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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 283, page id 175906937X:0307
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=307
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# Lines: 65 recognised, mean confidence 0.79
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M
e
CH
I E B. TI. C AL. LLL
Fxempla reductionis aequationum ad formulam
Theorematis XII ex XIII.
Si xquatio (Ic yy +
b X 
∞y -L = -6, CrIC y ∞ Z
b3
e
-
=c, eoque substieuco in locum
iplius y, atque ejusdem quadrato locory, sublatisque iis, qua le
invicem destruunt, erix  y bbX  2bc∞
 aat
Et Facta congrua transpositione,
y
fX a
66∞-
FXX
e
bb2X
a a
+ ex 1
2bc∞
Ld d- f.cc, hoc est, mulciplicatis omnibus aequationis terminis
per aa productoque dirilo per fa- L bb; ut quanticas x x ab (que
Fractione remaneat, fet
a422
(a  BG∞ X X
Deinde aTuptOV~X. 1
aa Cx  2abcx aadd aacc
a ac = 2 abc
fa + bb F fa + bb
2fa = 2b6 Ut terminus quoque 
quationis, in quox unius dimensionis reperitur, plane cranelcat,
habebitur X ∞V = a a c -2 ab0
2fa = =bb. uo substituto in locum ip(IIISX,
atque ejuldem quadrato locoxx, ablatisque iis quae se inricem
tollune, reducta erit aquatio ad Formulam requi(ItaI. AEVeTO UE
trat aquatio
 a e  2 abc
fa.L bB Scribatur 2B, IEa UE
+a + bB∞ X X  2 B~ a a d d + a a cc
fat bb. Tum 2u-
aa Z2
PEov ∞x. F hleux∞ V - h, eoque substituto loco x in aequatio-
nC, ac ejusdem quadrato lOcOX N: Crie
ad d = a a cc
aa2 2.
5a +- b
3 VV - BB. L
fa.  bB. Unde apparet, ance omnia hic esse consideran-
dum, ucrum hh sic majus quam aad d + a acc
fa-fbb an contra. Ei enim
majus siE, erit casus Theorematis Z II; SIn CONETa, erit ca(US
Pheorematis X III. Ponatur itaque primo majus, ac proinde a-
quatio formula Theorematis XII. Et constat exinde Locum
quaelicum Flyperbolam esse.
Ad cujus peculiarem determinationem esto in apposita FISUITA
ipsius x inicium immutabile A punctum, eadem que x in linca A F.
ab A versis P indetinite se extendere intellisatur; sitque angulus
n 2
que