# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068255:0027
# Permalink to this reading: https://leibnizlegible.com/page/00068255:0027?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 14r, page id 00068255:0027
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=27
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000027.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.96
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Elegans modus refutandi aliquam propositionem pro vera venditatam
reducendo rem ad casum aliquem simplicissimum; adhibendoque Legem
Continuitatis. Accessit correctio erroiis et ad verum restrictio in exemplo
Quidam hanc mihi propositionem pro vera venditabat? Si duorum triangu
lorum similium (ABEC F) ad apicem communem  easdemque rectas sub
contrarie positarum (ita, ut portiones rectarum recae ejusdem sint invicem recipioce
proportionales. FL ad FM ut MFA ad LFB, seu ut F(()A ad BM) B) r recta
per apicem communem (F) ducta CGH) unam oppositorum laterum (seu
antiparallelarum AB, LM) bisecans (velut bisecans LM) erit alteri (AB)
perpendicularis.
Hoc si verum est
cum
(fig. 2)
Hoc si verum esst, etiam verum erdt, ei LM sit ipsi LFM EA congruum
) o inits mataque etiam verum
erit angulo tam obtuso, ut AFBsit recta, adeoque LFM, quo facto coincidentum
B et LM, et puncta GFH. sed eo casu recta FG perpendicularis ad AB non
visecat ipsam AB, ergo nec ipsam LM. itaque non est universaliter
vera propositio. Est haec methodus exemalum ejus method
quod procedit per Legem continuitatis. Nota se perfecta coincidant A, rectam
constituant AF et FB cdici pores FG
aeterum ut investigarem quid verum inesset propositioni, sic processi.
redeatur aud si (fig. 1.) LM bisecatur in H, erunt tidangula FLH, et FMH aequalia
Ex H agatur normales Hi in LF, et HK in MF. ob triargula (ex hyp.) aequalia erit Hi. LF= HK. MF
ergo H HI: HK = MF: LF. Rursus Ob triangula HKF et AGF, item HIF et BGF similia
erit H: NF erit HK: HF = AG: AF, item HF: HI = BF: BG. Ergo HK: HI = AG. BF,:, AP. BG.
 FL : FM = AF : BF. Ergo AFqu: BFqu = AG = BG sed hoc non est
verum, nisi cum angulus AFB est rectus, seu cum AB est diameter circuli in quem
in cujus circumferentiam cadunt A, F, B. Habemus ergo propositionem restrictiorem
sed veram, simulque modum eam demonstrandi, ut sequitur
Si duo Triapguta similia ad eundem verticem sint sub contrarie posita, recta
per verticem alterum latus  alterum oppositorum vertici laterum, riecans
disecam
alteri est persend occurrit ad angulos rectos. Et vice versa
sunt triangula rectangula AFB, LFM sitque X FL: FM = AF: AB, sintque
A, M et F in directum, et L1B, F. sidsue posit Et recta FH oc bisesat LM in H
dico eadem eandem (si opus productam occurrere ipsi AB ad angulos rectos in G
Nam quia angulus AFB rectus erit AF qu: BF qu= AG: BG. ergo AD. BF AG
et recta FG occurrat ipsi AB ad angulos rectos in G dico eandem (si opus prodactam)
bisecare ipsam LM in H. ANam quia anguli AFG, et _ in G sun recti erit AFqu: BFqu=
AG: BG, adeoque AF: BF = AG. BF,:, AF. BG = L. L FL: FM. Rarsus ob triangula
HKF et AGF, item HiF et BGF similia erit HK: HF = AG: AAF, H item HF: HI = BF. BG
Ergo HK : HI = AG. BF, :, AF: BG. Ergo HK: HI = FL: FM, ac proinde FM. HK=
FL. HI, itaque triangula FHL, et FHM sunt aequalia, et proinde LH= MH. Quod
erat dem.