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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 63r, page id 00068196:0125
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Alaqe
Magnum Compendium intesi infinitesimalis salculi habebitur
si sit adhibeantur variantes Hombeoptotae. Nam omnes aequationes
X+ d Reg=, fit Cdx fidy .  locales seu ad variantes, reduci possunt
ad Homoeoplotas, ut si sit q = xty et av = xy
sit jam d =X + y t b fit dx + dy = 0
O = N b + Clxry) + C xy + f(exryy) fiet o: csilas ty) + C yA t X AGB) A2s (x Ax a y dy)
C B 8 0 = r et 160 + 16  in py + 120 (ex tyy) = 121 (XXy Fyy) + 130 (X  yt )+ 131Xy trurgy 1i4ot 
Cujus differenbratio erit
Et ita p.
sit data aequateoa
poldxttus) + 11Hdu
assare vr yyax tare
ex + 3. 131 xxy dx 4 4. 140 F + dy
sis exprineturd
R(dx ) + 2 210x dx + 201mdx + 271 Xy dx + 220Xx dx + 202Y9 dx t 
ly
dy
puu
yg du exx dy
differetialis forunta
+22IXXydx +212Xyy dx + 230∞ x + 203y x
ryay
xdy
 dysit 200 + 210X +201y + 2IIXy + 220 XX + 202 yy + 221 Xxy + 212Xyy +230 X + 203 Y
Aequntio
XXay,
fyy dy
seu = ax 200 + 210y + 2817 + 211Xy +230Y7 + 20d yy + 28IXHy + 2H XXy + 296y + 2637
ffrreulata 3) 110 +, idq + DMy +2. HIXy +3BDXX. F 121 yy. + 3, 13+ Exy t 2. 122Xry 4 4. 190 X. + 131 y
10 +2. 120y + 1IIX + 2. 121Xy + 3, 150y9 + 121, XX + 3. 131 xyy +2. 122XXy +4. 1470.7 + 13CX
quodsi duo valores sint ideubici suffecerit tantum Nunquatiorem Numdratori
ix quaesita 
vel oenominatorem devominatori coincidentiare, et fit 10 200
110 = 200 120 = 2 210. 111 = 201 121 = = 211 = 202 130 = ,. 20 131 - 5221 = 203
unde jam facile intelligimus, eos numeros qui vacios d plares diversos dant per subbractionem
unitatis, diversis ae quandos, v. 9. 21, dabil 220, et L 211. Nam dissimulato
1initiali pro (21, scribamus 2 et tollendo 21. et tolled H ita possumus tollere
Fit 20; cui praefigimus  semper
 sid quia id et ex ita possimus tollere unitalem vel, ab 1, vel a 2.
unitatem tum ab 1, tum a 2. si tollamus ab 1
si tollamus ab 1, fiat 20, sed quia gitur sub traxiums a minore transpositi fit,
202. totum unctiplicames per unitatem
21
seu 02. Huic praeffigimus 2 initiclem fit. unit et
tollanus a  2 fit 11. Cui praeficamus A. sit EI1, multiplicemas per
2
nemper per numerum a quo subtraximus. nitiem
 numerum a quem diminuimu, fit 2 ∞. 2Y itaque  121 aequatur tum ipsi 1
Eodem modo ptrocedamas
tum ipsi 20d tum ipsi ZF Z211.
a minore fit 03 mutabitur in oz, p divideur per numerum unde sustu
in 131, fit 30 31; unde ab 1 H ef sei
limus, fit.
90
praefigitur
3 Tollendo unitatem durae figatur
q dividatur per numerum a quo sustulimus 3, fit 3221, nec
Ie
sinsequia sustulimas
202 et 2. E1 203 et  211. Et
neq fit hic, tra
peveraliter quivis numerus qui cui praefigitur nitialis 2. ex quoc alius
initialis 2, fit
Hon Hiuc sem per aequantur
in quo (rejecta initiali nota) differunt duae sequentes, potest trans formetur in
in alium auciendo unitate uta unam noram, et diminuendo alteram;
et notas transponendo; aequatur huic et producto provenienti maefi–
sendo 2 initialem, tum uteus numems divide. ita Ei duo b ac lege
Et hac lege servat proveniens A eadem lege mutatus reddit priorem dividatur
ateoque per notam quae unitate multatur ad tansformationem; et fief
et duo provenientia aequentur inter se. Ha e ein eis Nota ubi
tunc etiam vil prodit
nolae non potest sublrari unitat cum scilicet est o
Hac leqe servata  quotces interdum numerus trans formatus reddae se ipsum
Hnc 202, non detalium, Z s
o at quaesita conjurguntur vollendo dy: ex pudibu
24
lequ
cratem
ex, 222 fit 31, adeoque 22F. 2
heMrinu lio
cum quaesita, id est per eam di
in aal u sunt