# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068194:0551
# Permalink to this reading: https://leibnizlegible.com/page/00068194:0551?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 276r, page id 00068194:0551
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=551
# Source image: https://digitale-sammlungen.gwlb.de/content/00068194/jpgs/default/00000551.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
# Lines: 28 recognised, mean confidence 0.94
# 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.

per pum
A circ cirtulium EGF
sit conus descriptus dum recta indefinita BI  puncto
meltur, gno
pendens mo per punctum fixum in sublimi B transiens, et sam
circulum EGF. Is, secanbus est plano AGH transcunte per punctum A
plano AGH transeunte por punctum Conicae superficiei A, et secante circa.
circulum EGF in recta GH. Bisecetur GH in K, et jungatur AK. Hinc A
dinta parallelis ut XY, non estordinata ad Ea ut sit diameter rordideata
X Y(Y) ab ea bisecariraeterasque parallelas ipsi GH ab e. Ergo
oportet ut  tangens sectionis Conicae in A, sit parallela ipsi GH, adeoque basi
seu circulo EGF. Ergo Erit in plano circuli, basi paralleli per A trauseunlis
ut bisecet
ejusque adeo et ad ejus diametrum fecli et angulum rectum quod si ergo ponamus
sumamustc esse ejus circulidiametru erit EF diameter busis circulivaseos, quae
bisecet GH erit augum ER ad GH rectus. idem est in circulo LYM, u
M diameter transeunte, per aliud punctum, L, quodcunque in rectae, AE
ut pempe diameter LM secet Y1) codam circuli lansem in qua bifac
bifariam sec ipsam Y(V) (hordam circuti in qua planum sectionis conicae circulus
 illum secat) bifariam divicat in X. et in universum, sectio conica AYG
A(Y) G, utrinque se habet eodem modo ab utroque latere plani BEF adeoque
planum hoc, visecabit sectionem conicam GY A(Y) H in recta cominum HX
etc
secabitad angulas
rectos alioqui, anguli AXY vel AX(X) non forent utrinque aequales. Unde patet
quae proinde ipsas GH, Y (V) et par allelas in
si ordinatae sectionis lonicae sint basi circulari paratlelae d eas ad
diametium Ak facere angulos rectos, seu Ak esse axem. patet et