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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 349v, page id 00068196:0694
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loco. v, W, X, y, Z vex, () (20), (X, (7) (2
Scribatur 117 12, 1, 14, 15, etc 21, 227 23, 24, 25 et
1t B = 11(1B -g - 13 21+ 1 = 213 23- 21- 29
et similiter
113. 131 +213. 231 = 2. 131. 12 = 2. 231. 22 = 0 seu 13. 13 -11. 11 +2323 -21. 21 = 2. (13 -11)12 -2. [3-21)22 = 02
124. 172+324 242 = 2. 142. 13 - 2. 292. 23 =0 1439- 12.1242924. 32. 22 - 2 (14- 17) 13 - 2. (4 - 32) 23 0
135.153425. 253 = 2. 153,14 = 2253. 24-0 Ah. 15- B. 13+ 25. 25-9. 23- 2(15. 12)54 - 2 (25- 23) 2930
Et eodem modo 22. 2+=12. 12 - bb
1616- 14. 14 26. 216- 29. 24 4 1 6- 19)15 - 2 (26. 24) 25 1l0
et 23. 23 (4) (13. 13 - bb et 24. 24 - (9), 14 = bb
Iis valores substituendo in aeq9. 1, 2, 3, et fiet  EK aequ. 1. 13. 13 - 12. 11 t 13. 13 - rg - X 11. 1 + r9-
=2. (13- 11) 12 = 2 (23 - 21) 22. seu sit 1+8 = lf eritque 5 (13. 13 - 11. 11) - (13 - 11)- (23 21) 2
Harum agg. 11, 12, 13, (4 etc.
Eodemue modo ex Lerit f. (14. 14 - 12. 12) -  (14 12)13- 824- 21) 23 =
mequ eramni quantulore, 13 per 1 et 12 Dx ~g. V) ex3 f (15. 15 - 13. 13) -  (15-13) 19 -7(25. 25) 24 =
14 per 12. et 13 X aequ. 12 et 15 per 13et 14 ex a, 3. Ep4, f(16 1b- 1414) (16. 14) 15-8(6 295 
Et da porro. quia autem 23 - ((13. 13, g) ideo utto
id tel daZ ad habendum valorem ipsius 13
et ita porio
assequemur, si faciamus +(413. 13-bH) ex trahibilem. sit nempet 13. 13 - bb - 913. 13 - 2913. 3345
opus foret ex altatione. Sed in fatsor brevins quaesitum
seu 2.913. 33 = bb + 33d seu 15 1 9. 13 = bb + 33. 33, : 2. 33 et 23 = 913 - 33,25 23
23= bb 4 33.33 = 2. 33.33,: 233 seu 23 = bb = 33. 33,:2.33. itaque ex aq. 11. fiet
C(b + 2. 33 bb +351 = 499. 35.11) - 5 29lb33. 12_ +ag293312 449935. 11. 2
= 49933. bb22 42993322 44993321. 22 = 0 Est autem 5 = 99+1.
Et ordinando aequationem F33Y +299. 22. 337 + 25bb33 = 29bb12 33 +fb =0
4915.. = 299bb 22
+ 4g911
ag12.
ultra pa sed 11 etiam ascendisset ad 1142, et 21, 12, 22 ascendisset ad quadratum, quod hoc modo evitatu
Equidem attntis 13 et 23 non
Rlura emersissent membra, nec 13 assutrepisset
+499. 21300
Hinc similiter ex aeq. 12 faciendo 914 = bb +34. 34, : 2. 39 fint 24 = g. bb-34.34, : 2. 34
et f34 + 299. 23. 3_ + Ef.bb 34 = 29bb13. 34 + fb =0
+ quooutue
+499 22. 3) fict
= 299bb23
perians ds
per inansos valores
534+ +gbl. 35) 54 +2 flb3+ 34 - b1. 534 + fb
24tg9  bb33
Ubicum 33 assurgat ad quadratum, ideo x
= 2bb. 3. tgm
ope aeq. praecedentis pro 33, et hujus tollendo  33
ascenderet 34 ad octavum gradum fiet et haberetur
relatio qua cujus ope haberetur punctum  B ope
a anre
+291g bb. 37)..
