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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 164, page id 175905688X:0186
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164
FR AN CTSCF d SCHOOPEN
Cxterum uc Geomerrice inreniantur harum aequationum ra-
dices, (ciendum est, quod, dum omnes termini non xeque multas
habene dimentiones, totiesillic, ubi numero pauciores haben-
tur, subincelligenda sic unitas, quoties requiritur; ut in ae qua-
Eione X +30 - a X X L b b. GOLIIA IN CCTIMINO A X X ErES dHNEAXAE
dimentiones reperiuneur, _ in termino bb tantum dux, coei
eandum est, terminum ax x, ut dimentiones Fiant requales, le.
nel per unieatem esse mulciplicatum, terminum autem bb bis.
AdeOHE, SI PEONHIEAEE ACCIPLAIMUSC, RQUAEIOSIC X +D = CAXX
ccbb. Verum expedie unicacem illam caneisper distimulare,
_ aequationem hanc X X ∞ = a x -L bb usurpare, donec radi-
cem ejus Geometrice, uc traditum est, inrenerimus, nimirum
lineam PN, quae exprimitur hoc pacto: X ∞ - = a - L- V = a a. 1- bb.
Teauc deinde tantuum opiis sIE ex = 2 a  V = a a L bb extrahe-
se radicem quadratam seu inter inventam lineam P M. d unita
tem c invenire mediam proportionalem, ut Gcometrice obri-
reatur radix x ∞ V - = a- L V : aa L bb. Aeque ica in aliis.
Undeliquido constat, ad inveniendas harum xquationum ra
dices, nihil aliud requiri, quam quod circa priores eres Aqua-
tionum formulas, ee radicis quadrata extractionem AuctOr PEX
cepic. Adeo ut hinc simul manifectum siE, quo pacto, postquam
sic linca aliqua pro unitate alsumpta vel concepta tuerie, (quem-
admodum hujus Geometrix methodus requirit) Problemata
omnia Ceometria communis, hoc est, quae rectarum linearum
ec circulorum beneficio construi possune, per catantium, quae ab
Auchore per 4 figuras rmilibri expolita lunt, expediri queant,
quemadmodum pas. 7 MIOnUIE.
Duod si circulus, centrum suum habens in puncto N,
transiensque per punctum L, non secet nec tancat lineam re-
etam Mt DR, nullam uidem A. quatio radicem admittet, ita
ut inde asserere iiceat, constructionem Problematis propositi esse
impossibilem. Ouod itidem ex Aquatione cognolci potest.
Nam cum Equatio Cic cercum medium, quo Problema aliquod
relolritur, lane, si relolrendo incidimus in aequarionem imposi.
bilem, argumentum est, Problema quoque elle impossibile. AF.
euitur aurem impossibilicas illa ex coneradictione, quam invol
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