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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 16
# Folio 12v, page id 00068169:0024
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Theorema, 1.
superficies corporea homogenea habet
partes superficiri mediae cujus bedes Bases
siu duperficies com sunt planae, habet
partes, partibus basis proportionales
Theorema 2.
Partes Basees superficiei corporeae
sunt ut pondera Superfierum corporear
par. Bases planae superficierum corporearum
sunt inter se ut sunt inter se, ut superficies
corporeae homogeneae aeque crassae, quarum
sunt Bases.
Lrema
pro
sunt
defin. Superficies statica est
superficies corporea cujus 
quam
utimur ad superficies matien veras metiendas
problema.
superficiem staticam omnium
aptissimam parare
Theorema 3.
AY parabola, s. versex AX, Axis X Y ordinata
PY perpendicularis ad curvam erit AB semi-
latus rectum
sit ax producatur pr
sit 2a usque ad V ita ut YC sit constans
4X  d XY, y AXP+ a
et
b erit  PXp sit AZ Z
v..
PY = Hy+ aa)
L: Y
PX . Z 
PV = (9y. + aa) +b
 pV: pY- v:y fiet:
gy +aa) b v
= a + Y-Z,a
Est ergo X a  vV2ax  4a + XX traX 1Z) - X) Z: aa
fet et pet ava = et aD = ay + xy Zy, et
 +29 ay :y mitus Rarsus
Aet
frent.
ap a =ay. = X9 Zy et X - av 17y - ay
 rulsus, bys+ bg b: 9y + aa) = v: y
V -9,: g.
fit. bb: gy+ aa = vo 290 +y, yy, seu fiet
bb gy= Dvgy -2y)V + y + aa vv-2aay +aague
undom habetur ae quatione cubica, qui valor substituatur
qui valors sabstouatur in valore exi ipsam X et y substi-
tuantur in ceq. LaX, FG hallebitumta vtro d
curogem parmose parplletu si sit parillela eotra
pontur b, sinperraiela intra ponitur: = b
homogenea ubique
aeque crassa planis
parallelis contenta
 Bases superficictum staticarum suit ut pondera
bt Hy+ aad)
p
om nolri esse parabimm
exmnem ex eopates, quia
un de B, non est constans
sam ip
FY crescit
 nam manenle Xp,
pibum ipsa F. Y non manse
idedn sed decrescit
d Angulus. FW V, FVY
dmil ac qingis accedibperpen-
iculari icum ergo
cuescatu
mapente XA, tam
Crescit Z P.
us yt
X
inceq. (av: q +qLa X, et ita habebitur valcr X sine y.