# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0366
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0366?run=74
# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 124, page id 797435492:0366
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=366
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000366.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

a .    i cat
Probl. IV.
Sit angulus B D HreCtUS, S BF ad D HI parallela; e asymptotis
DB, D EI per P descripea lit hyperbola F X C; item centro D delerip-
tus sic circulus R Z L; lic denuo curra AM B ralis, ut in hac lumpro
quocunque puncto M, _x per hoctrajectâ recta D M Z, item sumpta
DI = DM; _ ducta IZ ad B P parallelâ, sic sparium hyperbolieum
BF X Laequale duplo circulari sectori Z. DR; currX A M B tansens
ad ML determinetur.
Ducatur D S ad D M perpendicularis; sirque D BX BF = R9:
Aatgue D R. R :: R. P; TUM DR. P:: DM. DT; e connecta
TUE TM; haeC CUIErAM A M BtanSCE.
AAIIOLECFUT CUEVX A MI B hanc esse proprietatatem; ut DI SiC inter
DB, DO (vel D A) eodem ordinc media proportionalis Gcometrice
quo arcus R Z inter o (seu nihilum) _ arcum R L est medius arith.
metice hoc est, (iD IEIt numerus in Perie Geometrise proprtionalium
incipiente d DB, _ terminata in D A; aC0, PL sint Logarichmi
iptarum DB, D A; erit RZ Logarichmus ipsius D I. Vel
rerro (pront vulsares Locarichmi. procedunt, sDI lic numerus in
Terie Geomerrica exorsa à D O. e delinente in D B ac oCIE Locarith-
mus ipsiuSDO, _ arcus L. R iplius DB, erit arcus L. L. Logarichmus
iptius D. I.
Ouod si absolute construatur curra AM B, ejusque tancons Me
chanice deprehendatur, inde patet lpperbolici spatii Cgelismum dari
vel Circuli byperbolismum.
Fujulce spiralis naturam, ac dimentionem (ut _ Spatii BD A di-
mensionem) luculente prolecutus est preclarissimus D. Wallissius, in
Libro de Cyoloide; quaproxter de illa plura reticeo.
Probl. V
I L. DC (rectis D F, DC, _ linea F HO
comprehensa) e data quadam R; curra AM B reveriatur talis, u
si vEcungue a D prOjiCIaTUE reCLADNM, ec D. I ad hanc perpendi
cularis (iF, SC M T Curram LLMB continsAE; (IE DT. D M:: R
dic curra laca in LXDB; iuplasui olC
rect.
2
E18, 287.
FrB. 168.
Sir spatium quo