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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 191v, page id 00068198:0382
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Et(et DF
videaum saltem an non aliter un data (urva conicae extensione, possit
ergo
perveniri ad (om superficiem cond scaleni
Elementum Conicum invenimus esse
hh + 2tx + hXX, :,  itX YXX) vel dx  tib + 1)
pehs chxtex
sit alxip -gus sie - 2itu
et Hy: heta, seo dx ylisiht si faciomus  Multiplicemus omnia per q.h. et q +   - hy pti9)
+3
dx se
fiet dx 
S(tq + EgX + XX, :, 29X + xx sit 49 + dgX + XX - 99 = 22 -99
pusito ZZ qul   +, q- x) se  Z = q. X fiet etaq + a7 = dx
e
1+
et x- Aryehq) qua
AX -+ (4 gy 149- q
=44) seu saZ 1 (hg - l99 - h 2 + Z2P:, 1399.)
1+ 
seu + Z B e  + dy ((- 2  +42B:, - 49 + 22) fiet 22 -  a 2i  eto
q
et dq = dv: (4) 2se, faciamus (Y) _  = 4 fiet  dq = ad t edv: 2Y V, et xElementum
conicae centralae erit 2dv. + (- 2 + CV, :  - 99 ev + eevv sit 945:, 1+h = ef
et fiet  = edo ((. f +V, :, 29V + evo) Res ergo eo redit, ut qqu + erv, v.f sial extrahibile
(ev +9q ur + fqq V) = C
3
sevr
ex = fggo sebet aequari quadrato, nan fit  edre
Qquten
Prosec  Elemento (omi scalem habemus 1 Sob  Y (am + n  t  (, : k p + p 4) =
fiet a
1+ Y
(posito 1 =a)
 fam K P + nk Vp +x VV +)  quod in radice est multiplicatum per 4
+am ipip + n iph + 2
gi  2020aa + naa 2. 20. 21 acs + 1ua 429
13a p
paa. 130 a
fit
perlinum in di  sic explicato tollere
21. 30aa K 9 + 21. 31 k Ge). 3oito ae 1 ho1 as ha 1 
2020a + 2. 20. 21439 + 21. 21aacg
21a: K et fi f20. 3oaK + 21. 3uaatie: 2o. guaa +, 30. 2a +   2t 1aa  = h p+ 9
v=
1
Eua
30. 21 a3
20. 20 a
et fiet dep, 3 XG  E8 f(am +n Y  YY, vida rodaque
L + 20.2a
mus et imus
sed e sed poterimus simfliciter videre brevo
Terminum suaum Explicemus K Y + YV
RIV = 3_ 3oak t K 20. 30 aK = 20. 31 aa K
fit1 3 = , 307 (in ratyr L V_, e  Dea +21 48) r0 toaex arisonius,, qu ( vax rut  aues)
el
com
compendio scribemus 10cF 1Z  +  +B a +14 
=20  20aa + 2 ag,: 30 a +31 8, prodiit formula in qua tolli potest 
1030. 35da + 10ca. 2. 30. 3, 48 + 10a a 31 3t g
et faciendo
10t
31 -
s. rouiu t. 
+ 2 30aa t
28. 30aK +20.214 8
20.  a
20. 30 ak +. 21. Paakes
Ou (t a+)  21 4 8), 2a 20ct 20 21ag
30 =0, vel 20 =0 ser
non simul utrumque
= 230 21d (31 2 a porro  explicanta ad huc per es
ag, 20. 4. ades . 21. 3. 908
qu (304 + 31 8)
vi, u
am +n +
palis  t
 am. 3oqoaa + an 2) d tam. A MEI. 2 CPC 20.3ORK + 21. 70aa k)
Ck
) 20.20t 20.2148
na. 20. 3oaa + na 20. u  a gr a
na 2.30 ac 2f Ma. 2121 4 98
unicae, nempe 
Hoc maltplicatum per ( 3ok + , conferri poterit eo quodatur per curo,
Hocmnliplicatum per 3oa+ 2 .  seu per 2o k +G_ dat A en sisabile pt
caru clomentim sunnabile ope altervis
carde (onicae hujusmodi qualis fuitC
21 a: K
0. 30aK + 2. 3vaa K∞s
Horum pdact Harum summarum differentia cum sit 2030aK+0. 20a 30H, in  summationem  psorum )
i per 21. quaa k + 20. 2a
sed idem (multiplicatum per joroar 20u
dati et summationem Elementi quaesiti seu oni scaleni, ope survae sonicae in rectam extensae.
2
21. 30aa K +20. 218
ed verto it eadem Nescio autem an eadem curva sonica possit inservire utrique, an vero opuis sit
31. 30aa k 120. 21 8
adhibere diversas, quod quidem non noceret, etsi reddat constrectionem magis compositam
incqudica spesserdisibnti usitaru nitiurer notudo p a Be
Y
+
oe yG + 28fZ + B (et dividendo) faeret Z2 ((fer = 1)X
ex XX - 2rX fietet _ ex- 2+ 2rt
er er
Nmsrator Hb qu( r.X) durr, seu b ( lrra l( bbgu( r - eZ- f) r + ez
quem dividendo per E fiet. Utr-qul1 +) A +
ee
irr
 et AG qust. s) r etZ
ee:
et ita contentum in fractine cyliadii scaleni, erit
Jam tranfformemus etiam expressionem Elementi sonici,
Dee 77
=Urr - Gu (r - f)  e - et y -
ec:rr
CiYr
AB+2t 2(t, - 1) 1LZ + Z
1e:
tam
+ firrerit.
possumus quidem et aliud puncto, assumere, sed ita sorum constans accederet
vel delederet ipsi X. quod si loco diametri, assumeremus parallelam diametro
et ita rectam quamcunque tantum u angeretur constante.
ee