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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 128, page id 797435492:0370
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=370
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.86
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L. B C F. ZII.
spiralis, ut pro arbirrio duct a rect a C p Z habeat areus F. L ad rectam
Curationem altienaram (pura R ad 5) Manifeltum est lineam 6Z FI
esse rectam, quoniam FL. (R O). CN (OV):: R. S, perpetuo.
undeerolura B M P fit Parabola; quoniam aXi PartES AP, AD CC
habent ut spatia ROY, KC6, hoc est ut quadrata ex ipsiIs OX, CE.
vel ex ip(IS L Ht, DB.
Corol. Theor. I.
Si adtiguram 6 C  erisatur oplindrions alticudinem habens sequa-
lem peripherix inteera circuli, cujus radius C.L; erit ilce cplindrions
aequalis solido, quod PKOCrEntUE EfigurA CCLIR CIrCA AXeM C. R ro
tata.
Theor. II.
Sic CMVa GuXPLaL E L B (cujus axis A D, basIS D B) _ CUrVA
ALLcalis, ut libere ducta rectaZ P M, CIEPZ = V ZAPM; SIE
item alia curra OY Ttalis, ut ad hanc productâ recta Z P M Z,
ad sumpeaque rectâ R, (IEZ P G. R G:: P M. PY; (itque denoD L.
L:: R. VF. _ per F intra ansulum L. D C describatur Epper-
bola F X Z; huic aurem occurrat dueta recta Z HI X ad AD parallela,
exie spatium P DOY aequale spatio Lyperbolico L. LI Si F.
Einc summa omnium
DM 2LEZ EI
PM
RG
TBeOr. TII.
Sit curra quaepiam AMB, cujus axis A D, basiS DB; _ curra
RZ L ealis, ut ad sumpea quadam R, es arbirrarie ductâ recta L P M
ad B D parallela, sIE N AP M. PM:: R. PZ; CrIE spatUM ADLK
aequale rectangulo ex R in 2 N ADB; ve
ADLK
2 R
= Y ADB.
Exemp. Sit AD B circuli quadrans, erit lumma omnium
ns
V 2 I A X arc. AB.
PN
E18. 298
Lheor. IV.
Sit evera quxepiam A AI B (cujas axis AD, basis DB) Cincque
F18. 195.
Eig. 199.
atbido tullea e dtuus h 2 L Matlalas  ClLVe Ln 11L6 Alupco sabp
aM
219. 200.