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# Title: LBr. 396 · Hermann
# Folio 24r, page id DE-611-HS-973581:0047
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 23v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-973581&page=47
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-973581/jpgs/default/00000047.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 310, 2026-09-10T21:47:17Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.93
# 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.

Sane prolixo quam ue existolae nunc inseri posie
Sint, verbi gratia, quatuor puncta data A, B, C, D per qua
oporecat lincam algebraicam AB CD transire, duco aliquod
punctum ut A, lineam indefinitam AG, Super quam ex
datis punctis B, C, D _c. perpendiculares demitto BE, CF, DG;
quae omnes data erunt longitudinis, aque ac partes axir AE,
AF, AGQc. Vocentur ha ordine, A, B, C illa vevo a, b, c; quibus positis, sumo
aequationem O1X + 10y + 11Xy + 02 XX + 20yy = 0 Statuendo Ase = X et HK = y
in qua aequatione valores numeroru assumtitiorum et 10, 11, 02, 20 c. ervedi
sunt, quod hoc parto perfici potett. Propter identitatem relationi omnium
punctorum B, C, R, H ad exem AG, habebimus eret sequentes aequationes,
ponendo successive in superiore aequatione pro X, velores datarum AE, AF, AG
Loc ese A, B, C et loco y, valores iquarum applicatarum BE, CF, DG vel a, b, c
et fient.
O1 _ + 10a = 11 A a + 02 AA +20aa =0, jam beneficio trium harum a quationum
01B + 10b + 11Bb + 02 AB + 20bb = 0 inveniuntur valores terminorum ahumq
D C+ 10C = nCC + 02 CC+ 20cC = 0 Litcorum o1, 10, 11, 02, 20. in quantitatibus
dati vel constantibus, qui valores in aequatione o1X + 10y + 11Xy + 02X + 20yy =0
Substituti dabunt aequationem pro curva quaesita.
Circa Dyadica Subinde in periodos columnarum progresiionum geometricaru
inquisivi verum nihil inveni Ractenur quod Ampl. Tui offerri mereatur.
Quod et. Albas Fardella tam conseanter in perficiendo negotio persevent
Tuae imprimis efficacistima apud eum commendationi acciptum refero, nam
cognitis ejus in Te animo atques eminentium Tuorum in rem publocum literarium
meritoru admiratione et veneratione haud miror si nullas non occasiones gratu
Tibi quid prassandi avidus arripiat et quicquid eveniat Ampl. Tuc semper
obserictisinus manebo pro incomparabilo sua humanitate et benevolentiam
quibuo me immerentem prosequitur et quibus etiam fit ut me secum videre
aliquando desideret cum potius eremea sit, Primarium inter eruditos Virum
Cont ardentissime ad desidevo) et coram salutare et insi pro acc esstis beneficis
debitas rependere gracias, si et quanquam forcuna huc in re mihi nondum
faverit, nesciens tamen quo mefata trahent, spem omnem nondum abjivio.
Hice Vale Vir Nobiliscime et me properro ama
Posilea 20. Detobrit 1705.
Cleverine Homernis sugu
Cultorem peopetum
J.Hermannum