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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 72r, page id 00068197:0143
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Invenire tres quantitates continue proportionalis quorum humma rit ∞ a, et (uboruum Xb.
sint quantitates X, y, Z, erit qu X + y + Z∞ a, et Z ∞ a - x - y, porro sit brevitatio
causa a - y ∞ V, erit 2∞ V - X, que duita
in
ergo
et
re
Vn = Xn∞ yy Eivo Xu - vX + yy ∞v.
X∞ =V + V200- yy prima
2 = X ∞ LV - V  v0-yy tertia couantitas
Carum Cubi igitur hunt
00 + - 0012 00-77 +1=0800 -yy + etc:
s
23 - 20014 00-yy + 1107200-yy = et:
2
+
= V
e
+ 3VX , 02 - yy ∞ b
live y + 2 -3Vyy ∞b, et lubrtitutis citerii erit
V+ a - 3 aay = 3 aYY - - 3ayY + 3y - b. ∞0
Eive a3 - 3aay + 3y2-b∞ 0
Tive V = aay + = a - =b = ∞ 10.
Mea methodus.
1)
XAy+Z = a X + y + 33 = b NG et XZ = yy
sit xy + XZ + gZ = M Ergo per 3 et 4 fit Xy + yy + y2 = m. et per 1 et 5 fit ay = m
)
rursus generaliter a = b- eM (per 142, 4.) jam Xry9 Z+  3Ma + 8XyZ 2per e.
jam ex Tabula Theomematum mea  per 1. 2. 4 s. b e2)  (7) Sa y()
A
a = b∞ 3ma +3Xy
day 
3
(per 6) (per 3)
Artis est ita calculum
instituere, literasque
ita assumere ut in
calculo irrationales
destruantur. Quoi
hos loco fit
seu 3 -ay + a - b =