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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 61r, page id 00068049:0121
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 62 lines, status machine
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quimlibet ex eadem
Tres quantitates compositas ex una inlos
incerta x et tritus de una extribus datis a, b, c singulas
aequare quadralis Xta X+b, X+C aequare ois
sit X = 10 4 n y 4 1 Yy + 1y r14 , et: 20. 20+ 2. 20 1y+ l. 20. 227, 12. 20. 237 12. 20. 24d, et
(.) 
+ 21, 2 (y +2. 41. 229 +2. 21. 23 y er
e, et quadralum cui aequandem quantilas xaa sit  fiet a  seu
+ 22. 2y4
seu compendio X = O: D et X+ a= f fiet 0: + a Y seu C + ga   q sufficit
ergo _ O  quuri differensit D Y 4 fiet O= 2- a. DD. assmsimus jam O et D supere
ut assum unus 2= 30 + 31y + 329 + 3393 ete seu 22 3030 - 2.30.319+ 2. 30. 32y +2. 30 39 7 +23034
(101
31. 31 2 +2. 31. 319423135
e et exaeq. 7, explicando 0, 8,2, fiet: 10 = 30.30 - a. 20. 20  et pari jure L 40. 40 - b. 20. 20 33. 3 
et pari jure = 5 50.50 - C. 20. 20 4 si scilicet ut 30, 31, 32, ete. pro a, ita 40, 4, 42 etc pro b
et 50, 51, 52, etcc pro c assumamus. Porro 11 = 3. 30. 31 - a. 20. 21 = 2. 40. 41 - 2b. 29. 21 = 2.50. 51 - . 20. 7
et 1 = 2. 20. 31 + 31. 3+ = 2a. 20.27 - a. 21. 21 = 2. 4042+ 4191 - 26. 20. 21 - b. 2121 250. 51+ 51. 51 - 2c3011- C. 21. 21
(16
et ita porro, unde sit 3 30 b 20. 202 40. 40 -38 30,: a b - a = 40. 40- 50.50,:, b -c
(22)
ex 13. A. 15 fit: 20. 21 = 40. 41 - 30. 31,: aec b- a = 40 41 - 50. 51, : b -c
Et similiter
Et similiter ex aequs.
(2
16, 17, 18 fit: 2. 20. 22. + 21. 212 2. 40. 42 + 41. 41 - 2. 30.32 - 31.31,: b - a=230. 914 41. H. 2. 50. 12- 31. s; b.c
Et ita pergi plterius potest. ponamus jam 20 30, 40, 50, non ascendere ultra 2. seu abesse 23, 32,  et
fiet: 13 = 24. 41. 42 - D. 21.22 et 14  et4R43 + 4242 - _B - b. 2221
et f. 21. 2227, 41. 42 - L. 31. 32,: b-a f 22. 22 = 42. 42 = 32. 32,:, b- a 4(38)
(42)
12 42. 42 - 52. 52,: b-c3
inciprendo a novissinis ex 30, fit 32. 32 bud 5252b a seu sit 52- 16. bu a. 32
X. 41. 42 - X. 952, : b-c.
(11)
et ex 27 fit: X de S1 buc, V- a (3.2) 31 et ex 24 fit
fit 42 42b-c . 32.32. buc ~ 42. 42 b a = 52.52. b-a. unde fit:
424 Haberi seu invenir potest 42 ex aeg. 30. et 41 ex aeq. 27. et 40 ex aeg. 24 e
et rursus 40 ex aeg. 22, et rursus 40 ex aeg. 20 quos tres valores aequando, habentur duae
povae aequationes, quas ingredicntur 30,31, 32, et 50, 51, 52 solae, et ita sufficienter
a99. 19. 21, 23, 26, 29 inveniantur 20, 21, 22
Eurgo habemus 7 aequaves, pro B literis 5 pro literis 9 nempe 30, 31, 32,50,51, 52, 2023, 22
hinc exit, habetur. superest ut per 19, 2t, 23,
Atque ita videtur haberi exitus, nam de literis 10, 11, 12, 1514 non est difficultas.
videtur in genere sic institui posse ratiocinatio de sufficientia literau
Ascendat  ipsius Numetator valoris X ad literas gradum g. Nominator ad
qui est quadratus ad gradum 2M. Habebit O Numitator literas e; at nominator h. Habeat 
quadratus 2 literus gradus 2l, et  utile erit facere g = El et h = l
terminos coparandos 9 literas g+ xP + I + h seu 9+ hd + Lg = 29
tabeluns
Hoc si denno faciendum novusque sit quadratus (4) literarum , et -
et terminorum g, habemus ergo in universum terminos comparandos 29, et literas
29 + g. Quod si tres quadrati desiderentur, habernus terminos comparandos
Generaliter cuiu scil. Terinee numerus com–
parationam est 9C, posito e esse numerum quadratorum, et, e gradum
39. et literas etiam 39.
ipsins D. Numerus autem citerarum est gr1 (ob B) et 9n (ob D) et cg
seu 8 p 29 per) ob numerium quadratorum quo solomu ex hibendorum; et ita
numerus literarum est: 39:2 + Cg: 2te 2 qui debet aequari gete (vel potius
excedere) si sit ergo l. 2+3g: 2 + eff. 2 = gete fa 2.2 = C: 2 seu 3-e Non
ergo pt methodus haec succedere ultra gradum 3. fiet 39. 2= ge: 2 + c: 2 seu
=
39.G41