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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 320, page id 175906937X:0344
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320
F L E NI. C U R Y A R A M
haereat Fractio, crune lacera tranlversum et rectum sibi inricem
aequalia. AC vero politis la sina qualibus, erit ratio lateris eran-
verli ad rectum ut l ad g.
Si enim descripea incelligatur praedicta FIrperbola per pun-
ctum C in veraque diametro versus Z e versis B respectire; lup-
ponatur que eandem secare rectam Z E, qua ducta lic ip(I AB ~-
quidistans, ue de iplam B L, ad dictas diametros respectire ordi-
natim applicatas, in puncto F: erit
FX ∞ y + 5,
C X ∞ y - f,
FB∞X L f.
C B∞N -f;
ideoque rectangulum
FZC ∞ yy - fF, de FBC ∞~N -ff.
Cum autem lacere recto ipsi crantrerlo aequali existente re-
per ropri Clangulum FX C = SIE ∞ quadratO ex Z F seu A B, hoc CA, X X;
icemque rectangulum FB C (ic ∞ quadrato ex BF, hoc ell, yy:
exit py = ff∞ Xa, hoc eAt, Yy ∞ X X L ff itemque
X X - ff∞ yy, EIYCy y DXX -fs.
Sed cum secus recto latere ips erantverso inaequali existente
unius ad alterum ratio lit, ue l ad e; Cimiliter que etiam ratio re-
ctanguli FX C ad quadratum X F, aut rectanguli FB C ad qua-
dracum BF cadem sIC 2, quae trantrersi laceris ad rectum, hoc
pruci hujus. est, eadem quxe lad8: exit ur lad 8, IFa yy = ff ad Xx; icemque
uE l ad 8, Ita X X = fFad yy. hoc est, reduetâ proportione ad a-
qualicatem, eric lX N ∞ 8yy -8FF, ut ec lyy ∞ 8XX sFf. unde
Xe X
dirilis omnibus pers, tc-- ∞yy- ff, hoc est, yy ∞
e ∞ x x =ff. Ouod demonstrandum erat.
X _ +ff.
Ac si quantitacum incognitarum primo conceptarum un d ex
aequatione sublatâ, aliaque in ejuldem locum juxta Regulam a(-
Cumpea, aequatio (IF
l2Z
y
IaX
L
+ ff (id CA, ZZ-- ff ∞
lXe X
D. vel
D XX -ff: auc Z auMPEa CxIF pIO y 86, vel PrOY 8 =, aUI
8. T. PrOy 8 = 8 6. Et quidem primo (iZ altumpea sic proy 8c, du-
cenda est per punetum A recta A D ip(I B F. parallela _ ∞C; ita
uc, (1Z Fuerit altumpea pro y -c, praedictum punctum D cadat
ab eadem parte linea AB, qua dacus vel conceptus est angulus
ABF. Sin contra Z fuerie allumpea pro y. +6, idem illud pun-
ctum
ni hujus.
Per 10
Casus 2dus,
cum LocuS
est H) per
b0la.