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# Title: LBr. 396 · Hermann
# Folio 77v, page id DE-611-HS-973581:0154
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 78r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-973581&page=154
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 321, 2026-09-10T22:31:41Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.94
# 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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AB et ab, duclisque per terminos B, b tangentibus BD, bd; anguli DBC, dbc
comprehensi tangentibus et ordinatis ubique aquales sunt, ipsu curoa ABMet abm
sibi mutuo congruunt. Et si loco arcuum aqualium AB et ab arcus utrinq auipi
antur in data ratione, et anguli DBC, et dbc semper aquales existant, euroi
ABM et abc similes sunt. Hoc posito.
Si eurva ADC et L N R (fig. 2.) congruunt, sequitur omnes lineas CR, 98,6P, B
qua connectunt arcus aquales AC, LR: AE et LP, . tum parallelas etre tum aequales
ipsi AL. Unde ducis per puncta quavit 9. E, D receis gH, E), Dx perpendiculari
bus curvi ADC et per totidem puncta prioribus respondentia in prima curva B 
N rectis eH, P1, Ns Tangentibus cuream, qua prioribus perpendicularibus ad curru
ADC occurrene in punceis H, 8, X H. quu ex hypothesi sunt in Curva CX L. Jam vero
anguli perpendicularium curvii ADC et parallelarum ipsi AL eo majores sunt quo propiores
fuerine eorum vertices puncto ultimo c. nam RCB est recous, sequens vero egH auutur quide
sed major qua n angulus PCt, et sui major adhuc est angulo ND N, et tandem angulas fit
nullus, quando DN coincidit, cum AL. Hoc sequitur quin curva ADC cava est versus eunde
rectam eB vel AB. Si jam angulus Pei statuatur semiredus, erit Et = D), vel curva
DNL = Curva AHC, et angulus E17 = arg. T1D vel alterno 1DW. Porro reclâ q8 et DN
ita ducea intelliganeur, ut anguli 8qH et NDK simul aequales sinae recto, hoc est ut unus
horum angulorum alterius complem ene um sit ad recum: atque hinc atubo eriangula rectangula
2gH et NIK propeer hypothenus as aequales q8 et DN aequaliu sunt ee similia; unde qH = NX
hoc est curva CH = curva NL, et angulus gHG = angulo XNO; et sic infiniti alii arcus
aquales in curoit CIL, et L N R Sumi possunt ita ue unguli tangeneiu m et ordlinataruntdue
tarum pes puncta contacens utrinque constant er aequales sint. Unde per Lemma superiu,
Curva estL congruit curva LNR vel aiquali ADC. 2. E. D. Calculum quoque pro luroin
huiu modi multum contraxi cum is unica analogia perficiatur, in qua ne quidem
seundorum differentialium aue exprenione radu osculi opus sit. Nam vitando AL vel 2N
= 2a, AT = X, DF = y, o D = 5, Dd = dx, Dd = ds. Fient Triangula Ddd et DN X sini
lia, et cum Nh sit = NL hoc est per hypoth. = AD erit NR = 5. Adeoque
Dd (ds): Dd (dx) = D N (24): NK (5). Hinc sds = 2adX, et 55 = 4aX. Unde constat solum
Cycloidem se inverso situ sui exolutione generare.
et naly sii grro curvis similibus parum differe a pracedenti. Si (fi. 3) Curva LN D sui
euolutione describens curvam Lte C, similii sit curva ADC descripta euolutione seunda CAL
ac prius
eodem fere modo probari potest omnes tru dus curvas similes esse, Unde linet siL, DN, CK