# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1040780814:0357
# Permalink to this reading: https://leibnizlegible.com/page/1040780814:0357?run=74
# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 339, page id 1040780814:0357
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1040780814&page=357
# Source image: https://digitale-sammlungen.gwlb.de/content/1040780814/jpgs/default/00000357.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.79
# 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.

OMta
ItIOH
1
M
H
miller
itan
0
em
nie
rente
N
d
L. IV. IV.
et CTEOMETRLOA H L EMEN FA.
39
scura disterminans: es ansilus verticalis trianceili per axet
est proaime aequalis aserentiae anculorum, quibus sphaera l
cida ex centro opacae  sphaera opaca ex centro lucidae viden-
tur. Et si conus umorosus secetur utcunque plano ad planum
vasis parallelo, umbrost circuli sie ceniti diameter ex centro opacae
Phaerae valebitur fab angulo proxime aequali intervallo duorum an-
sulorum; quota aler est accrecatum anculorum sub quibus opaca
phaera calcenth sphaerae lucidae e circuli umbrosi videtur, alter
angulus En qao sphara lucida ex opacae centro spectatur.
Sint dux sphaerae centris  de B, quarum altera est lucida al-
tera opacu: junsatur recta AB per quam traducatur planum, cu-
jus communes fectlones cum spharis sint circuli DF, FC; ducantur
rectae DE, FC biitos circulos ad partes casdem in D _ R, F_ aCON
tinsclcus a oueantur donec cum aB etiam producta concur-
TaNE II C. Patet mnorum totalem sive plenam, quam alterutra
Iphasa opaca ab ali d lucente illuminata projicit, contineri sub co-
nica superticie deseripta per soctam DC circa axem aB rotatam; hoc
CAt, superticie coni rec Cujus axis eA recta ABC, balis circulus
cujus diameter eA recta  vel PC. Superticiei conica annumero
eslindricam factam cura exposita sphaera sunt aequales.
Ex a ducantur recla diculum sx concinsentes in n ec Y, e prO
duplos, angulus FCD aequalis cst ansulo MBL, dempto r AHI ansulo.
Ponatur alterutra sphaera, v. g. F C opaca, e lecetur conus umbro.
ducatur A H donec cum eD ConCurTAE in X, _ ex B ducantur recta
tansentes circulum DF in L. _ M. PeF PrOP. XXXH. FL. I. angulus
AcD aequalis eA AKD, dempto xAB: Sed (propter suppolitam mas.
nam Ephaerarum distantiam) angius AL DCIC P BKIHCa UaLIS ABL:
 igitur a cD aqualis est ABL, dempto K AB. Ft sumendo horum
suS F CC utCunque Pla Vans Prane Pusunero su (per Prop. IV.
Lib. L. FV. Conic.) circulus, cujus can  a BF Vel LC
haratiblau