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# Piece: https://leibnizlegible.com/api/records/54543/text
# Catalogue record: 54543 — [Problema Buotii: Tentamen tertium]
# Incipit: Sunto segmenta [T.1] Nunc angulorum [T.2] Altitudines: [T.3]...
# Date: 1672
# Akademie-Ausgabe: AA VII,1 N. 005
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=54543&katnr=Cc2+534%2FB
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00067993
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folios: Bl. 164r (from the shelfmark LH 35, 2, 1 Bl. 164r°.165r°.163v°+176r°oben.163r°.163v°+176r°unten.165v°): 1 page, canvas 329, page ids 00067993:0329 to 00067993:0329
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=329
# Lines: 63 recognised on 1 of 1 pages, mean confidence 0.86
# 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.
# 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.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 164r — 00067993:0329
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000329.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 63 lines, status machine
Suito pegmenta A. B. C.
perpendicularis ex puncto quaesito demissa D.
seu distantia line puncti quaesoti a linea data
segmenta lineae per perpendicularem: E. et F.
sunt autem E + F. = A+B. + C.)
Recta ex puncto, anguli in alteram extremitatem ducta est
RG EE + DD.
et in alteram est Rq. FF. + DD. vel i
Restant duae rectae in mediae. Quod si perpendicularis
D. cadit in segmentum primum A. sumatur differentia
inter qua 2 excedit A excedit E seu A= E. hujus
quadratu addatur DD. summae radio erit linea media
prima seu linea 2da Erit ergo hoc casum linea
Ida RC A= E. 4. + DD., Et linea tertia, erit (qF-BtC, + DD, Rq. A. q A- Et B,, + DD n Rq
A -E + B,, + DD,  Quod si perpendiculais D.
cadit in segmentum secundum seu Lineam mediam Erit E.
major quam A. Et proinde  E = A+ DD. 3. Rg. erd linea
Ida Et linea 3tia erit F - C,, + DD. n, R4. Quodsi
perpendicularis D. cadit in segmentum tertium, muta,
tautum terminos primi casus A in C. et E in F. Erit
+ erit C = FAM. et M = C- F. Seu F = F - N
linea gdac - ~ + dd , rq. et linea 3tia 4 qc -F + B,, + DD. n Rg.
N et angulos determinemus quos aequales esse debere
suppositum est, denique perpendiculanis etiam cadere potest
in quatuor extrema, si cadit in primum, nulla est linea
E. et sola restat F. et D. est linea prima; si cadit
in posrem um nulla est linea . et = 1 F et D. est p ipsi
postrema, sicadit in Z punctum secundum linea 2da est d.
si in tertium tertia est d.
Sed screndo est impossibile
esse ut cadat perpendcntaris in aliquod punctorum, quia
ex eodem puncto ad eandem rectam non potest duci nisi
una perpendicularis, cum
Linea prima seq EE + DD, 2
Linea 2da
decq. + dd, Bq
D+ pA
E+F, =8 A1B+C.
A(F~AB. C)
Linea prima D. siperp. cadit in punctu L.
si
CEt DD, A9. si per p cadi
 
emuta utum
Linea IIda FE, DD, rg. Ni perp adit inp. 1.
2
Aline prima A= _ + G et G= A = E seu E-)
+ A + H = E seu A = E - A seu A = E, L
ant
in. II.
2D AA + DD, rg
A- E,9 + dd, r9. sinsegmi1.
sim p. 2.
IV.
A+Oq. + 3d, r4 ArB+C. FF + DD rq
F. CF, 9. +D.
BB+Dd, rg.
L 1d
E- A 9., A DD. r9. sin Segn 2. F. C, 4. 4 dd. r9.
BB+ DD. rq si in p. 3. D
 B+Cq, +DB, si mnp. +. CC = BV, 19.
 E-A9, + DB Bq. Si i segm. 3. C- Fq +DB, 19
(5 = A. 4 C.)