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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 283r, page id 00067993:0567
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sive -ft ad X - fl fy X
+ ad.
+ad...
+f.Y .. . + fy...
+ actg X
treytg
2acyg
eyg.
-++  ab
fy
et pro X substituendo: act + 2ey+ - 2ac y - reg fiet:
ft + ad +fy
ac t + rey+ -2acy-rey r st + actus i = f+ - ft  aeb 1.
+ad + ad
+ 2eyt9s
+ ad +ad tacy
+fy +fy) - 2acy9 +fy +fy
rey
Sed quoniam reductio hujus calculi nimis prolixa est satius est, opnor ire
per casus sumpliciores, et paulatim assurgere ad altiores, ut appareat, an
an progressionem pervenore liceat:
1) ab + acy + 9X p 0. unde  -29X +at b  Ac , 2 ab + 2cy
sive Z
atc3
LFIV
gc
y.
2
M
ac
Et hac colligendo + ex y. sed si colligatur  ex X, fier:
ygesy
19X+ - b - ac Y sive tp ac V et pro X porendo Y porendo - gX - ab
29X
fiet: + p gX + ab, adeoque sa p) eis erit  2+
aeb
 aet a 1
= 29X
2) aeb + ac Y + ad X + gX. p v. fiet - F Ex y fixt +  - egX - ad X, et
quia  uit vero eliminetur X, pro - 29X, ponatur 2a b + 2acy + rad X. fiet
+⊓ 2a b tac Y + 2ad X - ada  24)b + 2kcy + fdX, unde X B et - 2ab - 2cy
et X  5+ qcab F - +C +Y + + a b +8 abcY + +C, unde ex aequaluom
mitio proptosita eliminundo X, fier:
D) a b de (D acyd + ad t a= ad 2abd ad 2Cy) + gc+ - 4c ab9s l- 4629 2)
+ 49ab + 8 abc gY + 4cg Y) et pro + subistituendo ya
habebitur aequatio in qua solae ex incognitis restabunt Z et y
L
Sed calculus hic prolipus longe facilius expediri poterat, considerando locum esse ad parabolam,
atque ita ipsam , ac proinde et ipsam Z aequationis ab + acy + ad +90 facite
denivari ex habita  vel Z aequationis acy + gX 70  adhibita met hodo genent
ad exemplum ds, ui quemadmodum d atscissae ordnataeque unius directricis ex
alis alterius derivantur.
1a3 tacy