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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 289v, page id 00068201:0578
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HL
LG
G+
10
siu 1Z
Net pro  ponatur d, pro  ponatur R. et ideo Z- b
et ZH
Z Z.b
17
 + 1. ponalum: seu 1 + A. poratur jam AlL (  d A 4.
et LG alterm rectan guli insrb adserbendi labu 1+ a g. Datur autem D, et
quia supponitur dari HL
2G
HL  SA 9 si H BC + 2CR. seu t = 2W. ponendo W. F CR.
seu p
Ob naturum sectionis (gnicae universalem RG id est LG sive 1+ Xg ita
fit ex W S CR, ut posita ut dixi CR F) N, e futura sit RG seu 1 + d
2Wv = 7 12
erit
al ex priori aequatione q
d t w
+ 41d
vel ponendo 1+ 4
sive W0
1
4 4
le inde q 2rW + =W V 24 X 22
1+ 22 + A +F
I  4 4W + 4 W comparandoque hos duos valores
et L
e, fiet:
5I t2 + 4tW + 4w  + 2 +3 + 8
+ 14t
1Z. fiet:
ar 1
428+
W + 4
2r W + Z W2
4+
Va
∞+ etW
+ ertw + 4W
e
et J
Quae aequatio plana est,
et ipsa W ope
sive extractione radicis sive
cuculo descripto, statim
habetur. Habita
autem W, habetur et 4. Quanquam
Attae
sed hac cnstructine in ciru non nisi in parabola opus est ve circulu
tanto ambitu non est opus, nam sive sectio Condea est Ellipsis aut perbola
quo casu nullo opus est calculo, ad constructionem per lineas. Nam ad rectanguum
data rat laterum ratione ad ipsis ad scribendum ita tantum agi opus est
rectangulum quod libet a AB datam habens laterum rationem pro arbitrio assomtum
ita describatur, ut latus ejus, quod scilicet volumus axi, ectoms sit parabetum
et
Us, utrieque
producantur etum sectioni conieae oecurrant in HL CNH, g quae
puncto juncta deibunt recrongulum quaesiturum. profarabolt autem, ubi centrum
infinte abest calculo exigendum est, quod non potest linearum ductu; at calculus
ille fit facillimuset una aequationum sufficit. Sed conferamus eas probae causa:
d 5a9,7 + + 2W. ergo Vd Fq 5 t. vel 41. Unde
AL N SA q, gie HL F) _ LY sive HL  +. At LG, V4lin )
LGH . eritque
est autem YH Y + 1 neglectaque Y, ut infinte parva, fiet
HL
LGYI , jum fulat s, YI
SAg t
N
x
2.-
e
1 2
Hoc cum altera aequaitione conciliemus, ubi e LG  5) 2n D sia YB d
appele
+
40
duarum est indeterminatarum. Unde ecec frevissimam methodum qua rectanguli
dato ssimile parabolae ib concentricum ascribi potest ratio latem
rectanguli dato
transversi
ad rectum
et transversum
, vel
+ 1
rationda
 sive  posita duplicata
+
hie rationem simplriem, tunitate
punct residuum ducatur in latus rectum