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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 323r, page id 00068194:0647
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In omnibus untatibus seu Numeris non sunt tot unitotes quo
in aliqua enrea puncta di
imprrenu d. sit Curva, cujus applicatae sint progressionis harmonicae, videtitur poterat
api trreducibilis ad aliquam aequationem, et contra est tamen. cum sit Hyperbola.
moges. Ingumendum est in figuram, quae ad altiorem semper atque altiorem aequationem
del oposite scendat, ut ejus applicata maxina sit, r Trianguli sequens tamboli; nusus
sequens parabolae cubicae, et ita porro. NIhil video quid prohibeat eam
esse Geometricam describitamem, non potest, opinot. Sed puto tamen tan-
gentium ejus loca seu loca functionum esse eometrica: aequationis capalia.
A X  potent sic exprimi _ X = y. Et aequatio
a
erit: X Ya Unde investigatio tangentium haec:
ex  = ya su p = va
-
= pt
PXO
Et quomam numeri β. aescunt cum ipusa X. uniformiteus ideo
 tagens semper erit eadem seu infuite, parva et ideo tangens
ducenda in idem semper punctum, nempe verticem, et ideo figura
erit Tuiangulum. Si inverso modo sumas applocatas parabo
larum ad axem, erit  p = eX, 0 ideo infinite longa
seu rectangulu aqualis sigura ert rectan gulivu.
An fortasse infinita aenrationum varietates varietatum constonunt denique figma
quonitem infrcutae paraboloendes, tot scil. quot nuneri, non nisi linesam componunt
2aX + X = y.
fet 4apx + 3 pX = 3y3. Ergo p=
6a2= 323
ba XF3X - ZaX , 2
4ax + 3X 4a + 3X 4a+3X
hoc per P. dividatur y = B cax + X, fet (paXtX +aX F3X
4aX +3X 
16) 2aX  3 , 2aX 1
1bax 24 a + 9X
Aax + 3X
qax 1x H9X6
64dx +90a +sbx5
S9) 2av 1X S) rau, X Mrax
644X)+ 1aX  18C + 2x X 6=X + 1  1  aX+ 27 X
2aX + X
24 + X
hoc figura est quadrabilis.
64 a 2X + 11 a X 1 108 aX + 27X 64d
24X + 4aX + X
se
rax +XTAXEX
62a + 144 a X + 105 a X + 37X;
2aX + 4aX + X
quadrabte
in curgam
tcato sunt
nons
reometricae
aX= 3
2aXp = 37
aX 2
AaX+ 3x