+2ubt: 33)
-ggbl. 33)
gybbogue.
-21199225.
ad gradum B. sd si omissa explicatione ipsius 13 ex altassemus aequationem 11, ut habete
sin AB ex datis A et D, sed quae assurgeret
quadrat 23, Ldinabimus sic 23. 22 = f5 (13 - 2: 13. 1 11 +. 1) - 251512+25 1315+25 11. 13N- SII. 12
+ 2517 2 32 A = 2515. 21. 22 4 13. 17 -7. 13. 11. 12 + 11 12 + -2. 13,. 12. 21. 21 F. 11. 1. H. R
213. 22 - X bb 22 et ordinando seundum
15 - 25l21)  - 255 15 13 +4f 1112 13 + 5511
videndum an haec communislex determi-
2 ur
possit ex seriibus aequation qua lubitia 2
fandumentatiam
an  equo
2. 11. 12 21
a2. 12. 21. 2..
Quodsi ergo depressio melior statiar in aegq. ar. 1ra
H depressiones inseremus fiet
ef 23- 21 = 1(X 13. 13 - bb) - Fr1. 1 bb)
= 2f11312
=2f1. 11. 22
22, 11. 12. 11. 22
+ bb 22
Calculus institutus est, tanquam manentebqu semper punctis praecedentibus
nA, B, etc var epuncta C, D, etc. semper alia ali alia essent
sed scopus est rem ita risdlocia, ut manente semper netimoprimo et ultimo nunc
nunc tres nunc quatuor ete. hodae equales inseribantur. Sit ergo
punctum determinatur per H1 et 21  altimum determinetur per 19 et 20
Eodem habeditur
ut hoc aequatio es
inter 13, 22, 82, 21, 11
habelituenter 1a 29, c3, 22, 12
sed ili tae quae etia
est aei gnd prn 14 sed
ut tollatur 23 per 13 assur
getur ad gr. 8, et 13
ad gr. 4. unde cm
13 in duabus aeq
ad cendat ad e.+
Follendo 13 altissime
assur pet 14. ideo
metibr videtum de
pressio
eteaque pro duabus chordi inseridendis habemus aeprationem has ex cet  sutus parpinae 419. 19 429.29 - 29- 11) M =  dantur invicem 11e1 21
ergo ut et quaeritur semper punctum B, s seu recta AB, bis, velter) etc. repetenda
 -2s29. ∞1
 pordis aequalibus achitende aq. Ba 2 hocmodo 113. 13 823 23 = 2 ()- 11) tt9 19 + 2929 - 2(19. 79730
13 qu
1. 1 =21. 21 = 2(2] -_ X
2 422. 3 - 2(292 21) 23
ae quatibus adhivead 5 1. 2. 3 = 11. H = 2 et = 23 2g L 12 ,  - 2(243 d
e15.13 deste - 2(2923)G
ubi solum ponuntur aeqq. 1, 2, B, 4 etc nisi quod semper in ultima pro summique abscissa ponitur B9 et pro
Tamma ordinata 29. Itaque produabus a tribus, quamor, etc. chaedis aequalibus pro 13, 23; 14, 24; 15, 25 et espective poni
 debent 19, 29. Quibns a44. accedet demum proprietas invae exhibens relationem inter 11 21, velM, 2, vel
=.13, 23, etc vel 19, 29 ordinata. Semperant -e = 11. 11 + 12. 12 - 2. 11.12 + 21. 21 + 22. 22 - 2. 21 22
 I1 autem et 2_ item r9 et 29 semper sunt datae, itaque tantum opus inveniri 12 vel 22, quod non potest si
sed t cum chordae u aequales arcui inscrbendae sunt plures duabus nob plotest fier nisi intervenientibus pluribus, ut 1 item
penste pro tribus chordis, ipsis 223 pro quatuor etiam 14, 20 quio et etium 15, 25 et ila por
quacam seestio ducbus e
versaeassi
22. 213,225 3 14, 324, 19, 29 et it. portos ila quaeronda progressio.
ea relatio communis aiquot ternor oinuore