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# Title: De Constructione (shelfmarks LH XXXV, I, 17, Bl. 1 - 17; LH 35, I, 17, Bl. 1 - 17)
# Folio [7]r, page id 00066617:0013
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00066617&page=13
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 183 lines, status machine
# Lines: 183 recognised, mean confidence 0.74
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

ntur
minata
inatae
aliquae
per
rautem
quia
le
e
fier
t
6Va
ab
tunc
ipsa
minatae
50.
ipsa
ebitur
c est
quatione
nietur
tunem
sius Z
vel
cum
Y
ersalite
R.
per
m
rvo
n
e
nomina
late
nempe
5
le
versus D
axi
A, axi AE, par allela 64  Y. jungatur recta
2
2 K, et ex puncto
K ad eam normalis erigatur RH, quae possit + nr +rr, denique centro 2 aradio 2
erigatur circulus, qui cuParabolam secabit in
punctis Y unde demissae in k in
definitam axi parallelam perpendiculares erunt
rectos axi rarabolae applicatae,
ducta recta
V quaesitae,
designabunt puncta
ipsi parabolae parpendiculares sunt
quae ordinatim ssed angulos
ad quae ex puncto D
potest e
12
Nata ttsura s = n. haberi Germetrice non potest, ideo pro - n, poni debete
Veniamus nunc ad constructionem elipseos:
dam y + +2d12a24 1,3 (+41f
-24
cutus equalio est:
1.95V
Melius est resumere analogiam, quae iat:
C
quaedam contrahendi caus. mutare, ponamus: ) YZ
et fa fiet (E +d( + 4)7 Ex calculo illic patet, si (+ ++ ( +) f p0. tunc in omni sectione
conica problema Aeri planum, et constructionem brevissimami, quare datae sectioni deribttur
tantum similis; ita ut f hunc eveniat qualem desidlenamus
retenta 9 ad eam ducatur
minima quod utique brevissime fit, um ex calculo proposito atqui minima ad unam continuata
est etiam minima ad altram et forte alteram ne duci quidem necesse est, sed sufficit intelligi
Videamu quid ad duas sectiones conicas similes sive parallelas requiratur
AX  X.
BZ 5 Z
2212+7ut
1
Xo Y F.Y.
Item V F1dZaX Y a X
sive 2x +∞2
aGz + B
bive
b6
altpax axx
b + 2687 + bY7a
27t + 7v +.
vel b+ + 27bt + by0
.
a4
b
F 1
a
at
2xq. +X
a
FL: Jam
sande bo
2Z+7
7
Y. 1 a + a X
+
+ ab q+
27 + . qd
v
ponmus pi sed nondum ommes predemntis conditiones exhace
+2Xa4 + ax.
2Xq+ Xq
simus, superest
Ergo XG 1  7  hian BX p, 7 - a + a X + b + b 7
a
in ver
Le
CD S) CVa
L. 7 et AX, AB+ BX
ZY
e
Ergo Ergo Z B X - e + a  b + a X ponamus 1. + a 1Y. et 1.4 b 7  et - e + a , A.
7
 , +F + 1 
+C
1
-e
a
fiet Zri Y X + hat ba. Ergo 3
+ Jam ut X quoque et y alteram exale derinemus: ideoque
a qu+2 Xaq + aXc
2X qu + X 9
X4+ X
2
s
b f2
et
b+ + _)X + harba + gX + 2VXha +ba +ha +2tba b
bf2
2Z
Vraharba
cdv2b+
+V +
002t F
5
b
 khat) xbath a ttiba eb  F
WE, +
vel alterutram earum vel rationem earum pro arbitrio assumi
aqu=
Et
2ZX7. Eo et dividendo utrumque per st
+
+
habeatur et duae sentur 
incognita b, et F. patet
posse. Ponatur a
1+
fier
fier qu
exq + 274 FZ2t evitque enque et dabitur . eritque B a
2
expiiniamus es per sa + bp + n et Z per m + ba et q per am + 2ma b + b a. Ergo quae
2xqu +a
aequatio resoluta fiet cubraea quia ducenda in Z
ralio seu Z HP X. Quod notabile Theor ema.
reti 
se
x n Y
 seu b r7 v4 1 14 gv
i +Z + nx + nir
+n
y
(1 to
r
2a
si poneiltur t. + b  0 forat semper eadem
pone + dari; id enim necesse,  ex ut calculus mima fint brevis
2)
as
et
oncucta b
sive
tEpri
a F a X
b = BIX haba
d
cuim ergo una tantum aequalio