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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 173r, page id 00068201:0345
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Aequundo duos valores ipsius M ex qiput et nc. fiet
(inIFM. 13. (416. 315) U m no (483 = 405) nnG id. 3o5 qqui). + aumg Cosit a ) fbrac)
O=  112. 310 Mo 31a to5. 2o. 1 9) +2. 1s ui gn (gu gos, q2 (0) MM. + 3. 112. 30) 10, (91 a 5oz - 40) 310) l
Habemus ergo duas aequationes 8 et 121 ambas secunctum C et n sed quia una harum duarum
potest quidem inveniri pervulteram, sed non amba inter se, ideo debent coincedentiar hae
duae aequationes, ut vel prane plane sint identica, vel saltem ha eaedem, vel saltem
habeant communem ladicem, quod sufficit. Compendi causa sint duae aequatio
610 l + 603un + 613ln + 600 aa = 0 et poll + go3nn L7 13ln 4 700 aa =
Tollarmus literasB N ergo et d invirem fiet. brall 610. 703l(+ 603. 103 un +613.703 In + 600 o3da
603 2603
603. 710l607. 703 nns 603, 113 In =- b03. 700aa
(613 - 4. 610. 60 ) l = 4 600. 603 au - 613
2. 603.
703 nn + 703. 713 ln + Z 713 = 4713Il = 710. 703ll - 700. 73aa
fiet 703R + h 713L = N(4 713 - 710. 703) IL = 700. 703ac
(713 - 4. 710703) Il = 4. 700.703aa = 713l
703 f613 - 4. 610. 605) l = 4. 600. 603aa = 613. 703l ( 603 1513, - 4. 710.703) lL= 4. 700. 703 au -603.713
sed ut n habeatur per l rationaliter  nec tamen ratio n ad l fiat data; oportet
2)
g . 13F 4. 110. 763 = 0  et n L 703a . daae, b2d 60. vet ilatit lntie
Et superent.
Et superent 703t Z. 703 a Y- 600. 603 = 613703l ∞ 2. 653 a V- 700. 703 - 6og 7 13l
unde duae aequationes 703, 600. 603 = -603 700. 703 seu 1703. 600 = 603.700)
vel 608.703 =
et 1613. 703=603. 713 Ex.  et Z est 612215) 610. 63
et fieret. S (2 403
705
et ex + est
2 710. 703
610, 603.703=710703. 603, unde vel 603. 203 = 0 vel. 620. 703 = 111
Si 60370) =D non admitsitur fiet 603
Ex aeq. 1 et 2 
613 - 600 si 603 703 non aotur
613 4. 610. 607810.615
7132 = 4. 710. 703
710.713
610 - 603 - 713 - 600
610 = 710
000 700
et denique 613 = 4. br0. 63
itaque revera duae aequationes 9 et 12, quoties et n extant tantum
in  gradu secondo sine l et n si primi gradus, debent coincidere inter de
efficiamus primum aequationem 613 =4.610.603 quod in aeque Dabit
 613 = 2 1610603. et fiet L(410 -310). (403-303) = + . I4 (310. 303 + 410. 403) + s (410 303+ 310. 40)
en rgritio nene
seu +418. 403 = 410. 303 = +, 3102303 + 418, 405 + 2. 310.303. 410. 403 pro eiui 5i 1
410. 303 +403. 310 =0 seu 4W = 31
418. 3035 +310. 403 + 2. 310. 303. 410. 403
41403 + (2, 410 303) +(4). 310. 303. 410. 403  =0 5e u 410-- 30
3102. 3032
si = sib, , fiet
et nx 82d
aro 387l. 400 5 205) un +. = (316. 105 0. Aor. ) In 4 2 (30 303 o. 405) (ab tac)
2. 703
Hi duo valores ipsius n, ut aequentur, fiet
4. 10403..
+2. 123. 310, 40. (310 4032 410303 ln
et fiet - B sn = sial = = ((15- f10 Co1) U -1 600. 603 aa
seu n n-
seu n
+2. 72 n (3B0. 303. uo. 4o3) (abtac)
R e  603 nn, + 603. 613l1 + =613 l = 4 61  = 610. 603l = 600. 605 au
invenionius literam n
700
Sin + sit a fiet
4032. 310
4032310
403 30)
p. 110. 403 + 3 10. 303 =0 ff + g9 + f = 9 fit sf +59 + +99-
(2) 410. 403 =+ (4), 310. 303. 410. 403 = 0sin 410403- - 310. 503, gg - 99  2ddd
seu u
3. 3032
3102. 303
tantius et fit f+g:
priore. modo fit 410 303, :, 403. 31o =
postenore fit 41o 403:, 310. 303 = consenti  seu f. 9=
seu f:g = f3
= - 403:303 fiet 403 - - 110, 303: 31
prre do quo (BOZ pusterore 410  (4) 303. cum jam pri aequatio L()(
 adeoque cum sit = 31oval + 303 san, fiet D = 410 +al - 410(303: 310) an. seu fiet
283 123(410 -318) FL. V2. 310. 410 10. 13 40. 203) sisumamus qeo. reo
 orenes io at rodaa, in que atit at cocoerrod
si fecissemns 610 =0
et 603= 0+ adeoque et
710=0 et 703= 0
et 6131600 = 713:700
habuissemus n = - 600a
Sed  hoc non licet
Nam sive faciamus
n = .. l sive n =. 1 : l
foret In rationalis
contra intentum.
ebbe to
d  
et 6137 = 4. 610. 603
vel 7137 = 4, 750. 703