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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 1
# Folio 1r, page id 00068018:0001
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Aer ABpX. AE, ea
BE v- ∞ BC,7
 + aWX =X  P 
FG⊓2, GH Sae-x
SH pa +a
sine FH p, S2ae - X
jam FH DC a, ECHI
FGN DB I BCp.
Erg. 4P, pra- 2
Ergo PH 2a ae- x
Schediasma de Methodo Tangentium inversa, ad Cnculum applicata subi multa de
Octobz. 1674.
hor argineuto gene
mum ox alis productarum
Dota aego Data Ata aequatione exprimente relationem lineae BE, ad lineam AB
invenire liram relationem linece- BC. ad eandem.
BEr Z.
Esto AB, X.
BC, y. ECP Relatio inter Z er X
expressa aequatione, vig () y  a - X  Ert p a- X +  y
In qua aequatione tam X quam y duos habent valores aequales, a autem
et p non nisi unum, Conferenda ergo haec aequatio estcum alia in qua
duas constat incognitas duos habere valores aequales; X + b C X + b dabit
X + 2bX + b 10 Ducatur in  + 2CY + C2,. fier:
X Y + 2b XV + 2CHy  +b V + AbCyXF EK +2cb Y + 2bCX +  
Sed revera video hanc aequationem non pertinere ad rem, ita enim proposita aequata foret
davisibilis in duas, sic ergo malo:
x + y + b O x+ y+ bCX + 2xy + 2nb 15 + 21b +b
Aequatio autem 2 nempe V. X +q B, ut smulis reddatur quartae videndum est.
Quam in Din explicare necesse est ipsas V, e. X. nimirum, ponamus: V Y AZ + m.
et X  D + d, unde: X e AZ + 1ZC +  x p v + 2d + d,
et  Unde:
v- v + 1∞Z - V + E H0. Et loco aequationisque
Scribatur;
et p 2sa - y Mlultiplicetur atiaque aequalu pra v.
X +2XY + Xb X, + y  v + Z + 2YZ + ibV + 2b7
)+2VX+ ya  ra multiplicetur utraque aequalio per v + L Z + in 10. et fient similes inters
Uude aequatio. a
sie avtxex arav tosrima Nam 6ta per 7 mam dabit:
suvefaray sa-a
Cujus aequationis ope habetur valor et mutatis signis
a v - 2XVa + Xa- ya + yX
sive +P + X,y SaeX
quec tantum determinamta
uales radies
+  VZ + VZ2 + ib v + ilb Z + 2bl B7 + b. B +
 + 2bm.. + abm
+2... + 3l... 4 m.. + m.. + 2b..
Sed video me non quidem morem admisisse, sed tamen imperfectionem aeliquiss
amque et incognitam habere debito onsrem, itaque rea resumam non tantum
et numeros adjiciam, ut facitius calculi error in progressa vitetur:
sumamus: 1X +LHy m 0, et quadrando fiet:
BSl VX - B2m X, + 3bl y = EtiZm V + 4g m
Vucatur haec aequatio in aliam X + = ny - 54 5, o. ponendo np2. et fier:
Xe+ Glu XY a- _ 28mu X + 1+ en
+ B6l X y - O 7m X + 36I. XV - ( arln XY + +9 m X
+14la.. . - 1d 28 ma.. 4   + 168 (. ) p renius
-9101. . D 35 4m .. - 180 1. 18 noly
+119 - 45b +616
factenus incognitas habemus tres quatuor
1) v co + a 
490 esto jam aequalio data: (2) Consrequriro relar erio
et cop V +d fer:
quod facde in humeris essequemar, nam poterigendo
a  p D e fier a v-co  p 2pet CF 7, 0
v2= cor + e cumque sit y  2. ponendo dp 4, fiet)
cop 6. eodem modo quia X 1. et ponendo C er
v110 et p, f49 - 36) 13 + 1pj7. 2pp 1 +C,
se + 13, sive 2pe  C  13. porendo ei dfiert
Y 4262bp- 2636 B  P 64 + C
etiam sicu. P8
 e C 110, aps p. es 10 - 2,,
DF-IIX B oi a V Bs 
+emm. Deryx 4BXY y - 64y - D18dry
Simetuiimus ne forte non slatis sit incognitorum, in esfectu, (etsi numerus sufficere videatur) quia
ne articit i neque x, nqe y, hublant inditutimus idio altusa ab ipsis, v. 9. y potest intelligi multiglicata
1X2 + B) 9
tbi bas sse.
4. rardo