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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 258v, page id 00068194:0516
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 257r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=516
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.84
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

s
 Le naturel
y Mais il faut l chauger d’expression, a fin, de douner
Son tiers veritable ou approchant.
Donc il sera:
1. 2 191 39,  3y
exponer ee Donc l’exposant, c’est à dire le nombre naturel
dont ou a esté sontiers ou  precis ou approchant, sera q2X+1∞ 2412
Ergo Tris Donc le Triunsulaire: O dX X ∞ 4X + 2X +1 8X 4X
F2. +1 224+
on dispont naturellement: 24 + 2X + 1 2X + ZY + 3  2X + X
les naturels.
3,X + 1 ∞ 3x + 2 ∞ e7X
Multipliant l’exposant, ar son triangutaire
les exposant:
2X +1 ∞ 2X+2 ∞
Meullipliant l’exposant par le Plaire:
le Triangularieantrement 3X +1 34 4 ∞ 3XH 3X13 ∞ 3X 3X+1
Cullipliant  l’exposant parle Dlaire: 2X +1, GBX H, 3XM ∞ 1X+25 3X + E, 3Z ∞ 2X,. 3X,  3X +1
il viendra
a+bp ace. 4
acF ade
1) bce. bcf
bdf
2X + 2X + 1
2X +1
abuteu
aediontons
4X7 + AX + EX
+ 2.. 12. +
AX2 +6X +4XHI
2X F3X +3
+2
6X3 +9X + 9X
+4X + CX +6
6X +13X + yX +6
1BX 1CX
4X2 +6X + 4XH ∞ 6X 12K + M +b C AX + 2X
3,2 + 1 3.8 +2 3, = ∞  3.= + 1) 3, 2 +2. 3.2 ) 3 = +1(327.
Et l’expression generale: 3 3X + 1  3Y + 2. 1y Ecae expressiones
forum aequadionum disjunctivas.. Ergo erit numerus Triangularis:
son s+y 2X + Ox ∞ 2X + 2X + 1 ∞ 2X + 3X + 3
ve
bd