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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 83r, page id 00068255:0165
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Hubita jam comparatione sedium veniamus ad earum additionem.
sit a +b = 01 0iot a=
00 11 00 C
vol 02121262
et generaliter S+ 5+ 225 = 051305 = 05151505 = osis esis + osusosisisos
c+d = 00
obde di
a+ C = 0000 211
(O212) 2 (1202)2
99901111 00001111 = (04 14)2 (14 14)2
sinior 2 (10)2
CFP = 000011 110000I1II
0000000u 000000or
et generalite 5+ 45 = (0515) 2 (1505)2
010101 01 01010101 =  (01) 4 ((0) 4
a+D =  9000000DIIH1III
00110011 00I O3I 30I 051 00 001I = (021) 4 (1202)4
000000000000000V1II 1I 1H11S
et generaliter 5+8) = (0515) 4 (1+05) 4
Unde tandem generalisseme unu Sts = (05 15) (150s) e
caleus permet si omndams.
(osisttt oles s
s Lesisse  orespes
h+ C +d = o2 121202 + 0818 = o2IZIO2O2I2NOI, 0818 = o2nnOnoion
ergantus ad tria
1b11b = 0414140414040414
(d+ e(041414087 aria 1 e 14 i
dt  1414i4 14041404, (21 D2 1404)2
(.fisit + orsers = 401.s.7ossiosobis ositde sequestretur
+25+4s= os es +  (os. sis oste + 045 14) = 01isisos 1505ois
f+ 2 + 2( asis = ((0si sC sos) )fa  
((+ 25 + 8) = bosi) Act +08(∞185 = (0s.51505) 2(1505 6) 15)2
(+ 2( + 165 = (0si5 150) 8 + 016)+16s = (051 si505) 4 (15050515) 4
S+ 4(+45 =
11+214- 0001010
 qoe o
ibno
(Osissra sos)2 + oascas = (Osis (os s )2 fpotu li t it su quori g  osias (ofis) 8 tutsoits. s
(+ bis a5 = (0515) 4 + 0452s ss sist
(74 (+35 = ((5. 14 (50()2) 2 + obsi8s = (O1s) (50s) (s0s ) 2(8, 1P, 10c01
5145+165 = ((05.5) 4 (1(05) 2) 4 +01b511bs((osisp (150592)2 (150()2 (0s 1s)e)2
 ssosse
8 1010 10 = (0s. 1)2 (1) is)2
Et generaliter (L. 45 +4L5 = (0(. 5) 2(1 50s) 2) 2k + 08hs 1 8H = (( osis) 2(5o5) 2) K ((1505) 2C os 15) 2) K
Et sic quoque st B + 18k) = ((05 15) 4C 50s) 4) Zk + 150H5 1 16t5 = ((0 si 14 (150 s) 4) k ((. 50(9 4 (0 ( 1) 4) _
vt gaienaliter et generalissimepsrius. s. + 2hs + Ahks = ((05 .1) h (1s oh) 2K + ∞ 4htes 1ahls = C(0s. B) h C150() h) K ((11 osi hC a t  hK
Sed generalissime pro duobus sechseret (0sis ) 50(t
Anergo peneralssine uo quatuor. a s +hte ) + Ctit s eit CC(. A Cqosse)A ( As aBI o ne AB, cuet d ed
Et patet progressus in infinitum pro addendis in unum quotcunque sedibus diversis. Diversis inquam, nam
si eadem sedes repeteretur seu plus semel esset addenda, nonnihil esset sariandm regulaque generalissima
inmutanda, sed quia ita res esset paulo perplexior; et repetitio sedis  in additione semper evitari potest
cum eo ipso transferatur in columnam sequentem sufficerit regula proposita, quae generaliter sic enon–
summae ex sede nova prioribus addita
si catus siviei persi si casibus seriti ovae
tum quo sedes nova
