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# Title: De Constructione (shelfmarks LH XXXV, I, 17, Bl. 1 - 17; LH 35, I, 17, Bl. 1 - 17)
# Folio [5]r, page id 00066617:0009
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struction
ometicart
problematis
conici paucissem solidi paucissimis linearum ductibus: modo Termini cogniti
Aequationis solidae, u  +l y er MV + rtV
ior
+ r se
sin minus aut sint
rationales inter se et cum Y, unitate essumta in nund ita saltem instituenda res est,
ut ea eligatur unitas, quae sit commensurabilis plerisque, et eatenus certe 
ductuum compendium fiet, ac res nihilo secius geometrice transigentur. Et vero
considerandae sunt problematis dati literae cognitae sumamenales, ut a. g. d. f.
in pobleat calculo problematis perpendicularium ad sectiones Conicas ducendarum.
quae certe quantum ad usum semper assumi possunt rationales invicem. Quoniam
tamen calendum esst, geometricam constructionem etiam ad irratio nalia extendi
ubi arithinetica constructio non nisi mechanica sit tentandum est, ut
constructionem problematum solidorum generalemus nonniliil reddamus breviorem. Quem
in finem in ipsa construendi formula duas reliquimus lineas arbitrarias 
nempa b, et R. quarum ope destrui calculi pars magna potest facta
applicatione ad casus particulares. Sed ut in genere tamen aliquid praestemu:
o considerandum est quae lineae saepe simul  reperiantur, ut inde fat una
 s
fine  quod poterimus appellare e denide
 + 1 quad appellavinus) ductum in Y
rarsus in ipsius non g nominatare reperitur dctum in B nominatorem ergo valoris
ipsius g, scribemus. fB uti rm +  appellentur βY, dlucta in
dabunt +nm l + l sive Br l. sed et sape simul reperiai video: in + 1 + X ga
∞
et vel ejus loco rm + ( +G illud in sectione Conica data constrioenda, hoc in circulo,
2Sr
itenque  laru unum quam alterum duci in L. Iaque βBY 4 xgV D I rn (vel st 
appelletur (nY et et βY + g
 pr - A 13
+ r +
r
26
e
n
21
2la appelletur2.
unde fit:
quia etiam saepe simul, appellentur r
seutr
et EP +
et si rm
NEqu
O
et
1d992
et 2 p -r2
9
vocemus Dx t et O C)
erit
EFe Br, 2b. vel BY F=g - 2b) H
rn
+ t9.
PK ( Y= + b
Pr +
29
r
3+
s
qu
a
 + D
N
H p, =orl-gul + 2rn
292
Or Alren
h
assurgere
c quia nihil neessef
2
2
+SqcoY + 4b
+rm +
+2
bg rp
4bg - 199
gecce
oV.
et + 2 AY + 284g rocetur
ssigur
se
s
separationem istam labens facio,  quia nihil necesse est, 9 assurgere ad quadratum eq
Et quia Pr posi loco  Posin autem Pr loco
ad quadratum. Ergo valor ipsius pr est 4rC0
sunt ergo lineae ducenda
P 1 +8
6
d
u
+
2
vet corpus his
et iCor
esto
e
b
β7
erit
=7g- 26
e
Mmmae
.
X 110
eb
inis
d
plares
licatae
to
+Vn-
17
G+ to
_r - +bg-
t
g - r s
LG
2. et b sunt quantitates arbitrario
I PR
nt
n
ducta
licem
Irm
arjtus
2 5
C2g+ 79