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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 288v, page id 00067993:0578
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1Ergyro X- bX. b.
dici substiliui potest:
y = ax - b:
tunc solvi posset roblema ope parabolae, unc deberet
nnirum fieri aequatio talis posito y = X.
y = ax = b. vel X= aX- b haberemus solutionem
saltem per parabolam, seu aequationem soi locum solidum.
quare si quis exhibere posset segmentum circuli aequale cuidam sectori
demto quodamm quadrata cognito euius arcus est radix segmentu.
semto quodam quadrato, a rad cum  est alia a cadius essi
sed potaeram osus suffiat prior illa aequalo: X = aX - 
Nam X = y, et et b-a suit autem X et . cognitae
est enim a. ratio arus qui radix est segmenti, ad cirumferentram circudi
Hinc sequtur, si ista quae dix inus vera sunt posse deseribi parabola
cujus aliqua applicatarum sit circumferentiae circuli aequalis. Tautoque
factiora sunt omnia, quia sratio y. ad X cognita esst. et ratio
a ad b. Ponamus jam diversa assumi segmenta ejusdem sirculi
habeb quorm ratio scilice in quibus ratio arcus ad eircumferentiam et
sius ad radium cognita sit, et unam esse quam dliximus
bx - b 1. alteram, X = bx - b Muagantur
inter se aequationes, emn XX
XbX 7b
a+sn B+E
vel sic cum X sit = ibX = b. erit X = bxS - bd
Ergo quia X - l. x + b  eit  bxse b Ad- bx - b
Ergo bx - bud
Ca
tc
a
Ea
= b. Ex bx br8- b- b
C
Ergo X = xd = b - b8. Ergo X =
Ea
a
 ca
h = b s 2ba - bsc
(-
Jam datur ipsius. Imo coror fanile tamen reparabilis
Ea
81457
una aequatione differt a bm altra, sed ratio tamen cognita
est, ea ponatur esse V. ergo ita slabat aequatio:
bVXS - bγS = bx - b eut bx - 1)a8 = b 7 BY 
EX
ca
sive erit X = b - b) d8 Cumque omines termini praeter X sint
2
a
18
Ea
cogniti, X abduno incognitus ab uno
tantum cogniti tantum ab altero,
habebitur X. ratio ad b. cum
ratio habeatur b ad diametium, habebitur, quoque ratio ipsius
X a X cn circumferentiae ad diametrum. Et haec qui
demvera sunt, modo verum sit rationem segmenti ad quadratum
sui arcus semper haberi posse. So aequatio latis fieri non potuisse
Eatis tamen duabus aequationibus, et ideo descriptis duabus patabolis,
applicata duarum istam parabolarum communis fuistet X.