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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 123, page id 797435492:0365
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es E C20. L2110
Exemp. II.
Sit L oou quadrans et habere debeat YP ad P M ratiO.
nem eandem quam P Pad R; elt erso P Y aequalis tangenti arcis CF;
e spat. A P Y Y = R X arC. AF. adeoque P M = arC. AF.
PrODV. LLL
Proxonatur figura quaelibet ADB (cujus axis AD, basis D B) Eig. 185.
rEPETIatUIE CUrVa R Z L, Proprietate ralis, ut ducta recta L P M ad
D B utcunque Parallela quae lincas expolitas secet ut cernis) politoque
rectam Z E LaNSCRE CUrraI RZL, CI intercepta Y P aqualis ipsa
P M.
Hocita perficietur. Sit curra O Y Y calis, ut ad sumpra quadam
R, DrOtractaqUE PM Y, SIEPM. R:: R. P Y. tum libere ad sump-
EaDL (in B D prOTeNSI) (IDL. R:: R. L. F; _ asymptoris D L.
DC per F describatur FIyperbola F X X, cum (It spatium LFXII X
quale spario DO Y P, Se prorractae XII, YP concurrant in L; erit
Z in curra quaelita; quam litangat Z T, erit T P = P M.
AdnOtetur, S propolita Fioura Tut rectanculum Paralleloerammum
AD B C, quod CARVXR Z L haeC erit prOprietaS, uE sIE D HI eodem
ordine inter DI, DO media Geomerrice proportionalis, quo DP F18. 166,
inter D a 80 (Ceu nihilum) cA media Arithmerice; quod si libere
juxta proprietarem hanc deseribatur Curra RZL, e Mechanice re-
Periacur ransens Z. T, inde quadrabitur hyperbolicum spatium LE. XHI;
exit utique hoc x quale rectangnio CxTP, AP.
Subnotari possIE FOTE L. SpaF. ADLR = R XDL = DO. 2. Sum.
MaMZ P 9 == RX: -
DECaB. - DO cub.
4. _ Tummam Z. P cub. = R X
_c. 3. Siponatur e esse centrum gr. Figu-
ra ADL R, ducancur que  . t 2d AD, _x pE ad DL perpendicu-
lares, fore e it =
L. 
3de PE = R.
A D XD
Probl.