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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 215r, page id 00068195:0429
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 in aequationedata facle efficiemus, ut quilibet incogaite termin datam
accipiat rationem ad primum, si rade ultinum, si radicam in tri seu incoitam
multiplicemus datum terminum ultimum ta radicem per ejusmodi terminum multi.
plicemus ut quantitus per ejusdem quantitatis mniam dimentionem divisa
datam aecipiat raoem and quantitatem cognitam termini dati per eundem teminium
idem divisa; ut si sit aequalio data: X  at X FavX W
poratur X e7 βy, fiet B X X at B X + ar BX aW, et divitndoper β3)
fit X X at X + av X a W ponatur jan aE 6 a C
patet hiie sequi arodor, neque id hac metto do in quovis dato feri posse
Restat videamus an possit in aq liceat in aequatione arbitraria etiam noliere
numero opus sit.
va
E 1b v + 1 Unde Et quadrandto . st + ODY 11071 . 1 q 2) p.
tollatur in hac aequatione terminus secundus; faciendo
+2ga aga
X _20D  y, fitq Eoque facto instituatur comparatio cum alia requatione
in qua X in cognita est, inveniptur vulor ipsarum b. g. l. A proinde
habebuntur rectae, quarum ope si circulus ducatum Potestque valor ille ipsius y in
locum ejus tam in circulo, quam in lonica substitui, Caeterum aequalu
arbitraria itat stabit: X X 266Y
conferamus hanc aequationem arbitrariam
leum data, X  apX a rX s
OD, Cap P + 8
et ACis OY rp a p. et 2a p06+6 Ag 2.
minoreque arbitrariarum quantitatum
52by - f + 1 e ray + ay + g. Unde fiet:
a
et fret io per 3tium tertolenum:
d
e 4
607.
(+20Y
qu
+ 49a)
34) a50 (8O2V +403, 5 tg2
-
ser qt tia nt sro lico aliom
te, Sumatur linninus penultimus, ex eo:
9u D 
Aeg. 3.
=∞ + 3
-805 N Or DI
+3f293
∞
a)107 0
1454
(4) f207
- 8ga-
-403
1)520Y
od
rgas2
(21) 51410D
- 8gas v
O0 tugs s   juigatur primae habebitur
aer 9 +6 = 2
08
C
i
valor ipsius , at idem an inde habetur
collalis Aeg. 1. ed 2
Brerius p. Aequationem primam. S habetur ope ipsius D ergo postea pro  substituatur ejusvalor
ergo et 4 habetur ope D, ergo et 8. restabit ergo invenire ipsam D. Nimirum
xel D + Va, ob AC9. 1. Erga suls luta valore, si in Aeg. 2.
S765 ap s
frelit s D  ea  40D  Z p, ottrodent Enidem subrogando in etest. D. habebitur valar ipsius 7
a rempe per brachus logiam: + AD + na  quam subiogando in ipsius 4 locum
in aequatione ida, habebitur a D+   a D 1 a D = a5O g. conferatur
Entrobique 92, fiet:    conferatur cum termino ultimo
cum tno perultuu sublat
igais  contrarim alis e quia tunc utrobique a- X + as O, eo deleto, habebias
nova ex reliquo fiet aequatio, datura divisibilis per D, unde evanescet, D simplex restabet
d4 g2 et g, nimirum se D), X  a 4 +ah D 10. conferatut 
termino penultimo,, et habebitur tollatur utrobique  fiesuse et  a qui valor purus cum altem valore
pure ipsius D appe am adhibito ad ipsam  ivemiendam daud dubie consentue debet
Habita jam D, habetur b. ac denique ope  et E et D habetur 9. extermino 3tro qui consentire cum
et 9.
absolvat