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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 301, page id 175906937X:0325
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=325
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.87
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L 1 B. II. C A P. TII.
ne decenti; ut urraque aequationis pars a signo radicali liberetur,
_ transpolicistransponendis, erit
4bbX ∞ = 4 a a X X - + bb a x + 4 a3 X ∞ b + - 2 bba a. + a7 - 4bby y.
hoc est, Facta dirisione per +bb - 4 aa, erie
X X - - a X ∞ = b b = = a a-
6673
Gulam v ∞x = = a, exit x ∞V. F = a, eaque substituca in locum
iplius x, ejuldemque quadrato locoxx, expunctisque iis qux le
inricem destruunt: Crit x x ∞ = bb -
6b97
66yy
bb = a a lIve bb = a a ∞ = bb
=xX. Oui quidem calus est Theoremaris rztui, ac proinde L.0-
CuS quaesItuS Flliplis. Cumque r asumpea siE PTO X = = a, (1 ab A
versiis E sumatur AII ∞ = a: erit, juxta Regulam, II centrum,
e lemi-diameter tranrerla (relut HI F ab una, _ IIC ab alcera
PartC) ∞ = b; ita ur diameter tranlversa FO (quae quidem, ob
applicatam C F. ad eandem perpendicularem, tranlvertus quoque
aXIs est,) sIE ∞ b. Ratio autem transverlae diametri ad paraime-
erum, seu quadraci eranlversae ad quadratum secundae diameeri
erit, uc bb ad bb - a4. Unde per ca, quae Capicibus tertio de ul-
timo libri primi expolica lune, quae lica P lliplis Facillime describe-
tur. Porro cum quadratum Pemi diametri eranlrer(x (it ∞ = bb,
erit quadratum semi-secundae diametri ∞ = bb = = a a. AEqui cum
FB seu C A sIF D Z b F = a, _ BC seu AF ∞ = b - = a, erit quo-
que rectangulum FBC seu C A F ∞ = bb - + aa, nempe aquale
quadrato semi secundxe diamerri, sire, ut Vereres loquebantur,
aequale quodranti figurae ad tranlversum axem Factae. Ideoque
puncta A e B ea ipla sune, quae rulso Ellipleos Foci sire mbi-
licinuncupantur. Unde apparet, ex praemissis recte interri, qua
Seguuneur.
Corollarium T.
Dux a quolibet in Ellipli puncto ad urrumquem-
bilicum rectae ducuntur, simul lumpex erantverlo axi
aequaleS SUHE.
Duemadmodum aurem in Hyperbola superius demonstra-
cum elt, ductarum CA, C B differentiam tranlverlo axi lC a-
quari, ita e hic earum acoregatum eidem tran(verlo axi ae quale
elle oltendetur, nempe, li non per additionem ee compolitionem,