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# Title: De Constructione (shelfmarks LH XXXV, I, 17, Bl. 1 - 17; LH 35, I, 17, Bl. 1 - 17)
# Folio [7]v, page id 00066617:0014
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linca restat experrunda Methodus indivisibilium, seu fermatiana
culum egrego
Ergo erits
a si
t s +
contrahit. Pone scilcet circulum secare sectionem Conicam, in punctis
sed ea conicidere, seu X (X) esse infinitae parvitatis. 
D
75 esse Y GY + DG, et GY e) jam GY _ seu F4
sive (a co co a) f + (a∞4c0) X FI GZ. et 
DGH + DF - y
BB3)
+ DF -
= DF +
+ DF+
sive (aac0 4) d + (000aa) y. compendiiantem
ML AK
qu ae
I. AF+ AX
+ AF = AX.
inscribendo causa, pro (acoco asf ponemus simpliciter
pro (aacva) a, ponemus simpliciter d, quia non aliter occurrum
Nyfice
d et f. atpo et pro (a60)Xporant, pitac
ponemque
V. quia eaedem literae non aliter in calculi
occurrunt.
Erit ergo GY  f + X. et DGHd + y.
FX + X + d + 2dy + st, et pro y substituto ejus valire  ax fa r fiet
+ (B) af X + X + d + ( (3) id Praxtax + 2aX + a, et contrahendo βp aX A6), cos, fet:
(e ft d2) + bX (ponendo bp B2f + 24) + d XV sponendo 8B= + a) + (3) idraxtar
atidem
bjectisque
S2t) ho + bx + be + dX + 2 CX + 03 e +(sd Sraxtrae +a x pa ex + a eu ex deletis
communibus fier: +()) ad Prax+a+
be +d ex +. . . .  . . . . . . . . . . . . . . . . . .. Aquadrandontrobi
odax + 4da XV , bC + 45beX + + p
fiet: d
gdea ex + ada
16 4b + 168 be
e multiplicatis,
divitis omnibus
Atqan
vel
ad
EC
aer 
X+
at
+ abe+
X..... + gdax + ida e + 1d a +=
3
Can.
=2b9a
+ 54  2165b
-vdta 2
a
dua.
495a
ex, (d.....
4d 2aX = 2 X (abjectis scilicet omnibus in radice contentis per
+ 16  4 N e 46d a
ordinataque aequattione habebimus:
 168ba
1842 S2
tl
+21g
td
1 4 d’a c, 4 0d’a cX, et quadrando utrobique fiet:
IX + 10524
2
1n
d’a3 X
esa
est autem din parabola pa in circulo 0.
+ d a34
(1+ XD) 14 2X +
X xd+
in circulo
uunl nisi errvo in calculo insit erit X 5, 24. quod
~ X
utiue absunrdum, necesse est ergo in calculo eriatum esse. Unde in circulo d X+ daX + d a 4 0
X a + L aX + R.  - 2aq + a, sie fiere X - a- a
sive X + 2aX + a +70, sie X -a, quod est absurdum, calet ergo error in calculo
fieretque: f
gitur pro constructione Ellipseos redeamus ad calculum  nobis ab initio inventum exploratae
veritatis resumtaque analogia, et ponendo:
 stabit analogia generolis: d +2ddV +8
d + 53y
+
12
F
Y S9
se
postulat. Caelerum est his
constuni problema ope
1-
a 3
a L r2d
a
+F) 4(+ F)f p  h,, et d p, (+ +d let 14Z d
yg. Ergo si d eo. moblema erit planum, item si h0
a9 + gua
poncudoaq = Y Z Recet
, et solvi potit problma nullo et duq habebimus aequationes: dZ + 3NZ  v.
Le potius ag + y
autem ila est ad circulum aq+ yr
amlemqus ut res 
poncndo a7~
17
quae est ad circulum; aequatio
 a.
7 modo silices signa in caelenis prore nata
4. Hnc patet opame
acirculi et cugusdam Hyperborae tau rectum Z transversumque aequalia habentis.
pone. V2
Vaitgr
P) 
a  + V4a
Sagt yt + Sagtus et aqt
aquatio ( ordinata erit.
s
+
a V LddV’ + day
nuncquidem modum ostendemus, quo constructio 
tg..
qua
+ZS
i
gh
ert dq
L
Ya, uia aequatio Z alta.
et ra erit  AY.
ex
sive Y e  +qy2
+Z5
+ ddqa) +d a4 0 Eaque Atue ita
Ellip si quoque e Hyphbula
sic satis orevis
seddi possit Tantum ergo ponemus gBr. et O 0 idque univers aliter, iodeoque in ipsa quoque parabola, observari potest
dimo male, id non procedit, nisi in parabola. Ex aequutione
ebr r
F27 9
9 + 2 lege - 12 pg
26b + 4er dage pus  simpllici valoris  frant duae  nempe b r rex unde 
betur
uod si jam (extra farabotam,) ponatur - 6bY + hY, sivc 8 pl- bb7 + 2 4
9. entque
valor 
qq inde
Ahabela, 9 ex supposita b. sed c non podenda bps XB. possumu etiam facere 3Vgr10. atque ita sumere g talem ut fiai o
quod mea sententia omnium coblum est, quia universalis d tit ostructio, exceptu paribetu
atet autem
subi
se
pr
lin
de
u
er
pun
sin
sum
eristi
possi
rat
sui
in
pe
me
per
tane
in
ec
De
curvo
nobi
quo
non
tria
por
ide
in
Ipt
du
de
ter
Ei
OHtid
=AF + AX