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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 39, page id 175906937X:0063
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=63
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.79
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

+ 1b
+ 12
S = 1, 
ol
ces, opu.
bus eo
Caetacu
D, CC II
ciPICa
ouecun
rodue
Det a-B,
no M
roductum
endo boc
2BOUIM M
DHCOVH.
EYbC, G
dicle. si
tum quae
In PrOpO
Bb: qu
du5) Eum
Ia Cran
num di
le polio
NIA TA ESEOS IIH LYE RS A L 15.
_ quod oritur erit quoriens quaesicus. Uc ad dividendum V 75 aq
Per V 27 a a hoc est, 5 aV 3 per 3 a Y 3: divido 5 a per 3 a, Ceu
5 Per 3; ericque quoriens quaesitus = Peu 13. Sic e ad dividendum
V a- Laabb per V aabb L b, hoc est, aV aa L bb per b V aa- ] bb:
dirisis a perb, sir quotiens Z. Non secus V abcc scucV ab diri-
Tum per Vab datc. FE lic de aliis.
Ouod si communicantes non fuerine, dividendae CrunE quan-
citates sub signis radicalibus comprehensa, de ei quod oritur
praetigendum est commune signum radicale. UIc ad diridenduim
Va3b = ab3 per V a a - b b: diviliS a3 b -= a b3 per a a - bb, FIE
ab; unde quotiens qua situs erit V ab.
Ec quidem si signa radicalia fuerine diverta, reducenda prius
erunc ad idem lisnum, de deinde operatio insticuenda erie, ut jam
dictum est. Ue ad diridendum a3 - L ab b per V a2 L aa bb: mul-
ciplicando a3- F ab b in se, tic a L 2 a t b b. f a ab2; quare divis i
V a- F2a  bb = a ab= per V a t- L a abb, erie quoriens V a a- L bb.
Sic de li dividatur V a + - f 2 a3 b -- 2 ab3 - b 4 per a ] b: multi-
plico primum a ] b in se, ue hiac sub eodem signo radicali
Vaa L 2ab-]- bb, quo Facto, si dividatur V a- ( 2a3 b - 2 a3B B+
Per V aa F 2 ab L b b, Hiec quotiens quaelitus V a a - b b.
Non alià ratione aq ( bb divilum per V aa L bb, Facit V aa- L bb.
quippe dirilo quadraco per luum lacus, oritur lacus. Unde li
a= abb dividatur per V a a- F bb, orietur a V a a L bb.
Porro si dividendum (IC a3- = ab b ( a b V aa L bb per aV aa L bb-
dirido primiiim as- f abb per a V a a = bb, d FIE, uE ante, V aa L bb;
tum abY an + bb per aV aa F bb, _ Hb, unde quoriens qua sITuS erie
Vaa + bb + b. Non secus si dividatur V a = 243b - - 2 ab3 - b7 - aa + bb
Pera -= b, Oriecur V aa bb - a + b. Similiter (i dividendum pro-
Ponatur ab L b V bc per a L Vbc: quoniam ab divis a per a, ca-
dem exoritur quantitasb, qua provenit diridendo bv bc per Vbc:
hinc quoriens quaesitus erie b. Fodem modo aab - bbc - ab-+
Vb0 dirilum per a = Yb0, Facit ab--
bbC
Postea ad dividendu a a bc per a + V bc dirido a a per a.
_ FE.