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# Title: LBr. 56 · Bernoulli, Jac.
# Folio 18r, page id DE-611-HS-958800:0035
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 17v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 148, 2026-09-10T03:35:15Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.90
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Jam sit anguli CNd vel FPG sinus 5. Sinui compl. t sumto AH = a pro radio:
OG. AG:: DG. EG
Vraa -xx. x:: Vaa -xx. xsaa -  1t. S:: (PG. GF):: Vaanxx.  Vaa-xx.
raa - xx t. a:: (PG. DF):: Vaa -xX.  saa - xx.
EF = EG- GF = X saa - XX - 3 VaaxX AE = AG - EG = X - X saa-Xx
AE
2aa -xx
EF
:
AP.
PF
raa-xx
X - x saa - xX. X saa -xX -3 saa-xx:: a. = Vaa -xX; un de habet:
2aa -xx
2aa -Xx
5+X Vraa -XX - X Vaa -xX = tx, quadratisque membra, poritoque aa pro ss +, et facta
divisione per s+X, ont aas + aax - x = XV2at - 3aa XX + Xt. Unde porro
X4 - 25X7 - auxX + 2 aa5X + aass = 0: Quare si fiat curva AZaH huijus naturae
ut si AG = X, _ Ga = s, sit X4 - 25X - aaxX + 2aas X + aass =0, ac deinde ducati
quaevis za parallela ipsi AH, in ut D2 = Ga = 5, erit spatium dGr5 quadrabile,
nempe = trapezio XOPN - A MXW. B. sumpta Ab = avz, erit 6y -ar
=3 A6. maxima applicatarum.
Solutio Problematis de Minimo Crepusculo.
sit BLZ horicon; MER ejus parallatus 18.
gradibus infra illum depresus; PdM aequator.
EE, aR, ejus paralleli versie polum Au
Itralem W; Wa. WE: _ WR. WE. circuli
declinationum: Z P vel EV arcu declinatio-
nis paralleli ZE: Jam si sol describens pa
rallalum ZE efficiat crepusculum minimum
erit mora solis in ZE bravissima, hoc e, bravior
mora in dM vel CA, adeoque differentia mone
tolis in parallelis contiguis ZF, aR, nulla,
cumque et mora in 25 d TR differentia nulla sit, eodem quoqutem pusculo SEeaY
pertransibunt, ac propterea ipri arculi SE, aF, erunt ut celentates; quibus per-
curruntu, hoc e, ut raclu parallelorum 2E, aR, hoce, pp infinite parvam
distantiam parallalorum, dicti arculi erunt aequales, et quia sR, ZT, qqrunt
aequales, et anguli ESR, Q recti, erunt et ang. SER, FaZ = G_C = HZ C aequales,  proinde
(ob VES, DZH rector) ipsi GEV, dZP 4q aequales (porito =GB ee quadrantem circuli
maximi, tangentem parallelum Honzonti MEA in E) quare cu de GVE, deZ sint
recti