# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1066518432:0302
# Permalink to this reading: https://leibnizlegible.com/page/1066518432:0302?run=74
# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 274, page id 1066518432:0302
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1066518432&page=302
# Source image: https://digitale-sammlungen.gwlb.de/content/1066518432/jpgs/default/00000302.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.90
# 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.

274 DF V FRLBOS ET MIOTIBOS CORDORDM. L IB. II.
sregatum _ differentia CurVa AC ex ejus abscirsae vel lagiEX AI,
dati SInE. IdCirCO, (I AIAE UE 2MI~ seu 2AT ad AC + AI Ita AC = AT
ad quartam magnitudinem , deinde ut subtangens log-micxe cu-
juscunque ad log. mum rationis AC + AI ad AC = AI in hac l09a-
rithmica, ita magnitudo rel linea O ad aliam R, haec linca, juxta
Drxecedens corollarium, dabit ordinatam CL noltrxe relariae AC.
C OR OL L A R I u M TII.
474. Puxta 5. Tr0. erit media directio impresionis renti Alum
CAC instantis in aXC AW, nam haec media directio angulum à
tangentibus relariae ductis per puncta C, C ad utramque axIs PaI-
tem similicer lita contentum, bitariam dividie, quod etiam axis AW
Praeltat; cAque adco (5. L1O.) impressio renti in relaria, juxta ejus
mediam dircetionem W A, ad cenacitarem relariae in omnibus ejus
punctis eandem, sicut dupla Ar ad As, id eA, ut Cupra (9. 473.)
trabuimus, SICNE + AM. Ma ad AM L Ma, id eAt, SICuE + AC. AI
ad AO + AP. Onde, quia tenacitas relariae (num. T. 5. 4.7T.) eAt
V2. AB = (AC = AP: 2AT). V2, erit impressio renti in relariam
juxta ejus mediam directionem W A =V.. 2AC. (AC. - AV):
AC2 + AI
C OR OE L A R F U M TV.
475. Velariae rero aequatio differentialis ex allata constructione
Facillime elicietur; nam (I dicantur BA, a; AL, X; CL, γ; Cf,
dx; cF, dy; CC = CC = d5; Fh = dda, erit c0 =d,: ds, e anal0-
sia, in quam Lupra (num. L. 5. 47T.) incidimus ce vel di: ds ad Fh
seu adx ut AB rel a ad Cic seu ds; quae, multiplicatis extremis
e mediis, dabit aequationem relarixe differentio differentialem d, =
adsada, in quam Celeberrimi Bernoullii etiam inciderunt, ut vide-.
re licet in Acc: Frudit. Lipl. 2695. Pa5. 546.
A quatio differentialis relarix elicitur ex similitudine triangulo-
rUM ABMI XE MImu; esF enim ma: NIa = AMI: AB; unde quoniam
AB = a, Ho == AI = ∞, atque adeo AM = V (2a∞ F ∞X), mi = d ∞ e
M_ = CF =dy; exit dy = adx: V (2 ax + e_) prima requatio differen-
tialis primi gradus, naturam relaria explicans.
Sin vero BM vel WL FUCrIE =X, tUINC CFIE AM =V (∞X -aa), de
2y= ada: V (XX = a4), quae eAt altera relarix aequatio difterentialis.
ot