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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 15, page id 797435492:0223
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# Lines: 42 recognised, mean confidence 0.92
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# After the first blank line: the recognised lines in reading order, one per line.

E. F C L.
puncta quaeris P B rectâ linea connectantur, iisque responden tia
puncta BB recta quoque inngantur; quoniam reutx L B sibimet
aequantur (eterim nil aliud sunt, quam eadem ipta linea diversur eis, c
situm obtinens) ac parallelx secundum hyporhesin, erune rectae P F
BB aequales ac parallela. Unde patet curras F F, BB adaquari (i
oimet,  altirmilari. Adequari quia subren (X omnes F. P. SubTenlIS B B
Cinsillatim aequantur; altimilari, quia rectae A B cum CubrensiS adja-
centibus respectiris E F, _ B B pares angulos constimunt, adeoque
rectae ip(x L P. pares iis, quos rectae BB; ipix illa cum sciplis, 
tae cum scipsis (nam in trujusmodi proporrionalitare parrium, e an-
sulorum xqualitare, Peut alibi Forralle luculentius e Fusius dissere.
mus, omnis consistir linearum, de quarumcunque magnitudinum simi-
lirudo.) Ouod sivice commmurata linea curra B C Hac linea Oenetrix,
e recta B A diroctrix, hoc est si B C per B A libi parallela Feracur, Fis. 6..
producetur eadem ipsissima parallelogramma Superticies; ee lingula
rectxX B C puncta, veluri E, rectas lineas ad B A parallelas deleri-
benE; REUE NON INFEFCCDEX F F respectivis B B pares crunt, quod
ex pari modo ex suppolito perpetuo currae BC parallelismo facile con-
sectatur. Sie denique curra quaeris (vel c rectis ansulos efticientibus
compolica, quae currae quoque nomen meritoterar; Archimedes
saltem e rectis compolitas lineas, uti fgurarum circutis inscriprarum
aut adlcripearum perimerros, noununcor zeaunor nomine complecti.
cur; ut de vicistim curra quaeris lincae censeri possunte rectis, innu-
meris quidem illis indefinire parris, adjacentibus, e deinceps se-
cum ansulos efficientibus, conAatx) sic, inquam, talis aliqua curra
BC, in plano quoris consticura, tum in alio plano, vel super linex
B C. planum ut libet elerata, recta A B sibi continuo feratur paratlela,
modo quo semel ac iterum oltendimus; describetur hujusmodi moru
Superficies cylindrica (vel cerre prismarica, E linea directrix e rectis
ponatur compolita) ex. sylindrica quidem Aricte dicta, lidirectrix
fuerit linea circularis, ant olliprisa; latiore vero sensuralis, si curra
fuerie alterius generis ut parabolica puta, vel hyperbolica, vel alia
quaepiam. In hoc aurem motu linex quoque generricis lingula puncta
limiles e aequales deleribunt curra directrici lineas; aequales
ue in mox praecedence discurtu) quoniam F B pares ac paral-
lelx SumE; adeoque F F, BB quoque pares, ac parallela,
similes; =quoniam etiam anguli F F F; angusis B BB aGUANtT. 2O. XI. ELem:
Ouineriam reciproce describatur eadem Superticies ponendo curram
BC per rectam A B parallelos deporrari. Ouomodo lingula quoque
currx BC puncta rectus parallelaS _ pares intercepris respectivis
reCtX.