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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 101, page id 797435492:0337
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3
D. P C T. FL.
XXV. He speculatio prXesens, ob hajusmodi complures methodos Cy.
olometricas indios promulcatas, aspernanda rideatur, adjungemus con-
sectarium unum vel alterum, quibus Forre solistxc paucula meruerane Fis. 248.
impendi; a quibus nempe Maxima, Minimaque Cui generis innume.
ra deterinantur.
Sit Semicirculus ABZ, cujus centrum C; CIIque segmentum
ADB; _ huic adsexipra paraboliformis A E B, Cujus exPOnenS.
Sicitem AD=
 2 B
M
m n C A; paraboliform:s autem parameter (hOC.
estrecta, cujus aliqua porectas in poteltarem segmenti axis, Peu AD,
ducta conticit potestatem ordinarx, ceu DB) nominetur p; erir pin suo
genere maximum.
Nam urcunque ducarur C F ad D B parallela, _ ad C F pOsira
concipiatur paraboliformis, ipsi A FB coordinata, rujus parameter di-
eacur q. quum exso paraboliformis AFB circulum extrorlum contin-
satus exit OFC C F; adeoque C Fm C GFm; hoc est pm- n X
A C=F qm= n X AO=; Quare pE q.
Norandum est esse p 2 m = 2n = Z Dn X A D m- 2n _ 2m - 2n
=Z.Om X ACm-2n. unde L. D X ADm 2nC ZC m X A Cm -2 n
2n est maximum.
Exemp. T. Sitn = +, _ m = 3. erit ideo p=e = Z D= X AD =
ZDgX BDq; vel p = Z DXBB. IIem AD-
C A.
2. Sien = 3, _ m = 10, erit p 2 4 = Z D 0 X A D +
vel pZ =Z DE X A D= = Z D3 XBD+. _ AD
 C A.
ZIZVI. Sit item Byperbola (xquilatera) CUIHS CENErUI C, aXis
Z A; e huic inscripta paraboliformis A F B cujus expo Bi8. 149.
nens parameter p; birque AD =
MerIS MaZiUM.
m
n
CA; eriep sui gene-
NaM uECunquE duCatK E G ad B D parallela. _C ad F C= Constituta
intelligatur paraboliformis, ipsi A F B coordinata, cujus parameter q
quum ergo paraboliformis A F B hyperbolam inerorsum continBaE,
quare p 14.
 X AC n  g =X AC.
Notandism