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# Title: Où il répond à plusieurs difficultez qui luy ont esté proposées sur la Dioptrique, la Geometrie, & sur plusieurs autres sujets (shelfmark Leibn. Marg. 43:3)
# Folio 471, page id 82327652X:0499
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DF NIE DESCARTFS.
quadret hyperbola, ex quidem hyperbola quae non transeat per
ullas intersectiones datarum linearum, quemadmodum hic re-
presentatur: V+ exempli causa si rectangulum ex FC, in C D
debeat esse majus, quam rectanculum ex C B, in C FT, quadam
data quantitate, vel quid simile. Fiusdem breuitatis pudie.
nulla etiam hic mentio sic oppositarum hyperbolarum, non quod
ab authore ienorentur, vt pote qui paulo post in pacina 336.
quaruor lineas hyperbolae affines inter se oppositas, exposuit.
Sed notandum est illum faciliora fere semper in hac Geometria
neclexisse, nihil autem ex difficilioribus, inter ea quae tractanda
suscepit, omisisse. At que idcirco ip sum maluisse hic exhibere po-
sitionem linearum, cui quadrat circulus, quam alias, quibus
quadrent ellyp ses aut hyperbola, quia ejus inventio peculiarem
habet dissicultatem.
Pour l’Annoration de Monsieur Flaestrech à la pase
378. elle ne me semble pas assez claire, mais vous pourriez
MCEErC en CeETC POrTC: Notandum est nos vri posse hoc exemplo
tanquam recula vel canone ad quantitatem, qua radices aux en
dae sunt, inveniendam. Si enim proposita sit exempli causa haec
equatio.
∞ Y A x + b ∞ = c x = d X ∞ + e x Y F 10
Neclectis omnibus iis terminis in quibus notae t es  aliae
sunt quam in canone; nempe hic neglectis terminis b, c ∞ F,
oportet tantum considerare omnes alios ut a, d éx e, quia hic
habetur + A X, Ut in canone + H x ex - d X X, Vt in canove
27b n X X, ∞ + e X, V1 in canone 2296 n X. Oporiet
aurem sinculos ex his terminis considerare scorsim, es quaerere
quantitatem n, que non sit minor quam a, quia in canone
habeturn, obi in data equatione est a. Trem cuius quadratae
quadratum non sitminus quam= d, quia in canone habetur
226 n, obi in data aequatione est d: Tiem denique cuius super-
solidum (vel v1 Victanominat quadrato cubus) non sit minus
quam c, quia in canone habetur 2296 n obi in data aequa.
tione est e. Quantivate n ita inventa, manis este demonstratur
ex ipsa operatione, faciendo Y - 6 n  x, prodire aequationem
in qua nulla radia falsa esse porest; JLocque auchoritam facile