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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 120, page id 175905688X:0142
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12C
FZOR TMONDE DE BE AUNE
proinde cuin distantia puncti A a centro sic V 5bb, quae lemissis
es Laceriseran(versi (quoniam, cum duorum quadrarorum unum
alterius est quadruxlum, lacus tantum lateris fic duplum); mani-
Feltum es, punctum A rerticem fore diametri AL. IdeoquesI
Fiat M A ∞ V 20bb, erit ipla latus transverlum, e latus rectum
Crit, (ut diximus,) V = bb. Ouorum demonstratio facilis eAt.
Nam per prop. 21. lib. mi Conicorum Apollonii, ut latuseran-
verlum M A ∞ V 20bb eAt ad latus rectum V = bb, ita elt rectan-
guLMIm ML A ad quadratum ex L. X. FA autCM AL ∞ V E X 2
Llinc si mulciplicetur V 20bb + V F x 2 Per V =x =, habebitur
Mulciplicando rero id iplum per latus rectum V = bb, exlurgie
400b+ x 2 L V 200 bb x +, quod divisum per lacus tranlversum
20
80
V 20bb, exhibet Y b b x 2 L V 10 ∞+ hoc eAt, Vbbx = +
1600
25X +, CCub~ L L∞ =, PEO quadraTO ex L Z, unde ip (a I. Z FE
Vbx F = x 2. Jam si ad lineam L X addatur linea L. K ∞ = X,
obtinebitur linca XK, hoc est, y ∞ = ∞ L V bx F = X =, aC Pet
consequens V bx L = X = ∞ y - ZX. Vnde duct a utra que equa-
licatis parte in se, Het bx L = X = ∞ yy - x y L = X =, seu
yy ∞ bx L xy. IIinc utb. Fy Schabet ady, icay sc habebit ad X.
Ouod erat demonstrandum.
Proponatur adhuc aliud exemplum, reterens eum casum in
quo nOn reperiatur = x in aequatione. Hlabeamus itaque ae qua-
tionem hanc ry ∞ - = d y .- bx, cujus radix eA y ∞  d qu
V d -= bx, quam CONSTTUETE OPOFECAE. SuPPONatuE in FIgUFA
sequente AB ∞x, e angulus AB C ad libitum, B C aurem, in-
delinite continuata rersus B, ∞ y; hacque BR ∞ d, quae hic idem
peaestat quod min superiori Formula, quoniam habetur - d. Du-
eta autem NK indetinite parallela ipsi AB, SIImatUE K I XquIL-
lis AB, prouc ostensum fuic pa5. 27 & 28. Ouo facto, relinguetur
tancum V d F bx, _ pagina sequens docet lineam quae sitam el-
se Parabolam, quoniam non habetur x. Praterea puncto N
existente rertice, linea IN esse deber am:
23 hoc CA, =, in hoc
exemplo. Terminus denique, qui explicar latus rectum, erit --
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