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# Title: LBr. 437 · Huygens
# Folio 98r, page id DE-611-HS-3595205:0201
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Fractoria
in spiciatur AAsta lipsiensia  et Tab. V. ad pag .387. anni 1693.
ABX; BC, y. TC, +. ET, e et ET+
at
TC= constanti in
dicta figura, seu e+ + = r datur autem relatio inter + et y erqo
ex data et lege declivitatum curvae CC. Ergo datur et relatio inter
et  e, et y, seu inter ET et RT, adeoque natura lineae E)
sed qui videamus, quid faciendum si relatio detur inter X, y et t.
Replicetur filum A  sic ut sit CTFTA et in puncto A pro arbitrio
aiffrahatur caeteris ut ante manentibus manu traheate extremitatem
sili ab A tend ente versus p.. et
+X + AAt-gy + EFR2 C-h + C = constantiC. Detur
e
A
(2).
jam relatio inter qu datur relatio inter X, y, F, quaeritur
relatio inter y et e, item inter p et _AT seu inter p et x+
Tollatur sit X+ AAt . gu = V ope aeq. 2 et 3 l et 2, et 3. tollatur
X et t, restabnt  restabit aeq. (4) inter p, v, y e. Assime
V rationaliter ex C B, B, y et ruasu B rationiliter ex e,
quos duos vatores aequando debets exaresem formeni destrui posse  quicquid
tinet V A ut siat relatio (7) inter e et y
uitu
ubi duae tres a indeterminatae quatuor, facienda jam es
95
assumtio unica, cujus ope defur relatio inter p et vi itemque
inter y et e nam so duae fierent assumtiones daretur
relatio inter v et y quae non debet dari. Assumatur
Generalis relatio inter p et v; ejusque ope tollendo p ex aeq. 4 debent
ita explicari arbitia riae id aeq. 5assumtae, ut simul evanescat v
sed hoc video non posse fieri, nisi possint P et V solae
haberi ab una parte aequationis, et ye, ab alia parte
Rus eu redit
sed hoc non semper hhaberi pb
Quod si simpliciter i velimus filum reflexum alligari
in puncto fixo A, et sieu fieri motum,  non minus
res erit difficilis