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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 174, page id 175905688X:0196
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174
FR A H CESCT a SCHOOYEH
Ordinetur, ica ut x xunam ceneat aequationis parrem (((IEN quam
invenire rolumus, relinquendo. y indeterminatam), invenietur
X X X
4a a b b - + a b3. + b4 -- bb)
4a a - + a b = bb
vel x x ∞ bb
bbp0
44 a - + a b + bV
UInde cum aequatio non ascendatulera quadratum unius ex quan-
ticatibus indeterminatis, quemadmodum ee superius in Iyper-
bola erenie: constat, lineam curram delcriptam esse primigene-
ris, quippe qua alia non est quam Flliplis, juxta ca qua secundo
capite tractatus nostri de Oroanica Conicarum sectionum descri-
peione demonstrarimus. Ubi adrertere licet praxin (quam de
Clarius lib. 2. Tuae CnOm. aferE pFOP. 26) describendi FIliplin
Per puncta, qua ex inventa aequatione collisi porest, quae que lig-
nariis e camentariis in extruendis fornicibus tamiliaris est, acque
in orthographicis Sphaera delincationibus ulum haber insignem.
Nam si producta A B ad I, ut B L sic ae qualis B F, CenErO R inter-
vallo AT circulus describatur, secans AD, hinc inde productam,
in L _K: erit L K axis tran(versus FIlip(IS. Rectus auteminve.
nitur, si ex eodem centro, interrallo DF, circulus describatur
pOFs, secanS ATIn F. Frir enim AC semissis axis recti. PF (1 d
puncto F ipL AD ducatur F P. parallela, Secans PN in P: exie
punctum F unum ex punctis, per quod Flliplis cransire debet.
Ouo quidem modo intinita alia puncta inreniuntur. Ouod de ex
calculo tic manifeltum: FA enim AI2 a - b, _ AN y; eAque
uc AIseu 2 a = b ad A N Ccu y, ita A F seu b ad A n, qua ideo eAt
ea b
6b7
44 a = + ab + 6C Ei auFeratur a quadrato
ex A F Ccubb, remanebit quadratum ex n F∞ bb --
44 a A a b + bb.
urpote aequalex a quadrato linexe N L. Ouemadmodum tuit in-
VENEUIM.
Eodem modo opcraberis in quaestione sequenti, quae ultima
eA propolitio lib. qe collectionum Mathematicarum P’appi Ale.
Xandrini.
Ouaeritur cujus generis sit curra linca AFDB, cujus haec est
proprietas: uc, deducta, a quoliber ejus puncto, ut D, per.
pendiculari DC, in rectam AB, Politione ee magnitudine da-
tam, id quod sub perpendiculari D C de alia quadam data lineak
continetur, xequale sic rectangulo, quod sub segmentis AC, CB
comprehendieur.
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es
indetere
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lact
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Venea A
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LappudIB
Nond
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esse prinie
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linea Hyper
tione, ubi
aliquod para
e alierum 
DH, ABI