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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 210v, page id 00068194:0420
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Res ergo rediit ad duas aequationes 63. 64 quarum prior est ad lineam
multiplicatam
rectam, ut vero priorem cum posteriori componendo aequationem ad sonicam
datam nanciscamur, sic agemus: pro aequ. 63. scribamus compendii cansa:
19  t+ _ caequ.
ducatur in
addatur aequ. 64. L . s  sit.
duta in d. fier:
195+ 20 + 21 aequ. 0
s + Y + + co fiet.
+co,19s +co2oF co21) (66)
+l.9ts + rot +u.aqu 0
+X yst + 91 20..
sa
e
E11 B)
to, 21,0
lap e
-8t oot-dad aequ. o)
datam
Quae aequatio 67 comparanda cum sequenti ad lonicam sper E multiplicatae
(66,
ea s  -E t +cas +c2+ + aqu. 0
ex s et t. fit X, 19, 4 aqu - Y, 20 et  qu t. sit d. E +qu , 20
∞, 19
1, 20
19
aqu Y E= 5, 4
aqu S-E
+42o Y aequ - 113b5
(69
6 aequ.
per 52
19, 9
Ego _ ∞ + 1 aqu C-8 q 1, -
et 6X
9, 19
19 + 20
Y aequ. d - E Ermo pr S+ fer. 5 - E, 19 + cad, a, 20 10b 5
per +2 20
9, 4
et
seu 5-E, 19, 9, =, 6 - C, a, 20 + 136, 19, 20, d  b E, aqu un b, 9,a
et fer d = 12b, 19, 20E
aqu
+E  Ergo
192, 4, = u, 10 4 13b, 1
aequ 59 - a, 20
1974, = 928 + 1136, 19, 20
EEt per altaum teminum Cd go d ad
(74)
1
199 - a 20 seu  - s o  s 
eex compendum deeq e qu 14 iibiy 2o 5. seucopeidiot
s
5+
Ex termini s. sit: , ad 19 ∞ + a 21 shX + F a B aequ 38 + Xs e
F
pei s aqu. ad, 19 - a n 
3
+
9
19,9 51
+ a8
et ex terminis t. fret ad, 20 - Ah,  + p
gd. =
67.
2120
C8)
Constat autem quomodo aequatio  a pr t + sus + 2t aequ. 0
universaditer constituatur, rectangulo scilicet conicae datae inscripto
cujus latera sunt N. 2. lateribus recto et transverso existentibus a. q
quae unde constat conicam esse datam. Ope ergo aequationis
ad rectam, 65 vel 63. et ad conicam datam 68 euplicatam per
76. 77. habebuntur s. +. in aequ. 14