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# Piece: https://leibnizlegible.com/api/records/17927/text
# Catalogue record: 17927 — Johann Bernoulli an De Volder: Auszug aus Bernoullis Brief an de Volder vom 13. Februar 1700
# Incipit: Demonstrabo vires per quas corpus ascendit ad certam altitudinem uno s
# Date: 1700-04-17
# Sender: Bernoulli, Joh. — Addressee: Volder
# Akademie-Ausgabe: AA III,8 N. 159
# Other printings: -Pertz 3 (Gerhardt, Math.Schr) 3,2, 1856, S.629-630; --Orio de Miguel: Obras 16A, 2011, S.609-610 (span.Übers.); -Lodge: Leibniz-De Volder, Correspondence, 2013, S.172-175 (tlw., mit engl.Übers.) -Leibniz. Matemática-Física-Metafísica, hrsg. von B. Orio de Miguel, Madrid 2025, S. 305-306 (span.)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=17927&katnr=30337
# AA III,8: 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-iii-8
# In the Akademie-Ausgabe: AA III,8, p. 492 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdIII8.pdf#nameddest=159
# Work: https://leibnizlegible.com/work/DE-611-HS-3653099
# Title: LBr. 57, 2 · Bernoulli, Joh.
# Folios: Bl. 8 (from the shelfmark LBr 57, 2 Bl. 8): 2 pages, canvases 15–16, page ids DE-611-HS-3653099:0015 to DE-611-HS-3653099:0016
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-3653099&page=15
# Lines: 55 recognised on 2 of 2 pages, mean confidence 0.93
# 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.
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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 8r — DE-611-HS-3653099:0015
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-3653099/jpgs/default/00000015.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
Excerpla exlitterit ad e volderu eparalia d. . -. 1700
Demonitrato viret pquas corpus arcendit ad certatu altitudinem uno
saltu esce aequales viribus ejundem corporis 4 impultionibers ierum
quitii
desendentis oemque vim suam, quam siagulii impultionibus impendentis
in teationem elartii; id eit aequales esce viribus _ clachorum hoq
modo tentorum: Conamus corpus cum ascendere incipit habere
duos gradus velocitatis, quandoquedem itaque velocilatet sunt in
subdaplicata ratione altitudinut de quo mecum convenis, et
cum ex hypotheti elastia illa quatuor quarta parte altitudinis
totuus inter se dictent, patam est corpus ad singula elactra appel
lere uno celeritatis gradu, eaqe Leadere hoc toto celeritaris gra
du consunto: digitur solua jam probandum incumibit mihi, ut
ortendam (nulla nunc atteatione facta ad gravitatem) corpus illud
quod ut perferte durum concipio, re in elarticis tantum idva
lere putes) 2 gradibus velocitatis motum lendere posse pracise
quaruor talia elaltia, ad qua singula seortum tendenda unus
celocitatis grodus in corpore illo hegrit: Nam finge corsus
Cincurrere oblique in elattium L velocitate CL ut 2. angulo
inclinationis Ct pecirtente 30. Grad.
cujus nempe sinui CF eit semroscis
radio CL. Jam quid fiet port
incursum corpolis C in elattium
L, sane quonam motus per CL
componitur ex duobus collateralibus
per CP et PL, et cum CP seundum
quam corpus direrte impragit in
elastium L, exprimat dimidiata
celeritatem corporis per CL, consumetim hic motus per Ct tento eta
Hro (perinde enim estet ar si corpus C celeritate CP perpendiculariter
incurreret in elactium, quod per hypothesia eam destrcere potert) re
manente corporis celeritate et directione PL, produrta igitur PL in Mi
ita ut LM sit = PL = V3 (ponitm enia CL =2) et applicato in Mi
alio simili elattio facieate cum LM anculum LMZ, cujus sinus LQ
sit = CD =1; per eandem rationem manifertum eit, corpus C port tentio
nem elattis L tendere elattium Mamisto motu per L9, et servato motus qn
8

## Folio 8v — DE-611-HS-3653099:0016
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-3653099/jpgs/default/00000016.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 18 lines, status machine
prolongata itaque 2M ad Nut fiat M N = M = sa, iliique substituto
elartio constituente cum mx angulum MNR semi rectum, quosc.
MR iterum sit = CP = 1; patet similiter motum per Ma totum
impendi in tensionem elattio K; corpore iateria moveri pergente
directione et celeritate RN = 1; denique si hac celeritate resideu
impingat perpendiculariter in elathum c; huic flertendo totam
suam vim reliquam dabit. Hine ita pramistis argumentor
lunc in modum: Potentia corporis C tanta est ut per se solum
nullo aupilio nec gravitatis nec alterius rei adjutum lendere
possit praecise qualuor elartia talia ad quae singula sevicum ten
denda reguipitur ut corpus dendat ex quarta parte altitudiris
ejus ad quat corpur sua celeritate initiali assurgere porect.
alqui eadem illa potentia tanta eit ut corpus assurgatuno
saltu ad totam altitudinem; Ergo ad ascendendum uno sallu
tanta potentia seu
tanta veres impenduntur quantae in leationem 4ela
etiorum in deceau corporis. Q. E. et
an