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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 112, page id 797435492:0346
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L B C F. XII.
nibus p Y X. p ut Par ), aquatur subdupto spaiii: PL. O.
VII. Omnia quadrata ex rectis u. l. (ad recram ae pe applicais) sequant
C RX C P X P X (hoc est paralle lipipedum Base Rectangnlo AC. PD,
Altitudine C S).
Llujus F.ffari demonstrationem (quanquam resxaesr) cransilio; quo-
niam aliud Schema discursum que pra reliquis plerisque lonsiusculura
expolcir; neque rem ranci video.
NIII. Curra APYtalis sIC, ut FY aequetur ipsI AS; duct a cum rect a ZI
ad AC parallela, erit etiam sparium A C IYY A (hoc eM summa
Tancentium ad arcum AMt pertinentium, Sc ad rectam A C applica-
tarum, una cum rectansulo FC. IX) xquale subduplo spatio hyperbo-
LicOPLOO.
Nam spariumaYu (A) XONatuE rectansulo AC PD: hoc est
roctanonto F C IY (natB est C A. AS :: C F, FM; vel C A FY::
CF. C P. adeoq. C AXCP =FYXCF) item sparium v ant (hoc est omnes
rectae TF ad a c applicacX, quotquor ad arcUM AM PertinenE) (b) X.
quatur spatio A EY; erso spatium A C I Y A aequatur spario a y al H;
tioc est (ut mox octensum) semissi sparii hyperborici P L O..
Alirer illud, (eique connexa) dimensus summ, hoc pramisso Lem-
mate.
IX. Sit LEyperbola aequilatera (axes nempe pares habens) F R R ac
cujus ares C. E.D, C L; ex ad hos ordinatX RI, KD. Sic item curr
F V Ycalis, uc in hyperbola libere sumpro puncto R, ductique recta
RVSad DC paralleta, (InESR, CF, SV concinue proportiona-
les; conmena recta CR, eric Sparium C F YI Sectoris hyperbolier
R C E duplum.
Nam ducatur RT hyperbolam tangens, _ R HI ad C I parallela.
FAtgne CH. CF:: C F. CT. quare C T =SV. vel HF = = RV.
itaque Spacium FD R Y duplum est segmenri F D K. item rectangu-
lam IEDC crianculi C DK duxlum est; erso reliquum spatium
C F X Treligni sectoris F C. K duplum est.
X. Relumpra jam quadrance circulari AC B, SIC CF = C A;
dE aXC A F., parametro eriam A F, descripra sIE LEyperbola FRR;
Dolitoque curram  Y Y calen esse, ut ordinata quacunque rectâ
M E Y, Sic F Yransenri A Sxqualis; dueatur recta Y LR (rectam
F18. 167.
Fi8. 1660
(a) 2. Lect
EII
Tell.
FiB. 263.
20 Fect. XI.
F18. 1C9.