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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 341, page id 175905688X:0363
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COMMENTAREE EN LIORuNIII.
342
tis utrinque aequalibus, reltituro que ralore quanriraris alumpcx prioris sogni
e C3, HCECd 3 - b d 3  bcd d -  - bb d d -- b3 d - a ab d =- b3 C b. c. cum
 aaCy aabC∞C d- c3 b - bccd.  BbcC - bC a abc per senum
b3d.  2 a a dy - a ab d. Uibi si demum demantur vrrobique d itcls-
aquales quantirates, _ quae in y ducta lunE EranSFCTANEUE; uEU
namtaciane aequationis partem, reliquae autem alceram, ac can- 8 intelligi-
dem dirilio instituatur per d =c, orietur cd d + 5c d - b d d -- il -: aur
2. bcd. F bbd - F bbc = bcC∞ 2 a a Y.
Similiter, cum rectae HI F _ FM aequales (INE, CruNE quoque
earum quadrata =
4
2. 2 2 
a 
a
L
a = bb - 2by. Fy y aequalia. Unde ablaris uerinque aequali- cellisitur. +
bus, reliquis que mulciplicarisper aan adhibeatur porro transtario,
utquanticates in x ductae unam ceneant aequationis partem, reli-
quae vero alteram, Aetque 2+ -- b + F 2 a a by = 2 a aZ y + a a Z 2
aa b b ∞ 2a ZZ ~ 2 ab b X. DividatUE jaM UEraquC ParSPeF
Z n b, _ Orietur 23 F bZ Z F bb2 + b3- 2 a a y + a a 2 + a a b
∞ 2 aZ X.= 2 ab X. RursuS diridatuF UETInGUC PCF 2 aZ L 2 ab. 8
trabebicurx ∞ 33 F b22. f bb2 + b3- 2447 + a a2 + a ab
2a2 + 2 ab
Ouia vero ee supra quantitas a invenea fuie
C3 - bc0 + b bc - b3- = 2 a ay + a ac = a a b
24C -- 2 ab
23 . 622  bb2 +. b3 = 2 aa y + a aZ + a ab
2aZ  2 ab
C3- bcc- = bbc -- b3-+ 2 a ay + a ac - a a b
2ac = 2 a b
Crune
catis caussa, Scribatur rurIuS 8 e 3 pro - b3 + 2 a a y - a ab, 8
8 e3pr0 + b3 = 2 a ay- + a ab, ee mulciplicat d ueraque aequali-
catis parte per 2 a, Ceu, quod idem est, dirilo ueriu sque denomina-
coreper 2a, insticuatur mulriplicatio per crucem, ut Fractiones
eranelcane, Hetque c23 -- b23 -] - bc~Z - bbZ Z L bb62
b32 . - a4CZ =- 4 4b Z 8 c e3 8 be3∞C3Z -  bc3 -- b662.
bbcc. = aac2 - ]- b3C - L bbcZ   a a bC8 Z e3 8 b e3. Ablatis
Porro uerinque aqualibus, relticuris que raloribus quantiratun
aumPtaruM B e3 _ 8 e3, HCLCZ3 - - bZ3,L bCZZ - bbZZ
b3 Z = a ab 2 -  b3 c -- 2 a ac y - f a a bCD C3Z- - bC3 - bC6Z
bb0c - = b3c- = a abc -- b3Z -  2 a a Z y - - a a b Z. UIBi Ei rursuS
urrobique demancur aequales, ee quancieates in y duetx ad unam
PaTECMI
iu cun
per sienum
cum per sie
bum et in-
tum per sie-
num B in
2bb x telligieur-