# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0356
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0356?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 118, page id 797435492:0356
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=356
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000356.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.85
# 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.

E E C Y. ZII.
dinatam B D in I, _ lineam R S in Z) SIEMIP. ME:: VO. 1Z.
vel, sit linea AL colis, ut ducta MIP Y ad B D parailela (qux seceF
axem A D in P, _ lineam A L in Y) GIEPF. M F:: VO. PY; erie
tunc urrumqua spatiam (Cingillatim) B R SP, vel ADL duplum (i-
perficici conica, quod es recta per V e curram A M B mota progene-
rarUE.
Namm sumatur ML PI indetinica currae parricala; _x per H ducaneur
rectae AOK T ad ipsam AD, _ N QZ ad BD parallelae (que li-
neas expolitas, uc Schemamonstrat, secent) connectanturque rectae
V ML, V N. eAgHC M O. MEI: : MF. MF:: VG. TZ. quare
DS FIX VO =MOZIX = IKX IX. ILem CRHO. MH: : P F
M F:: VC. PY. Unde MN KVO = HOZPY =OPXPE
PStantem ME _I X V C. duplum criansuli M V N. quaproprer tam LR
xIZ, quam OP X P Y duplum eltrriansali M V I. Parirer aurem
ubique tic. ergo conctat Propolitum.
Fxemplun.
F18, 177
Sic curra AM D hyperbola aequilatera, cujus Centrum C, Cicque
CV = C A = r. SC CP = x (nam hujulmodi calculo plerunque
rem expedit peragerC) LUM COnMEXA MC; Patet esse PC =
SEM C 9 = 2 X x = er (Na P M 9 = X X = r r) item est MC9.
CP q:: M Fg. MI P 4; hOC CAM Cg. C P9:: F C9. C69. hoc
eAt 2X X - rY. XX:
2 y p X X
2XX 7
2XX-rr. Guare VC9-
Vx. CC9-
V AgXC. P4
MCq. vel VO=
2XX pr
V AXCP
-
MC. Quare
VG, V A:: (CP. MC):: MP. ME. hinc consectatur in hoc
cala, quum ubique sIE IX =V A, lineam RSfore rectam; _ rectan-
sulum BRSD superficiei conica A M B V daplum esse.
Caterum hoc elexans exemplum luppedicarir Generolus, insenio ac
erudicione pexstans, Vir CCollesii nostri, quod olim Sociorum Com
mensalis incoluit, Ornamentum) D. Francisens Fessopius, Armiger
cujus in hanc rem perquam ingeniolo mihi comiter impertito scripto
Ciplius injustu quidem, ac spero non ingraris) seu Gemma quadam au.
debo mea condeCOrATC.
F15, 177
Prop.