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# Title: LBr. 437 · Huygens
# Folio 43r, page id DE-611-HS-3595205:0085
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Ctm
dy. dx.:  2X4 7y sit  y. x  v. a, fiet
ya = ex et adu = vdx + xv. quos vatores substituendo in
aequt. fiet: vt vdvo  d. v + v: 2 seu
14 d8.d e . v dv. dx = pa. v f3v.2 vel erit
+v. dx = +34ur CBe d ed =c du era 4 2a: wr,
DB: DC:: dx: dy As et = f yy: 2X 4 2X, y. sit y. x = v: a fiet ay = vx seu ady = vlx + xdv
Uende ex org. 1. fit v + xdo.dx  +a vira + 2aa v si xdvidx - g r. 2 - 1 v + raa. v
suex e vet per compend.  Unde ex sg.1 siet: adx:  vax + xav = ( v. 2a + 2a: v
et =) + vo + 4aa: 2av. unde +2aa vdX = Y, ve dx f, vuxdo . 4a avdx f. 4aa X dv
seu fiet dx: x du, voftaa,: βaa v Y3
1P i +
(
ijam e L4 2 voremus B fiet o 4 vocemus B3 fit β aa vax  V dx = vexdv aaaxav
piu ad destro
facio
+2. -
in
 Zure
seuplx. X=
asq V at v
(1g. 9 X. u
logeaa vera
seu fiet
jam
FX: X  Sav. V: paa _ v- (d: Paab .
H sit E B a a = , et Z = VBB. BbC. jam momentum figmras FIG) ex
e Ex  axe aequilibius est Z 5∞Zav. seu bs  vav: bba
Et idem haberi potest per summam quadratorum GG, s demto sumua quadratorum
inter GH seu summ. FG in EF, sumindo omnes FG inter FG et (F HG) inter De) G et (G)
sed idem momentum etiam aliter haberi potest, nam moni 1C) mom
nam mom figurae GHH) G seut suum qu. HG inter G et (G) demto momi. rectanus GH)
addito momento rectanus, =1G). sed rectanguli G,B) mom = ZC in  HG, = FG-   in HG
et rectanguli F (G) mom. = (F( in FF) in 2F+ L RF) = en FG) in (D= EF in EF + E) - LEF
seu  (B(G) in EF)= EF. _ jam sit EF, D, E() (1), FG,Z (5)(5) (2) et fiet
mom rectanus. G(H) = Z - (2) in L vD et mom. rectanus F(G) = LZ in (VD)- vn, ergo denique
fdenq i sum qu. HG. = = s uvaZ jam - vv Z + bbZ = b3 seu bP = - b: Z + bb et set
sovaque = - b sAZ. Z  Lb Z. (2) describatur Hyperbota LM (M) ubi HM sunt bb: Z
erit spatium H (2) = bb: (aZ. Z. itaque tandem prodit talis aequatio:
rn quo
+2() (vV)- vn
B3 (vav. Bvv = - 2 li in spat M(M) +: B Z- Z) = 2 rv Z. (E + L ((VV) - +s vV
faciliore pro
n ne quis enor sit admissus, instituemus comprobationem, in exemplo
 linem GG curva ad hibento rectam oposito SEK esse triansulm rectanus. isosceles.
promentum trianguli _NFG ex axe EK est _ tianus.NVFG in EF+ LFS  et similiter
nom an. SiF) (G) = Manu sBG) in EF)  = (F) s jam SVEChianus: L FGii FN et
Fs= sit EN - e, fiet FN = e - v et d NFG = G C- D m EZ, _ sed Z= C- v fiet E A E. B = NVFG
et LF e - (0) =, 5V(F)(G) et EF+ L EN = v + C V seu C + 2v et fiei mom itrrem
et fret momi hiam N FG =  Cn + L (D C v seu ( CeV erB + (V + LC(LCD + eB (1V,
= L0 + V - L evr similiter mom. tianu s (F) (G) =   + + (V) - = e(~Y)
smoctntum spulis differentra momentora hora bragulorus seu cubim, spati F(G)d EV- (B): eop aL etV
=dif inter .V + ev, et inter h(V) + es) u  idem jam investigemus priore via
nam idem nom est samum qu. HG= mom rectavus; G(H) F momi rectanus ((G) Jam (quad. HC
sic datur. suum. qu. HG inde a K seu sDdqe seu f.dZ  L. HH =  B et i KusgriH)  .
ergo (quad HG inter G et E) = 2(p3) = = V jam um rectanus G H) + mom. rectanus. P. (G) est
 supia  i  in B( Z. Z) + L Z (BV) un sed in casu rectae q- ev
et  e (1), et fer -  V Z (2) et Z - (Z) = (e6 ( ()  v, ergo fiet
on Z(2) +  Z (on) - vn = L (v) vV = + v) + = e(vv) - L v (VV) - = e DV (+ L P)
sed non osentit itaque monenta ducrum sctangulerum denno calculemus nempe
rectanus  G(H) = _. HGseu v in H(H) seu in Z-(2), quod ducatur in LHG, siet rectanguli GBC) mom = : vo 2 (2
sed rectamus F(5) = (8) Ae(C) (E) seu (Z) in F(F) seu in (V) - v = (Z) (B - v quod ducatur EF+ L F() seu in v+ L( B
sm v seu in V + LV, fiet mom. rectanus FG) = + (2) ()- vn. iteque in eo paulo ante peccaviquod posui
G.Fat
Z pro (2). jam in casu rectae Z- (Z) = (Y) - v et (Z) = e - () ergo tandem fiet
 sum quad HG inter G et G) _ - mom rectanus G(H) + mom restum G) F = = (V). L. v- = (BrB+ : V + e V) -x v- V L (V) p
seu = = V- LIV) - e(V) ut ante. itaque calculus ut correximus est probus
Rursus jam suplr est inveniendu summa   (dv.  bbB 
s
4 M 1+ mVtro  P+ qV+ YBZ SB  1bb + mbbv + ubbx + n v + nv + pb + quo+ rre srt: 6bB +V
aderque DC + .  b+v
bbton =  bb
vobtr
rubi ponendo m, n, P, Y, S, esse c et relinendo l et 9 fet 1 = - q
et L. + V
bb -vD 1F bbV - ∞3
tatem (dBv: βaa - vV - 4 aa sodv: BBaa v - P. Et quia =
Ergo + Baa aa B  - 4 aa
(3aab - p3
ergo  Y
Baa- vV
paat p. = ) 2a Ba 1
ga
 bb
bbv. B7 
Bac- bV
Habemus nos ineundam summam
hinc etiam -Baa
BaaD- V aa- BI
+L. seu 4na
eaav. B3 paa- v = +aa - paa + L. sed 4 - β = + 2
 ud B geo b Bet la  pan (4 . v. .  Quod spitus tertum siet Experiei montiil
  ee eb ditet om 1la tar  4 t . eri er o . Br. en t   e u tar dund a + Bet eitet . B0. prse. X eb
cin ncb
b0Baa et talecus
v
. P   vo- 40a = f 2aa V. pr. H, v
si
r  us
E CH 1
BB - 2 - yy. 1