repetantur secundum numerum quo sedes nova supremam priorum
renet si casibus prioribus si casus priores per rum primum ip
tiari potest, it
cum oppositi p
quiod exponentes metitur. Unde patet etiam quomodo puncta anjeantur, quae notant tranclationem in columnas ba
cnenaliter ubi Ad estn catibas (. trans certur in opposilis in columnam sequem
supremam priorum metitur, repetantur
10 000
fiopt os eisoes M o 3 hnsi cusonn oi ik osiB  Ces oB)HK)Im (ote E is ite in ce alotes esors
sertis = (05 1sth (1505) h
(0(os)h (osesIE
AchsAhiK) = ((0) isth (505)L) K CC1505, A (O (11 ) H) K
((0505)h 19515)H) K ((05, () h (1541) h)K
einitio tamen, seu in ea additione, quae tI
(+ s ratius M)  ((C0 5. sh (1 ( os )h)K ACC. 505) h (o sish)K) L (CC. 50)H (os. s) HK ((oS. 5) M C15051) L) L prioris
(Cofas)h(osos) 2) H CCoses) h (osts )h)K
((0F0))h (051 5)h) K ((OSiAhCCIpSHK) 1 ((osiBh ((pS)h) K ((111() h (sos) LX
ost(s R e ofas Tass )Ch Cssh) K (Tosis A E. Ld) B Z) L
C ofos) h (osos) h) H (( Bsos) h (0ses) ))L (esos) h (0sos h) H ((0 fos) h (b si s) L) 1) L in secundas
Itaque generaliter culumna secunda tatis summae opponitur primae, et ceptis primis casibus numeros, ubi oppositio pustula res 1, sed est o
phis-. Hs
Regula generalis
= (0( .() . (1s es) in prima columa suam multitudo hm no coefficiente comprehensa
transformatur in du
ubaeque simul comprehenduntur uno
ientes quot addendi
Cxtralis = st ia(tales y = 0onm o B dli  1 =1 vtiroch odeo pd coefiliente naco; ita, ut tor sim cosicit ot, fiat 11. e
a 
00 1u0 110000 oovodiso
cobi C(ahstahk segtiX Isriblikelms = (((osist h (st) k (. (o 1h (op ) H K) L(((.50)) h (us s) LIH ((Os. s) k (150s) H K) 1)m (CLC, s0)) h Cot. Bh)K (Bs. 5)M C so s A B) L (1. 1al. os a LLBVB a  )
le000vo ovemI
(6sei t e sti k. ot.  uC isis) )L ( os syh C. sis a 1k CC s iB  Ceso s ti X) () in AL COsi(s) hC t. ) t X (. s.pta (1sos h.119) LCer. s h (.50) hi ka is t6. isti1 m
B  cy 50 a 4
C Oc, 12,, 12, 22m 12, 23, 27, 349, 12, 23, 23, 341 23134, 34, 45,, l2, 23, 231 341, 23, 34, 34, 425,  23, 34, 34 451, 34, 45, +5, 56, 111)
  a 20 51 11 21 10 oc 2 2 21 49 1001 62 e1 11 10 11 10 109∞ 31 10 19 4 19 44 9 21
iemperascenditur, dum
prima ad columnam propositam tansit, un
1 ponitur non nisi ultimo loco. Etita et
pro ausimento ex osos fit o ex ofit
ex asososes fit osolosis
osoliteta im prmocat eneintsio medtetu
ita potro
eum excmf. 63 est nies ut 5. ncmpo in pariois smma lauaerum  it impindis ua us
52 est ILIIo dat 5
Aumerus lacipdans notas
minuta iact nmerum notam loci
ita tandem regulam habemus pultherrimam.
paru us p at pt edis uge tate, d mcteut sita   st a b enteti tue
am col pir
de sig aut
hinc + 1.) rest. 22 ausad u g1)
  ntitr i brpe t utibr 110210 lisi put.