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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 2
# Folio 83v, page id 00068202:0166
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problematum solitorum sine reductione, per ciculum  quamlibet sectionem soncam
datam. A Esto aequatio: a + b a X  bd, unde Analogi sinus: d, a7 bras b.
sit e media inter b et b +a. fiet aequatio ad parab. b+ba  e ad parab. ac
duplex analogisum: da) b + a) e. item d)a)e) b. Unde aequationes
ba  a  de, derum ad parab. et ac  bd circa Asympt. id Hyp.
duae parabolae sibtiahendo junctae dant circularem, unde facile Caetera siunt
Si Aequalio sit: a - pae +b a ( bd sive b a - b par - a3. unde
irs
a (P - a ) a - d. et sumta inter p- a C a -d media e. fiet aequatio
ad ciculum pa + da - a = pd 7 e. C) duplex analogisinus, ) a) p-a)e
a b)a) e) a-d. unde daplex aequatio be () pa-a ad parabolam
ba- bd  ae ad Hyperbolam crcaosumptotos. (iculus in hoc excuplo
statum se offert, si vero non occurrisset, prima aequatio composita cum
alia aequatione ad parabolam sut in primo ex emplo statim, eum
obfulisset, nunc autem dat Ellipsius, vel aliam parabolam.
Inter Nequationes aeti gradu data sit in eximplum Aeq. 2ba a b
(2
q2 + b - 2ba positoque (a2 d  
est ad Hyperbolam aequalium laterum fient proportionales: bsa (b. a)e et
entus
a eu
a2
aequalio ad parabolam ba -a  acujus duplo auferendo aliam ad Hgperbolam,
N
emanebit 2ba - a- d (2be 4 e ad Nirculum.
a
(N) D
Sisit sequatio b’ a - a , b d, vel b4 - b d p a erit ) a ba - d. Et
veo
posito e 7ba -d quae est aeqe ad parab. habebuntur tres contrnne pro
portionales bs ase. et ruisus aequatio ad parabolum be, 1 ar. quae allata a
si sit Aequatio pua + ba = at ba, fit b)a) p +ba - a) d. et faciendo
pnon dat e- be ba -d aeq. ad circulum
+ba-4)  e A9. ad circ. fent Poportionales b(a)e) d. unde aequilio
ad asynntotos ae  bd. cujus duplum sunctum aequationi priori dat
N
2 +ba = a + 2bd H e + 2aC. sive p+ ba Y 2bd p a  C + 2ac. aeq. ad pamb.
cujus dimmeter indlinatur ad diametrum circuli angulo emirecto, applicatae vero
sunt eidem circuli diametro perpendiculares ut supca in prop. 14. Ct 15. Id est in
sis casibus uti ope asgmntotorum aliae aequationes compositae sunt. verum
quiniam tam in hac aequationum specie quam in aliis manis affectis, inventio
liquationis ad circulum secpo difficilo est in prosto est Regula Jenversitis,
pro quaelibet aquatione solida, quomodo libet affecta:
Nam ver ad 4tum gradum ascendunt, et  vel substistunt in ztio si hoc multi-
plicatione per a, sive incognitam ad alum giatm promodendae sunt
 Hoc facto vel sub cubus etiam erunt affectae aequationes quarto gradus
vel non. si sub cubo, sive affirmatioe sive negative facienda est aequatir
ad parabolum quamtibez a + vel- ba p, qu sumta q. ad libilum, et b dimidia
coefficientis ad Tubum, scilicet si ponamus esse a + vel - 2b a si vero sub aliis
gradibus tantum affecta fuerit aequatio sufficiet aequatio ad parabolam quamlibet
a
H4y. In exemplum sit Aequalio quadvalo quadratica, cujus omnia