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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 78, page id 797435492:0302
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=302
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.90
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

L F C F. 22
Hujusmodi plura quaedam cositaram hic inserere; veriim HXC ex-
iltimo susticere lubindicando modo, juxra quem, cirra C alculi molesti-
am, curvarum tangentes exquirere licet, unaque constructiones de
monstrare. Subjiciam ramen urum aut alterum non aspernanda, ut vi-
decus heoremata perquam generalia.
Z.L. Sit linea quaepiam L. G F, cujus axis VD. ad quam impri-
mis applicatae perpendiculares (VZ, PO, DF) ab inicio VZ con-
tinue urcunque crescant; sit item linea V PF calis, ut duet a quacunq.
recta FD F ad V D perpendiculari (qua curvas secet punctis E, P,
iplem V D in D) CIE Semper rectangulum Ex D F, e desionatâ qu’a
da R aequale spario respectire interseptoV D F Z; Rac aurem D F
DF:: R. DT, ex connectatur recta TF; haec curram V IF
concinget.
Sumatur enim in linea V L F punctum quodpiam L (illud primo si-
Dra punctum P; vertus inirium V) ec per hoc ducantur rectae IC ad
VL, ac K L. ad VD parallelae (qua lineas expolitas secent, ut vides)
estquetum L F. LR:: (D F. DT::) DF. R; adcoque L F X
R =  LRXDF. Fst autem (ex praestitura linearum iltarum natura)
L F X R aequale spatiO PD FC; CrGOLRXDF =PDFC 
DEXDF. Unde eAtLR = LDP; velLK = 1 LI.
Rursus accipiatur quodris punctum I, intra punctum F, reliquaq.
tiane, uti prius; similigue jam plane discursu ConAaBILFOrCL R XD L
PDFGL DP XD E, undeja exIEL RL DP, vel LI. F
quibus liguido paret roram rectam PR P R intra (seu exTra) curram
VIFI existere.
tildem quoad extera politis, si ordinatae V L, PO, D F, 50. CON
tinue decrescane, eadem conclulio simili ratiocinio colligetur; uni-
cum obrenit Discrimen, quod in hoc catu (conera quam in priore)
linea V IF ConCaVAS suaS aXI V D obvertat.
COrOL. NOTCTUED E X D Paequari spatio VD P L.
ZII. Eixinde, deducitur hoc Theorema: Sint dux linex queris
Z GF, VR F carelarae, ut ad communem iplarum axem V D ap.
plicata quaris rect a ED F, sit semper quadratum ex D P aequale dis-
plo spatio VD F Z; lumatur aurem D Q = D F, e connectatur FPC.
HXC CUITVX V R F perpendicularis erit.
Concipiatur enim linea V lF, per P trantiens, talis qualem mOx
attigimus (cujus scilicer ad V D applicarxe se haDeane ut sparia VDEL;
hoc est ut quacrata ex applicatis à curra V K P in praesese hypotheti
lineamque
18. 109.
RIg. X10.
E18. TTF.