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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 237r, page id 00068196:0469
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ia r
adt prax (ax
positor ax constante Ergo
sado p
1
Radius ACBY. AX FX.
KE
XEHγ. Fpd
A
DE dy. FEF da 
Arcys CEHa. (5LAngensarcue CE
tangen arcuscoplementi p D
+1 CTF, E5, tangens acys CE.
DZBB E0 tangerarcus cyptti EB.
spsecans AS+, AY
66 psecens conpl.  A6VH AV.
ACL Honresci tangens semiaru
BN H A tangens semiarer copletnti
CMpi m.
C(nH p.
Nonacalculum instituems fautem
per Trigonometriam indivisibiliu
ubi prae monueriam, esse L
LEp CL. UCM CX
BM= Bk
SA( ATBAF S. quia Ia A3G,
simiia et unum habeut latus idem AC, es sl.
Ergo erdem modo 860 L + AB AOV 6V
un calculum per Trigonometriam indiosibilm
instituemus. Ergo
se
Nine Tiangulorum similium latera proportionalia ordinemus: 52s + A et 60 B+ C.
Ax V + or
dy X Y
ta Y. S. 60
YX  )
 n
l
e ry
+
I SAS+
AB Cor dinata cyroidis
00 nA6
∞- S.X X
 s + + B, 500 7b +
rx es-
Y+ X B
appercanda ad axem
seu ad ax.
AXX Xdx B y dy. Ergo x quia crescentibus G st q V- y scribendum Y-y. quia uno ipso
A3Ep X. crescente decrescet y. inde aliquando pro X. substiluemus 1-Z. ponendo Z CX quod et semper
et sax pss  x. BY
Ergo apiis ex
alias in tali casus observandum, ut cum opus faciam, utiamque indeterminatam simul
crescere. d
 haneus ad basin seu tingena cobabnt
yda e ∞X
Eodemque modo Exda ariturry
ex y Ergo rax H da y. Ergo dmonentm curvae ex axi h
da ur. ∞
dx +. Ergo s
ida H)
du. B. Ergo Sovdu 6 (B da
dahor
nom. curvae ex tusi sevax + syd
Pax (7 + da. Ergo ) Sax 1 A da
Hyperb.
tanqu e curvao insister H sclu
dy- x Asyd
se Saxr (xda seoda syda (B du
axt
Hypert. tang. qul curo insissens
. Ergo OV a.  Ergo (ov ax B ra. Eodem modo S sdqe Bra 1 sita- xda
tu n
dx F
VL X
Secn compl
ad axem
socans ad bosin ( Seca H+ dus sed nihil
Ady Y) ra - YX) hinc novi.
Ex his jam facile inveniemus quadraturum conchoidis seu Tangntes adaxim, seu tangentes
da
complementi ad basin
dx dy. da. ex
Eodem modo
y
Nam
 Sa A Ergo Restat novissima comparatio inter
S. 0 ++B. Nimirum dx
+
S. Ergo da Bst dx +) bdx
da IIF+ B
37
Sa da H S ux SB du + S+ ay seu  amddus , rdx
Est aitem sd ax a Novi adhuc instituendi culculi hoc modo:
ex B da. Ergo  Sax  a H Z et S+ dus 
quaeritur er 
14
ced
d
sey
sux B  YX
F saq B Y X
ib 6 da. et habebimus da , SAdys, YX. Est autem da2
e mandtasten  . et
a
Taer-X
videquae ostrips.
figum
s