# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068129:0026
# Permalink to this reading: https://leibnizlegible.com/page/00068129:0026?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 5
# Folio 13v, page id 00068129:0026
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 12r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068129&page=26
# Source image: https://digitale-sammlungen.gwlb.de/content/00068129/jpgs/default/00000026.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.92
# 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.

(13)
(7) si spatia percursa sint ut Legarithmi sinum (A V, arculen
quae
sinuum (KV, arcuum BK) tempora insumta sunt ut logarithmi
rationum, sinum complementi (BY, et (VM) complementum ejus ad
(BD) diametrum seu duplum situm sinug totiu  (AB). patet ex
collatis propositionibus 4 et 6.
Artic. VI. Si grave projiciatur in medio uniforui resisten-
tiam habente abrespectivam, seu feratur mota ui compo-
grammo MASF
E13 inveniri potest linea projectionis (seu relationiter AS et AM)
Ex _ spatio AS datur (per artic. 5. prop. 6.) velocitas descendendi  p
se ins seu in p. Ex hac =(per prop. 7) datur tempus insumtum
Ex hoc (per artic. 4. prop. 3slatur spatium AM seu SP. Ex datis
igitur linea e abscissis A5 dantur ordinatae sp. ac proinde
lineae puncta inveniri possunt.
E2) inveniri potest lineae tangens seu motilis in ea directio. In AA
frimatur Ma quae sit ad MP ut velocitas in M inventa per tempro
insumtum Cartic. 4. prop. 4) ad velocitatem in S inventam per idei
tempus (artic. 5. prop. 4) et juncta NP  tanget curvam in
puncto P.. Et cum eadem sit velocitas descendendi in  quae in S
ilemque directionem projectionis per sequendi in P quae in M. pat et
etiam quam qualis illa sit in puncto D. patet etium qua vi arobile
in ipsa s linea projectionis feratur, velocitas enim est ad relocitatee
 enim in linea est ad veloritatem descensus ut  NP ad MP.
Pas Multa otri possent praxi accommodata sed nobis
fundamenta Geometrica hic jecisse satis erit, inq qu maxima
consistit difficultas. Possemus etiam in unum componere resistentiam
absolutam eires ex articulis +∞ c. 2. 3. et respectivam ex artici
4. 5. 6. sed prolixitas hic vitanda est, et sane in aere resistentia abso
luta minis considerabilis videtur quam respectiva.
locus motus compositi P habetur completo parallelo- Plondellus in libro de jactu Bomborum, putat impne posse negligsi tpi considerationemm p
sito ex motibus duorum articulorum praecedentium. Sit prjectio
Sitfig. 3) projectio in AM et parallalis, descensus in AS et purallalis, angulo MAS quocunque
demeura quadan
Etrmin im
ini his actis dedimus
autr
esonnia enim nes pondent
nostrae analysi infinitorum
seu calculo differential
se summatorio communie
quoat livt verbis expros
ai
Et sans altente considerantu quae
hic attulimus novas fortasse via
quasdam apernisse videbimurt
sua .  s) =  sar i
al x au vB = v. 1)
catis antea impeditas
sotassis
Futi certe revera
concurrunt in
tura
noves vel certe