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# Piece: https://leibnizlegible.com/api/records/37355/text
# Catalogue record: 37355 — De methodo tangentium inversa
# Incipit: [Fig.1] Investigatio rectae BD ex datis rectis
# Date: 1673
# Akademie-Ausgabe: AA VII,4 N. 018
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=37355&katnr=Cc2+905
# AA VII,4: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-vii-4
# In the Akademie-Ausgabe: AA VII,4, p. 392 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/VII4A.pdf#page=392
# Work: https://leibnizlegible.com/work/00068097
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 2
# Folios: Bl. 5r (from the shelfmark LH 35, 8, 2 Bl. 5r°): 1 page, canvas 9, page ids 00068097:0009 to 00068097:0009
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068097&page=9
# Lines: 62 recognised on 1 of 1 pages, mean confidence 0.84
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
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## Folio 5r — 00068097:0009
# Source image: https://digitale-sammlungen.gwlb.de/content/00068097/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 62 lines, status machine
de methodo langentium inversa
Investigatio rectae Bd. ex datis rectis AB. et BC.
AB - x. BC = b. BD = y. Ergo CD - 5 15 + b
ZC 7 + b
BL Y
Nunc faciam X quoque intrare aequationem opo  non conideaato.
imnifestum est triaagulum suppositem ipsam ys jum cognitam
esse. Intellis antur autem duae esse y. rectae y. altera
minima, altera in cujus X est 1. seu unitas constructionis
IL- 
DF- 1yt Y
LebD
CD
Y + by DE-
1y+b.
DE C- C D s. Z + b+ 27 - 7-b
altera maxima seu basis, cujus X est altitudo. Unum vocabo . simperater
se s Y +r.
alterum X  Y  V. E7 AE = Z. Z EF= v. EG. data est = β loco BC = b.
Jam H- BE. Ergo HB - B4EF Jam B BG- X- 5 - . hgo HB = XB ∞0 - BV
E
et Fi = EB. xF BGLX. F-3) + EG (. B.) = X -Z. et BI - EF Ergo HI = 1B (x = C ) + EF (1)
Jam  IK = FV = X + X  - 2X Z - 3X + Z - 2β x3
HI
ro -70.
XV - ZV.
=M. 30
sed nunquam hactem X et 9. hcin eandem aequationem convenire voluere.
Ut tangens ad punctum curvae datum ducatur necesse est criangulum quaeri ABD cujus
ulcunque continuati applicatae omnes sint majores applicatis curve demta una sola, quae applicate
Curvae aequalis est. Hujus Trianguli datur bagis. 3d. dantur et omnes applicatae ipsius curvae
dquaeritur altitudo. Contrasi detur altitudo altitudoque figurae, quaere applicatus ie
curvae. Videtur mihri problema istud ex AE datr, vel ex BC datis definite
ipsam Bd. non esse definitum. Videndum ergo quid praeterea essumi possit, ud definiatur, an
vaga assumi possit qua data BC. assumi possit quae libet AX. 1V. g. posito BC. esse applicatas hy-
perbolae an A2. possunt assumi applicatae parabolae. Vel etsi 2b dato BC dato EA non deter-
minetur absolute, an saltem sufficia ipsum determinari relatione quadam ad incognitam
ipsum Y. Quae pro hibitu assumi potest, ut si AB posito = X. BC - b. BD = y. ponatur
AE= y. vel an possit absolute poni v.g. AF= . Quo casu videtur fortasse niminu
supponi, quemadmodum assumtis tantum BC et AB. non satis. ideo AE. exparte assumto, ex parte
ab incognito pendente, vel etiam omnino ab incognito pendente, res facilius exilum sontiri videtur.
videanus primum an AL assumi possit ubsolute, vius = X. fiet BL = X + . , Jan BL BC- 8D.
Ergo BD= Xb +b7. Et BD , X b + b Ergo _ Xb + b + b X cD.
Jam BC = cD? Ergo BC LC = CD.
CD
LC
Ego Xb + 6 4 bX = X + b + b, b. = bx + b + 62
Ergo Xb+b + bX = bx + b + bx. sed quoi
Sed nondum ista satis probant positionem esse possibilem. Hoc
ergo ut appareat clare retexendo examinanda positius est. Positoque
esse Figuram datam Cujus od seu appercata sit Y X 6+ au 
ipsa BC. futura sit -B. et AL = b. idque melhod Targentium
a Cartesia prodita investigari potest. Et vero puto nos
reperturos problema esse definitumr, ac proinde suppositiones
istinsmodi fieri non posse. cum enim demonstraverim
semiquadralum ipsius Bd. Semper aequari summae omnium
BC. inde a vertice. summa autem omnium BC. semper sit eadem
necesseert summam omnium ipsim od. quoa esse desintar.
2a4
Va
a +
e fuor son 2ra fit.