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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 145v, page id 00068200:0292
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et apparebit si q sit major quam a, fre aequationem ipsarum PO, axi ordinatum applicatarum
fore ad Hyperbolam Ellipsin; sin minus ad Hyperbolam, adeoque superficies Sphaerolidis Motigi pendet a quadratura
, superficises spherocidis lati a quadratura Eli Huperbolae. Quae jam et ab Hugenio inventa
videamus jam an adhuc aliud curvae Elliptiiae momentum exalia quadam recta
determinata habere liceat. Jungatur VT. et ex puncto in cura . ducatur in VT. ordinata NC
sunt.
sit VAHX H AOH Trax - 2 X  ut ante VNNZ. NONW
Anto omnia VAHX,
quAc
Tagrier
Ergo AB, XYaq. et BO, y - XYaq
et X VBr SXer Naq H X SIt a. et BNB Z- X S1+
H et NONCor  = 2 yx Yaa (+ X 4) - Z - x (X a) - 27x Yi1 9
rursus VB
reca
1 1 ∞ - X saq acit y -r saq Zsira - + 2B
Z= YF1+ 2
sive V4 ⊓ 9Z 5. +29 IX. et XC Z s+ + - y et Y ( ZSi r2 -Y
sive. X adg, ut quem valorem inserendo in equatione co fes:
2v age fia + 29= Z Z + 229 Fi  y
Ulnde in aeq. superiore, explueando y. fiet
rax - aX, - 2ZX SiF  aqu + 2X saq., - Z1 - X - 2ZX Y1+   cor
ursus quia y HZ +Z4, + X, - 2 12. 1 + 4 5 cax - 2 +
va + (7ZX S1 +q B -1ZXSira Saq 
fier Z + x - 2aX + a X +  ( 2aX - 2
et  sed his non est opus. sufficit habere nos Y+XeZ. Unde 4 ut
omne
obiter dicam, sequitur  Z. semper haberi posse.
Sit2
Caeterum rectius videmur factari si gene alier calculemus: sit
 sinq
Aequatio est A aq a vt. pone 91 V et Praa a x. Et perpendiculoris sp ae
sive VH eag- 2 v. (et S seu quad. a perpendiculari
reritar
2 +, y 1 (a) + a9 - a ∞ (= a) 4 a v
sive SH aq + 124∞) in aeq. 5( aq - a V. pro y ponatur _ +  - bco. et pro vfias st eb +b Z + aco
ad -cYeeb
se +bd
a 2. adeot percompendim Ve +b rocetur d. et eb - cra metur f. fe. Ve rbo
et  valoribus pro y et v substitutis, sier. E + 26Z - 20bc0, + eZ- 2ebZC0 + bC0 daq, - af- 2a flz- 2 ao,
(4 baZ 2b a c0Z P a3co, sive  +e2 y + b co -2eb ZCo + 2eZ- 206c0 + e+
+b2 +a. +2ab..
+2afb. +2af.
-d249
+acis
A Quae est
aequatio ad Ellipsin aut si 4. quanlitas vgativa su, Hyperbolius quam maxine variata.  Compendti causa secrilamus
9Z + h + lZco + mZ n Cd + p B0 quam ad tangentes ordinando scribemus.
29Zt + lEd + + mt p - 2hco - elZc0 - nco
. Porro co p P. et co +co  s fiet
A aE coC AS jam ejqs i literas arbitiarias
mempe e. b. c. ita explicare tentemus, ut omnium s.  per Z. explicatarum haberi possit summa. sicenim
novum curtae vel Ellipticae vel Hyperbolice momentum habebitur. Est autem t -2hco2- 12co nco. Ergo erit
Co H 6297C0 + lco + nco
=2hco - 1Z - n
pon CoH 32 - 1ZCo- m Z= nco- P Y
ponamus -9Z - lco- m H Y. per trachy logiam, et fier : - 4Z- nco -p,
c + 1Z co + pr
1
vide sec. fig. Li
a -
+ 8 22
+B: la Z
1 n
m.
2
1g
sed culculus paulo prolixior
292. + 1c0 + m
S1 N SigEco Uo mco +1
sa
2tco 1Zn
etico- 1Z n +
AcoplZ +)V Z atatn Z + n
-24
amus
-+pg
t punctum in cunva E inde ordinata CB. verlex Ellippos A abscissi Axis AB Y erit
CBriSZar = a r2. ipsa C9. sediameter sit b CHIg- 219 +r +2ar - a
into in curca puncto O. ducatur ad diametrum Cy. adinatur (tangenti paralleta) OD quae et posita CD pZ
alere recto respondente diametro 24. fiet OD( Y26X - bZV producatur usque in E, ula perpendiculari CP. occurat
in calculo superiore essent G. et nejo; foret co  29Z + m. e+ co F1 - Z- niZ= P et SM Sg2+mrI Z  
Enor in praecedentibus inde a signo quod sureseron  Codco +2. curm debeat scribi co 1. Est autem +, co ( 2t - 17.
cortoem
2t- 1Z n 3 =  si, Yoiir YI S. Unde poncndo l to frerci 29Z + m Y S5- 1. Quae est aequalio 32 + co tm
ad Hyperbolam, quod si ergo fieri potest 0 et nullus est error incalculo, haberemus momentum quoddam curvae lonico ex quad.
aequi, 9 aq + a9  +1 v = in typ +. in cir. etEll. -
sit in Hyp. aequilatera: vaequ. s bF + 2by t
12 + y conferendum priori,
fec. Mro res non procedit
Ergoer ll
hypertio le. ut autem sit 10. fiet C⊓ a
aquatio ad curvam conicicae Etementur
pater triangula si esset er. sed haec quoque puto inutilia
mullipticato elemento per