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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
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oh. Craigii Methodus pro quadraturis publicata in libello
in 4. edito Londini 1694 ubi meum calculum differentialem adhibet.
Et primum quidem pro Quadraturis Algebraicis:
AM, y GM, x Me seu MPZ.
A
EG L qu Gm = AMCA
AMCfigura quadranda
AG linea quadratrix
Expressio Analyticae ipsias MC seu PC,  (ide est valor ipsius Z.) reducatur ad
vatorli secZ Cey 2davatur ad
formam simplicissimam, liberando terminumy quantum fieri potest a signis
radicalibus (si talia occurrant) ita tamen ut quantitas y extra oinculum generale
non habeat exponentes diversae denominationis ab exponentibus ejusdem, qui sunt sub vineulo
Expressio sic reducta multiplicetur per quantitatem y; et apponantur omnes potesta
tes (quantitatis y) per quae sub maxima producti potestate continentur; tales autem
exponente maximae potestatis in productos; afficiantur E teraini coefficientibus b, c, d, et
abdem atatas  tot 
erunt hi termini (quibus vis signis connexi) altera pars aequationi quaesitae, cuncs altera
est XX. si se licet valor ipsius q, in y maltiplicatas habeat ii erunt termini
useu 1. sin habectit y, emut apponendi y, y et
vel sia maxinus producdus sit y B emnt potestates apponendae i y3 y, y yt y sent
apponendi yt y5, e y, y y
Ex. gr. sit 77 =  + aagy. fet Z - y Syy+aa hunc valorem malsiplica per y, fiet:
ju syytaa ergo habemus bgus  quia ergo y extra vinculum sic assurgit ad yy
scribemus bgy + caytreaa hanc jam formulam mastiplicabimus per irrationalem
syus taa Ahoc autor monere neglexit, patet tamen  exemplis, et fiet
lx byy +cay+ eaa, saa-yu = xx- GB unde ostra Methodo tangentium
Leibnitiana facile habebitur MP. qua aequanda est qui valor comparandus est
say. -a hic vator
7- ip te
eigo maxima dignitas extra vinentum
sit
valori dato ipsius MC seu Z.
- a
0
b + C + d, aey -a
per y maltiplicatus dat yu a
est y et cubemus et scribemus y, q’y, seu gy ay aa
1
di
idem prodit vel aequivatens ex
sit ZZ = gy: conta scribi pt. Z- y, syt
fot  primo modo fit byy + cay + eaa =xX.
Habet et hoc commodi ista Methodas quod eadem Methodo
reliquis cotandi modis
ryta a
inveniantur, qualiscunque sit errationalis vinculi, ut si quaeratur
n- 3
sit Z = y yra fiet b yr + e. Y + d y + ey + fy ett, V yta = x
y, Vyta
fit b = 2Y: n1t, rI et c. Ira C c - 2V:, n+
C= 2Y
RTIY +I
d-
A. 2Y
ncrEI, E netI, nrHI, 
p-2
e = nHIYHI nrE, h- 1YEI, n. EYHI
n. n - 1, EY
si sit 7 = 5 + g, Vgra fint X = Vera, b.  c. s + dy + c. y et
1t
n, 1- 1, n - 2, 2Y
n sit ratio
et fiet b = 2r:, n+IYHI C= EEC 2Y, NHIYFI,:, AFCYHI, nr+ d = 2Y, rtI, :, n + 1Y + ), ut Y1, n= IY +I, (n . +1
(==EY, n-IYHI, :, nFITE, nrFI, n - IYEI, n -2Y +1, f2Y, A - 1 - 2 +1, :, nF CBAI, nre 1, s B1,  2I
tria prima signa sunt afftrativa, reliqva deinde sibi socedunt alternatum,
Modeore quando abscissa assurgit ad multas aequaves, cal culus habet plarimum laboris; Neo
an s saepepossumus reducere curvam ad simpliciorem ejusdlem Graeris. Si AC: (G:: HK: CF fiet DKK = BCF O
dmc mnihi dab calulus ut non sit opus fgmist sit BCx: CF,7. GC vel dH, Z. HH, DN
m
equatio rata b = Z+ aZ, 5Z +a
sit Z- Xm et siet y = mt X + m pak 
um defiait qui valoc ipsius y dat omnescurvas similes datae M
sed brevius pro n poni potest Zn. quia semper hic in mulliplicatur per pare nume
puro si n = l. resolvetur aequad in simplieissimam
Area inqusror pt quadrari (inguit autor p. 31) quando aequatio est
 = sZ. +B a. 3n -C 142 +a si n er c sint numeri integui positivi, et nmajorgm c
 (+ semper in hoc casu procedet quaedralum, etsi plures adsint termini quoed ego sine calculo
intendum figum reduci ab ad simpliciorem, hoec riisus ad setupliciorem, doace
andem permeniatur huc intetado ad simplensuna
t