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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 110, page id 175905688X:0132
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=132
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.76
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FL. O R LMONDI DE BE AMNE
sint aequalia: hoc est, sI PONAIUS A D ∞ b, AF ∞C, _EDF
∞ d, quod b: -= c: XquetUF d’, Quacenus delignanE vera qua
drata. Ouod quoque rerum eAt, quatenus delisnant lineas, ino-
do eandem incer se relationem obtineant, quam lixc ipla qua-
drata; uc demonstratum est a nobis, atque etiamnum in hoc
exemplo palam Facere conabiinur.
Alumatur pro lubitu linea aliqua major rel minor (perinde
enim est) quam D E, quae quidem lic unitas, e ad quam reliquae
omnes reterantur: ipla autem eAto BC, parallela existens ipsDF,
ducaturque perpendicularis A F, iplam, Si opus elt, producendo.
Deindetiac, uc B C ad D F, ita D F ad HI M, Hetque HI MI ∞ d.
Tam rero, licut hx lincae BC, DF, TIMT SUNE CONEINUC PFO-
portionales, ita quoque linex B C, AF, NNI, nec non linex
BC, D A, IIN. Compolica enim cA ratiOBC ad AF, CK Fa-
tione BC ad A C, _ Cx ratiOnC A C ad A F. Fst aucem ratio
AF ad NMI composica ex iildem rationibus, nimirum ex ratio-
ne A F ad FE, qua eadem est rationi BC ad A C (PFOPEeE (i-
milicudinem triangulorum rectangulorum AF I _ B C A,) _
ex raTIONC F P ad NMI, hoc CA, AF ad AM, quae cadem est
rationi A C ad A E (per constructione.) Id quod codem inO-
dopatet de BC, AD, FIN. FritigituF NM ∞C, X FIN ∞b,
quae quidem limul sum pex aquantur ipsi FI M, hoc CA, d. Quod
erat demonstrandum.
Cernitur praeterea illa in hac Mechodo facilitas, quod eriam
lineam aliquam hocmodo,, aliitre similibus, exprimere pONi
mus; aut quod eo icem modo tractionem aliquam Arithmetica
communis, uC =, 3, Rc. denotare raleamus; hoc Pane compen-
dio, quodliceris tractio exprimi possit, cujus numerator ad de.
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