# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068195:0163
# Permalink to this reading: https://leibnizlegible.com/page/00068195:0163?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 82r, page id 00068195:0163
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=163
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000163.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.91
# 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.

EX puncto dato in plano perpendicularem ducere ad rectam datam extra planum
sit planum BDF, ex cujus puncto F ducenda ad rectam datam AD pta pl planum perfodientem
in D, rect perpendicularis FL. quia data Ad positione, dabitur D. ergo et FD, et DB in plano verticaliter subjecta
ipsi AD, seu in quam incidunt omnes rectae ad planum perpendiculares ex punctis ipsius Ad demissae, unic norma
B) normatis ipsi D. jungatur
AP. Eritque ob angulos ABP, BPD rectos, angulus quoque APD rectus rg ex puncto l demiss
liter occurrat FB et ex B erigsatur
id planum normalis ipsi DA occurrens in A
Analysis linearis. quia Et Ponata data quaesita ponatur inventa, ergo habita FC
intelligatur lh. perp. ad D)
(ob ang. FLd rectum, et Fd datam) habebitur lD. Ergo ob triangs. FID, lhD similia
habebsitur et lh. Rursus qquia lh ad AP ut B ID ad DA, habebitur ad huc semet
unde habetur aequatio, et proinde FL squaesita
Calculus: A Fd AP aeq. AH + BP BPC DB. FB: FD.
Ergo AP aeq. AB. FD + DB. FB: FD. jam DL aeq. FD - FL
1h
et In aequ  LD. FI. FD aequ. SFD - FL, FL: FD. Rusus Ih aego. SAB. FD + B∞r. eB : FD, SfDF;
quos duos valores aequando, fiet: FL aeg.  TAB. FD + DB. Fp. AD. seu seu fier
FL aequ. F D AP FD. AP: AD. idque potuissemus praexidere et calculum contrahere
nam in tiangs. DAF utique AP in FD aeg. AD in FL. sed ut solis rectis in plano datis
rectas quas per alias possumus explicem
FL aequ. AB. DB+ AB. FB + DB. FB: Ad, sed si brevitatem expressionis quaerammus,
e
quaeratur recta quae sit aq. eB seciamus FD aequ F BB.  B  YFB: AB, et fiet
utamur
FL aeg. FB frrA DB: AD Aliter Fd aeq. DB. FB: q, erit q. aeqBP. et fier.
FL aeg. DB. FB (AB + BP2 seu FLaego FD. + AB + BP: AD quod etiam
jam constabat BP. Anam habebamus FL aeqo FD. AP: AD. Co
Constructio per B ducatur paralleta ipsi. fd, et in ea sumatur BQ aergo. AP. junga–
tur BZ. D recta ex _ per F et alia ex F per  produtatur utounque, et in recta
ep producta si opus, sumaturR
sit solidum coniforne AFF generatum recta Pait+A
est puncto immoso A circa planum FC finmum planum 
 plano sit GG (.
datur punctum B, et magnitudo rectae AB, parpeni
es
dicularis ad planum FBF secans
E. ad quod plasso
planu
similiter datur puncta
in plano GCG et recta AC perp. ad hoc planuis
recansplunum F BF in D. jam
datu ex natura curvae FF, rela–
tione inter BF, BF. Opoaeritur
relatio inter cG, EG. seue natura
curve GG.
CE
CE tG normales ad AC, et BD, BF pormates ad AB.
IL parallita CG, est BM parillela FB
datio FL, et AL per leu praecedens problema datur
et AC, ergo datur B CG. similiter quiadatur
Am et BM dabitur CE  entu