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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 18r, page id 00068124:0035
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observation de mons de Mariotte,
soitur les generaleuis oes Triangles ictan
gles eu nomtres : 1. 2. 2. 1+(32) 5 2 + 35) 12 6. 5+(2)12)
n
25
de
e
sive progressionis: cujus temmino  uno posito a.b. sequaus per. sit b at2b et
29
primum omnium sit  1. 2. Ert Triangulum a generatoribus, a
later ahabei, b. habebit latera:
a. 2ab. a + b. Tiangulum proxime sequens t:
a +4ab+4b.
et ab +4b2. et b+ a + +ab f 4B2 seu a + 4ab +5 . Ait Mariu observati
in
a 12
a se inductione quod ia hac progressione riangulo productorum latera lircu rectae habeant
differentiam unitatem. sive + a 4 4 ab +3b 
2ab+ 4b p7 1.
sive: fa + 2ab jb2 p 1. Erpor  + Hoc demonstrandum.
eut a +2ab - V p) 4 c. et a +2 ab +b p 2b2XC
est ergo quod non nisi unitas dupto quadrato
haberetur desideratum
generator
a. b.
si a +2 abY b24 1. erit a + 2b+ b2+
vel 2a45b
sit p c
si probarip
olendiset
vet subtracta
addita faciat quadratum
 sed  proposito generalius.
prioris posterivis Trianguli in
6. atib a+ 2b 6+2a+4b 2a +5b
Sa 4 12b
a
id est secundus
a + 2b, 4a+ 10b
54 + 126
2a+ 5t 410a + pb Ad exemplum hujus inductione cyquiri poterunt, quorum
12a + 29b
lascrum if triangulonum latera differant binario; vel
temario, et ita porro. Et eorum quarentur generatores.
a. b  a + 2bf b +2, a + rb. (a + 2b +2 b+ 2arb) b + 2 a r 2b + 2 a + 2b + Fbrrarit
seu
b
+27
2a
sive
2b Ta
2t 24
a. bsagib) 2a + 2b (2a 2b
et quonim b12a; fiec
a
2b
d
a
b
2b
22b
2a
24
3a
e + ea  Xb
va.
23b
a. 24 la,2a)2a + 2a. a +2a +2a+ 2a. ) 2a + 2a +2’ a + 2 a +2a
unde potent continuando era et simplicissima erin hujus progressionis enuntatio, qua habita
non erit credo difficile demonstrare theorema, cum ipse calculus tunc exhibiturus sis, unde in
talibus aertis maximae gevocare progressionem ad reguiam
2 +23,  2 + 24 2+8
2 + 2 + 2
3
1. (2. ) 1+22) 2+2+277 2+23. )142,+242(218, +2+d+2127+24242,213(22
2
1+2+8+2+ 224 3 +2 p +2+45+2 Jerc. sed ut adhuc alia exprssio
quaeratur, eum aliae similes invicem addudtur, id utit tnotari seu designari
W EtASI+K, A
+k + KH 1 +E vi
80782,195025. 43083 A k 11 2+ A + ra R7
te
+ C I ∞st E+ 1 AC (, 1208L
825
13D
Ai -k L
Generaloris lam lalem
f. 12
12. 29
29. 7u
1
2∞. 21. 29. Uternatre -.2.
3. 4.
119. 120. 169
munc latus
pno
695. 697.985  pavmuiu.
4osg. 70bo. 5741.
2+. AE + A. d 0+201 +k
5. 122 29. 70 1169. 10.90: 1960. 33461
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