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# Catalogue record: 26883 — für Huygens: Specimen Methodi meae de Maximis et Minimis ac Tangentibus omnium absolutissimae, ubi et certa pulchras constructiones inveniendi ratio patet
# Incipit: Sit curva talis, ut sumtis in recta AD seu axe punctis quatuor A,B,C,D
# Date: 1680-02-05
# Sender: Leibniz — Addressee: Huygens
# Akademie-Ausgabe: AA III,3 N. 023
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=26883&katnr=56572
# AA III,3: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-iii/
# Work: https://leibnizlegible.com/work/00068103
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 8
# Folios: Bl. 1 (from the shelfmark LH 35, 8, 8 Bl. 1): 2 pages, canvases 1–2, page ids 00068103:0001 to 00068103:0002
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068103&page=1
# Lines: 119 recognised on 1 of 2 pages, mean confidence 0.85
# 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 1r — 00068103:0001
# Source image: https://digitale-sammlungen.gwlb.de/content/00068103/jpgs/default/00000001.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 119 lines, status machine
Jannar. 1680
ratio patet
sit curva talis, ut sumtis in recta AD seuaxe
punctis quatuor A. B. C. D atque inde ad idem
curvae punctum E eductis rectis AE, BE,CE, DE
quatuor
aternis
sint ta solida ex  ternis quibusque simu
Sumta ae qualia facto ex omnibus quatuve
ad rectani datam G. applicatis;
Quaeritur modus ex puncto E, eduqe
tangentem quaee axi occurrat in T.
abc + abst ach + bcd aequ. abct
seu + a + d +8 aequ. 1.
et
2
e
aqu. 8.
seu rabe t1, ed Bd0.
9
sa
+9  aequ d 4
A Atd  12
et fiet:
 dh  +de + db  da aequ. 0
est autem h aequ. sk C
ergo fiet
l
5)
2Sk
exapus fest dli de db + da aequ. 0
Ph
2h
Ratio cur solis soli a ascrilum - haec est
quia ab E pergendo ad partes A. quoesum
tangens duci debet cescit caeteris HE. CE. BE
crescentibus sola AE decrescit
dit jam AB BF L centum figurae,
punctum aliquod in axe inter B er C. sitque
LF aequ x. FE aequ. y. LBq
est et AL aeqo ABequ. m. BL aequ l.
CL aequ n. CH aequ. p.
fiet:
2)
Notandum probe in aequ. 4. (et ex ea
pendentibus) ubique esse  signum + quia
omnes HE. CE. BE: AE. ad easdem
partes crescunt, sed si fuisset
A in loco A) trans F. tunc scribendum
fuisset. = da in aequ. 4. et - da inaequ. 7
et = 3 item - AF in aequ. 23.
cujus rei ratio ex calculo aequationis 3
manifesta est.
Exemplo hoc usus sum in expli
pub licatione mea Methodi
langentium.
AFaequ   DM et AE B aequa aequ. 3 + X - 2t X +H. et da e qu 2y dy tExdr - 2l dx
BF (9)
X - l et BC2
CF (10) n + X et CF2
HF (1) P+ n + X et HE
20,
2lin
aequ b aequ y + X = 2Ix + P2 et db aequ 2ydyt 2xdx - 2l dx
aeque aqus + X + 2 AX +n et de aequ rydx t exaxt 2n
aequt aequus X + 2 pX +  et dhi aeqo rydus tdx + 2ndx
2pr
jam pro du scribamus y, et pro dx scribamus T aequ. TF
et ex aequ. 7. fiet seqens:
(17)
2CF, +
BF, 
2AF, +
2 a+ Exton+ ipt W+ Ext+nt, 2y+ 2Xt _ 2lt = 2 + 2Xt - 2I+ )
vel
v2y
53
c
L
43
HC+EF + BF, AF
21)
aequ. t.
seu taqo
eccccecece a
2m equ. 0
abetabt ac
BI
abeHF+ absCF a  BFABeti AF
est autem t quantitas negativa, quia EF non ducitur versus
eas partes, unde crescunt rectae adhibitae, sed versus contrarias
aeterum hic notandum non opus fuisse ut adhiberemus punnctum L. et literam X. satis est ad hiberi
(25
HF. CF. BF AF. quia d HF, dCF. dBF. dAF. aequ. dx. calculus talis erat
a aequ Y + AF. Ergo d a aequ 2y dy + 2AF dx. Eodem modo. Ab aequ. 2y dy + 2BF dx. d eequ. 2ydy + , (F dx
denique de dhi ago 1ydy + 2DF d unde nascitur denique aequatio 22 vel 23.
((25)L. y + 8 yt 8y+ 27
Constructio autem clegans ex hoc calculo duci potest, loco aequationis 23. scribatur: t qu
Exhibeantur octosrece prina
retu quarum V.
sit ad
1 Secunda) tertia (quarta(quinta sexta) septimas Utava
in ratione triplicata...
HE
sit ad
7 PE+ B C D BF, BAF
... A CF BF (AF Eris TF ad FE ut summa quatuor
.....- sin rat. tripl..-
1.-
Gad
CE BE AE HE (CE (BE (AE
u
rectarum priorum, ad summam
quatuor rectarum posteriorum.
hiaec constructio talis est
meliorem ex datis inveniri
Poese n’on putem. Rethdo S vix aliquot dierum labore inverietur ac sortase ne vix quidem.
Specimen Methodi meae de Maximis et Minimis ac Tangentibus omnium
ct absolutissimae, ubi et certa pulchras constructiones inventendi

## Folio 1v — 00068103:0002
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