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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 78r, page id 00068255:0155
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huc si b +c siu notae dyadicae poterit in hac columna poni earum
differentio, et in sequente eammi rectangulum, sed differentia et differentiae
quadratum idem est. Ego fit differentia b + c- 2bc. Et erit
Atque hoc modo universaliter cuilibet columnae suum assignatur
Addatur jam d et quidem in columna 1. ad b+ c- 2bc. sunt
ergo duo addenda ut b et c, unum bt c - 2bc, alterum d,
utrumque nota dyadica. Ergo obcalculum praecedentem fiet
Quadatum i porentur haec duo ex et duplum rectan
gulum ex ipsis
dima columna, nempe btc - 2bc + d
=2bd - 9td + Qbcd. in 2da vero ponetur simplex
rectangulum, ex ipsis nempe  bd + bd  2bcd, quod
addatur ipsi bc Ergo columna prima erit b - 2bet ab.d
in columna ida be - 2bcd
b + c +d est in columna 1 b_-2bc + 4bcd + , quorum
summa facit b -2bc + 4bcd + e - 2b + 4bc70 - 8bcde1
seu b = 2bc + 4bed = 8bcde. Et in columna sequente
ponitur, bze-4bcze + 4bcde una una bc - 2bcd
f colauna rda bc - 2bcd + Abcde sed quia
pefieret
quando omnes b, c,  e. sunt unitates, traus ferenda
est unitas seu sactum ex ipsis in etiam columnam
Hinc 2bc ext ida tran bede tertiae columnae
est 2bcde secunde, Ergo in secunda tollamus Abide
et pro abcde, ibi manebit 2 bcde, et fiet
prima columna ut dectum, Wa bc -2bcd + 2bcde,
3tia bcode
b+C+ d + e+f. in prima columna +b - 2bc + 4bcd - 8bcde +f. abis
seu
+fibus 4 4bes Hbid f. + 16bcdef
b = 2bc + 4bid = 9bid e + 1bbedef
in secunda columna +bc - 2bcd + 2bcde 
+ bif -2bc+ + 4bcdf-8bcdef
sed quid si hic repetas resumamus 2bcde ex 3tra et ponamus 4bcde, uniformuitatis
causa, sed pro = obcdef ponamus -Cbcdef ponendo bidef in coumnam
equentem. ita columna 2da erit bc - 2bcd + 4bid e = 6 bcdes
Et inatia epte bedef 10. 20 +40 -6
video difficultatem in hoc progassu
Et incntineul bede
Vs
B V
aV
105) 1,
156
Ergo
redeamus ad viam regiam quam desemimus jam in be+d
Nemie columna prima erat b 2bc + 4bc.
columna ida erat bc, unacedit bd + cd - 2bcd, unde secundum f
compendii causa
Egulam in columna hac ida bc) + bd + cd - 2bcd) - 2bcd 4 4bcd = bc.
bet
et reclangulum bed- qbed quod deberet poni in col. seo ztia esto
 ita hic calculus viae regiae dat idem quod nos compendio quaesieramus
l 217 1
bed
siPro qua quatuor eodem modo pergamus. in col. 1. est ob tia b - 2bc + 4bcd
s
cui adicribatur re, et praeterea  adimatur duplum rectanus. Ex utroque quod est ab 7e + abcte- Dbide
fit col. 1. b - 2bc + 4 bcd - 8bede Et in col. seq. est exat bc cEbed cui additur
b ld bpe = 2b00 + 4 bede, et fit, bc - 2bcd) + bfe- 2b17 e + 4bide 1- duplum
ectam. ex his duob,s quod est . 2bce- 2bde 2b abede 2bce 2bideede- 2bide 2bde ude
generaliter bc per b est bbc + 3bcd hoc loco bc + 3bcd ergo bc in bze est - 2bc(  6bidC
be per bc est bbic +2bbcd + 2bcd ergo - 2bc per - ibise est + (4 bc - 8b1d) e lnde - 8 bcde
eadem duaumus  4bed in bKe- 2bcze + Alde ufile eul prius heoremata
rere dietducendes in semonati coinationibus
is
15
2b0
2bC
4bad
+2bed
+aled
bide
Oe