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# Title: Leibniz-Handschriften zur Philosophie LH 4, 2, 11
# Folio 8v, page id 00068571:0016
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Ponatur dari
Genealiter: Curvis VC ordinalis positione datis invenienda est tangens
curvae C (C). posito ipsam  ejus puncta c  inveniri utcunque data
relatione inter AB, X, et VE parametrm a var
secundum curvas variabilem, curvae VC. Hoc Hoc quidem facile
est, si relatio sit ordinaria, sed si sit, transcendens
v. g; si arcus V
debet aequari quantitali datae vel relationem debitam habere ad AB
vel si idem pelatur de sermento Trilinei VBC V area tunc cum
quo scla BC odimata curvae, C (C) detur non nisi quadhatoriae non
potest connunde  apparet modus differentiandi secundum a, qui tamen deside
non
cu hunc defectum supptericiim jam semper procedetus calculus sequens
ratur.  sit 1BC = G et y=  Yt (xia) entique bu a da a, _ rt (70)
et  de y d (eC a) 1 erit F. C = da d sec) rltaius sed ha
pr queadatur val Y adhuc semel ex X et a uno  Nam unus modus est
ex natura cuvva Sed nostra metendu differentiandi s
sit sit A se aequitur data fit siddx dydus = h ubi
semper haberi potest
cum involvatur a aptil. paramerta Vaciabilis cinet moclvatur in vorcuro
Habimus dua aequationes
ordinatim dariando dates
masit
(1) y = (rl. Xia)
curvae (V. C2C aequatio talis -y = 1r (X; a) ax sed
rat cujus tariens ducenda est diver
aequatio curvae quslae
Sitmy = (do) y =  nol)  a) motlendo etue
a duo vata Aequanto tuos balores, ripsius y, fiet:
(IXa XBisus ut X (rdt) (72). nd Bs) (d to) a = (X (YL. X)
tio
jam ex ag. differentiando fit
(5H) ayn du na) rtxia
5to) F1C =tos da ( d (sec. a) (Yl.Xia) sed aeq. 3 differentiand
aadta
tsda  dx d ffl. X) Ergo tandem  ex5 et 6. fit
dy sol. a seu FiC des  dx d (r lox) (ec. a) (r lo Xsa)
1e
e
Ad dus secix sus DiC
db se dx d sex. X (Yb. X; a)
at sed GC seu dus sect curo.   C() 1 F, C - D C Ergo tande
ad
fiet G1C   = dx; + ffl. X) d sec. a) (Yl. X, a) = d Sec. X) (YL. X; a)
si non dapeternaequ 2,
sqE et l’ambae fuissent tractabiles et tolli
potum a jam habeissemus aeq. ex X et y quoesilam
si daretur 6 qu. 1. sed pune abesset aeg. 2. tantumque ipsa 
curva it 1(C) daretur equatire differeatali exi g duit
seu si daretur 1C  GD (C) per X, 1y, a,  oideu modo
proced tamen res
succedit.
S.  sit ob curvam BC VC
y = (1mo) (rl.
1) u nErgo
FIC, (230) = da  (r X: a) et DiC = dx  AeCX) (Pl. X; a)
et G1 = da (dec. a) (Fl. X: a) = dx A (seC. X) (rd. X; as
u
so
2do
sed  _ ex data conditione curva GIC: Gu x;yia. seu
per 1. 4 Bt) G1C : G15 = (r2l, X; a) seu G1C = dx (YEl. Xia)
quos duos aeg. 3 et 6 aequando habetur (7mo)
relatio inter X et a
intervententibus dx et da, qucujus ope si ponatur inveniri a
ef.
pona, ponatum valor ejus vel ipsamet actu quantitas inventa, substi.
tuatur m aeq. 1 habetur valor ip relatio aequatio (8 va)
quae extribet relationem inter curvum B et BC prc pro curva
migitur circ thobo sive detur curvae
1C (C) quaesita.  Hac
determi, c(C) determinatio habetur tangens, sive contra detur
curvae, jungentium propiretat respectus curvartim odinatim datarum
normatis ad 
angentius propreetatem ut si curva