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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 70, page id 797435492:0114
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.84
# 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.

I
FiB. 100
R. F C X.
Z2.
V. Elarum caluum primus ad unum duncaxat ab una axis parre radi-
ura percinet, qui reliquos aliis casibus conrenientes medius dilterminat.
de posteribus itaque duobus separatim paullo dispiciamus, Sit jam
itaque primo A C = AC, = AV; unde quilibet incidens caro(+B V
racius (uE A N) major erit quam A C; hujus iraque reHexus axem
secet DunEtoK; dico, li semidiameter C B dividatur in Z; ut (IE CZ.
ZB:: AC: AB; FOrC CK C CZ. etenim ob angulum ANR
bilectum, erit A C. CK:: AN. NK. vel permutando AC. AN
:: CR. NK. CA aUFeM AC. AB- Q AC. AN erGO AC. AB
DCR. NK= SCK. BK. erpo cum lic, ex hypotheli, C L. LB
:: AC. AB; erit CZ. ZB +CK. BR. componendoque C. B.
ZB. = DCB. RB. inde Z BC RB; ICu C: L = C.R: G.
E .D
VI. Tlinc punctum Z. est limes intra quem, Vertus cenerum, nullus
reflerus axemm intersecat.
Coroll. HIinc (i puncta 2, E sine limices punctorum A, a (quorum
A remOTIuS) erit CZC CE.
Nam BC. AC - 1BC. ~C. componendoque AB. AC.
aB. 2 C. HOc est LB. Z. C = EB. CC. vel compolice CB. Z C
DCB. CC. ergOZCF SC.
VII. Ouineriam erit in hoc catu; A N 9 = ACg. CN 9::
AC. CK. Nam duCATUE K Had C H parallela, prOtrACtA AH
occurrens in H; ec connectatur C P; _c eodem plune modo quo lu
perius (in iis qua circa convexas partes accipimus) octendetur Pore
ANKHP. CNg:: AK. CK. unde dirilim crit A N X N P.
CNg. CNg:: AC. CR. eA aurem AN R NP = AH9-
ANXAP = AN9-: AC9--CN9 = AN9.- AC9 1
CNq; adeoque AN x NP = C N9 = AN9- ACg. ereo
derum erit AN g - A C g. C NG:: AC. CR: G. F. D.
NOretur; E Fuerit A C minor semisse semidiamerri circuli re-
Rectentis, quod punctum A duos socoshabebit ad caldem cenrri par-
res, quorum alter ad parres D, alcer ad B pertirebic; Cn A C major
fuerit ilta Semisse, Focis qui ad diversos verrices B, ec D percinen,
centrum C incerjacebis.
de
VIMI. Etiam hoc incerteram Theorema; praemittis contorme: Si
Hiat 2 CR. C H:: CM. F, iremque 2C A: CN :: CN. F.