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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 441r, page id 00068196:0877
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Paralle
A.C.
discrimen inter Elerutura ordinatarum, et
impressiones eamen
quolies scilices vine
imprestiones cora.
ponantur
ie
ubus ordinata
rullero granim
resullant
jungatur B(3, Ex puncuss B
ABEd in recta Ls sa puncta fixa H, X. unde ad punctum B ducantur
HB, KB. producatus HB in C, et HCB in A, et compleatur parallelo grmmum ABCC
ta sint duo puncta F,G, data unde ad punctum Y ducactu
rectae FY, GY; producendae illa in Y8, haec in YV compleatur
paralleto grammum )e  _YV(Y) et juagatur Y(Y)
Ex Yet (Y) ad rectam per. F, G, ducantur normales YX,
(Y)(X). Et ex Y in LV) et Y8 ducantur normales YE, YH
ctumt modium A
t
Quia datur punctum Y dantur FX et X Y, simit et quia datur 4G dabitur et 
Astunatur inter F1tG pun voretuo AF, A et X F, y aguum ut ui s s  )D, EC 
AF = AG vocetur a
AX, X XY, y
YV, V et Y8, 8
FY, S, GY, 9
Ut ergo a constructione rem cad calculum transferamus et calculo invenramus valorem
V Exsit rectarum, quae ex caeteris determinantur. Et reseramus omnia ad directicem  quae transit per bG
sE FX = a +x GX = a X, f = HC qu at) +yn) = F G) = i qu a ) Fyy)
VA = = V. att: 9  n = . atk,: f
invaniendum jam est punctum Y) secu t et DN). Deterninatum est untem puncdum (Y) complindo parallelo-
t BDYV = FX: FY, seu WH X) (. _. D = at2. f
Et fiet DY = 1B: A Cauxt - (: 9) (a q e   Et quia D)  D,1. + A Y et DA -Y R = Y(Y) G: f et YX -
grammua Y  (() satis lateribus
Vr. HX. Gr = V. a: g. iritque DY = Gg.5 +Y e  rVy. 9
Pari jure ob ()a ot friangula YN et GX Y similia  et _ H 1(Y)a  (Y) e - gn - DV
e un ya . t  
siet DY= _(S seu DY) = 9( +X). 
A ob DY = G + n Y fot DY = V9. 9 +y. 5 rursus ut ante
Donamum jam seneam Y(Y) descrivi, dum fest mobile Y directiones EY tendit ex Y in 
Celeritatebu, YC, quae sint ut C), posito ipsas C) dani en FY, seu  f. Et dum simul mobili Y, directionilius
GH tendit ex Y in D eteribalibus Y) quae sint ut D, posito ipsas D dari ex GY seu ex g. sit
linea tempori proportionalis, cuius elementa sint dt. erit V8 = d dt.  et 27 = 9 at -)
.F
Fantem DYent dy et WV) erit dx etque ex int entis fest  d 
dus =
ex
e 1B
d
pro D. f, P.g
ex scubanu, fiet du
D. 8
5+
ipsis sa qdI 8 f a qu lat) rn at g- Aequ sa D B DCaX) - Q (a X)
6. a Z. a
Otatu) - Z. (a X)
jam curva ) constici potest, saltem par quadraturas Nam dist
ubi 5 et Q dantu
gu = aa + XX- 2ax + gy ff gg = 4 aX n. st 
et dx =5 a5 gg et Z adx = fdf gdg gy = ffD qu (a + X) = H  qu (a + a
st =  tat aatextraxtjus
= ff  tsaa (Bna B _- 16ia f8 aa B) + 8 aagque NfAg + 2ffg4: 16aa
ydus = fdf- (atX) ax  = fas 4aa + g (  -43. fif - 9dg
et fia fat Baatae aaas de +4u agdg - 5.g. + (+9dg = 99faf. r 93 d9
seu gu a
fa5 - (2 + B 23) (1d5
bs qu la
E
49)
6+ G
(as 919) 6Ca+
-
2a
Q(a -  33
ra
ubi  sunt E(Y)
d9 sunt HI
Nam obitumen
sam
Nam ob distantiam inmensam puntiorum F et G a punctis Y, (Y) comparatine distantiae
2a
55- qu(at e
punctorm Y et (Y) _ F(Y) haberi potest paralleta ipsi FY, et G() ipsi GY, et
proinde peypendicularis ext Y in (HY et X (Y) s,  vel () perinde est ac si esset perpen
dicularis 
de
(b Triangula
Simna A e (s) R. (1)D  
F.