ad aeq. simplicem. Had
quem cutum e
puu  it
u 10(7 4- 11 C20 20)
102)22 2 (10(11)21 + (112) 20 =0 a (0) = 10. 25 - 10. 20. 22 ~ 11. 20. 21 + 12. 20 _ (11) = 10. 21. 21- 1120.251i e ad
Has jam si sit . 10X + UX + 12X+13=0 et Guicaccedat 20X + 2X + 2X + 23 = O. multiplisan fictH10. 2IX +18. 2IX +10. 23 =0 RC
sent 1_ Di o- 11. 20. 2HO 2 I C
duas aequationes 1oxSFX FuX LB =Det (1D) XH (21)X + (22) et fiet (20 = 10. 21 - 11. 20 et (1) = 10. 22- 12. 20
et alia quae sit proxime inferiscasita; si datae posteriiris coefficientibus positis 20, 21, 2, etc. m proxime inferioris coefficientibus 10), (1), (22) erc. datae autem communus
sencealim; cum tollendae est litera per duas aequationes; inficit poterit per aequation
10.2- 11. 20; 10. 2 - 12. 20; 10. 23-13. 20; 10. 24 -14. 20,
=X quia -13. 20 deest, cum
ut ut ante. Vanc ergo habemus regulam
ad iss damen incuis
in sonpe atus userais hadsferteur ad possne
in tequoitione t periater. Ha cere hotis neeu
Accedat jam 20X + 21X + 22 Verum hanc conjungendo cum
ioda nam sit aequalu
1D. 12. 21 + 11. 12. 20 e (20) = 10,22