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# Title: LBr. 705 · Overbeck
# Folio 11r, page id DE-611-HS-861255:0021
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Ex mea responsione 3)
palcherrimus est alle numerorum signorumque cocnsus quem observasti in calculo. Res
in forma cajus ualor quaritur; a volb vel C ex prim utur per (1); et a vut b vel E et per
ab vil bc, per (2) et a b vel b1 per (2). abc vel bed per (3) et abc per β), et abe vol
Similiter in terminis valorem formae ingredientibus exprimantur X per (17), y per 
X per (1), y y per (2), Y per (2). Z2 per (), 2 per (3y3 et ita porro
gradus (exempli gratia) invenietur. +6 coefficientem ipsius X yyZe seu ipsius XI gZ n
coefficienti ipsius utqui in valore ipsus abed. Hoc nova  notatione ita exprim
coefficiens ipsius (1) (2)) (3) in valore ipsus (1) (1)3
aequatur
coefficienti ipsius (37 (571 in valore ipsus (4) (2)
paebed
Superesset jam ut errgremus ipsam Numerorum
cofficientium nem unde etiam hauddubie pulcherrimae illius Harmano
ubi simul ipso aspecta apparet re
inversae cujusdam decussationis, 
valori transeunt in notas efi habentis oefficient
notae priores in posteriores, notae superiores exponentis
in inferiores (ex ponendi), et viceversa
haberetur, demonstratio. Ad hoc via fortasse parabitur ex ea methodo
coefficientes in valoribus ipsarum formarum a, ad, a, a, et conssituentium; eamque duplicem unam pasientem
ex ipsa serre comparatorum inter se valorum a on pro a, aa a, a erc. alteram perfectis imam ubi
numerus coeficiens datae combinatunum
forma essigrrandus exhiberi potest ex ipsa forma Exmplicausa in xemlo ipsius ab noumerus numerus 24
inde pendenti quadam ratione ab omni serie atque comparationi euu extraneo
coefficiens  ipsius XrZ seu ipsuns 19 29 g erui potest ex ipsis notis ex ponendis ex ipsis notis Exponendis
(1Y, A) (3)), et exporentibus 1,21. Memoria modum non teneo, sed seheda consignavia quam
et cibi monstrare olim memini Hanc mecum afferam; incipeendum autem faciliore Mehodit, nempe
ab ermendo lege seriei, quae, initio empirice procedit, sed ad scientificum altur oud viamlapent. It separatiu
comparando valores ipsarum formarum ab, ab, ab erc se statim aperit progressio
ab -
ait = xpy - x2 - 29y +43
Vde abacus valde illi convinit quem constituunt valores formarum a aa a etc. Sed hic 
ab = By- X Z. 3xgy +XB + 5yZ - 5)
ilud singulare, quod Ubi 9, Z R ete. simplice, multiplicantur per X, coefticiens semper est unitas
ab = xty - pZ. +XStXB+ ye - X try - 372- by 3 +6d
ab = Xy -XZ SXtXBGey-X) +SX. axdey BIXd - 7gy Z + 7Zβ +7y)-73
ab = Xy -XZ. 6+ 5 1APy. XV +9py 2G CX 1xy B r X  a 17X 2 + 9r Bt guys -xE - 29 48, 2 + 85 - 4B- 87]- 9yd 18
oporcit autem ad abxlvendam progressionem, ordinare reliqua decundum y, quasi X esset = o, et secundum Z, quasi X effet =3, et y - 0 po
ita secundum y ordinando prodibit
eserogd
-aec 17 18
Et ordinando secundum Z puodibit
ab = + 4
82)
= +72
+Bβ+8
cEntiam simuli disponendi ratione in abaco valorum pro ab, ab, a b et c, harmonia apparet, immistis
quibusdam in speciem irregularitatibus, quae intoto, coreganturm in abacorum collatione cotrigentur. Ecce
abbL gy - 2 F2B
abb- xyy - 2X Z + 5XB - yZ- 5)
ae bb = X,9 - 2  Z +2P 3 + gxy -6 p) -2y - 372+293+65
a bb = Xyy - 2X Z + 2x(3 +6∞y 2- 2X) - 3X - 7XZ Z quy B3Y7Xd 1392772(3-39)-73
abb= Xyy 2XZ r2X 31 8Xy. 2X)4 y. 9eZ- 6X P DX L0KysBaru)  + 29 4 2y22- 4 gy 3-aβB- g )+ 4yd + 8b
Et ordinando secutuu flle)
abb - gy + 2
a lb L 2y +L Ber L3y)
elbus die
ed 
377+60
172B.18
tryze t 4yd
+(B. 82)186
Et ordinando secundum Posilo X =0 et y-0
 n
5). 37 46d
18-4188