# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/55419/text
# Catalogue record: 55419 — Leibniz an Grandi
# Incipit: Alteras Tuas accepi, qvibus verbum qvod non cogitanti
# Date: 1714-03-14
# Sender: Leibniz — Addressee: Grandi
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=55419&katnr=54726
# The Leibniz-Archiv's transcriptions of the letters of 1714 (pre-edition): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-transkriptionen-1714
# Work: https://leibnizlegible.com/work/DE-611-HS-973069
# Title: LBr. 324 · Grandi
# Folios: Bl. 11v (from the shelfmark LBr 324 Bl. 11v°.12r°/v° (=54725)): 1 page, canvas 22, page ids DE-611-HS-973069:0022 to DE-611-HS-973069:0022
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-973069&page=22
# Lines: 61 recognised on 1 of 1 pages, mean confidence 0.88
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# 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 11v — DE-611-HS-973069:0022
# 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.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-973069/jpgs/default/00000022.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 61 lines, status machine
Viro celeberrimo quidoni Grandio
odefridus Guilietuus Leibnitius S. P. d.
Alteras duas accepi, quibus verbum quod non cogitanti excidit, ex
rei ipsius evidentia explicas. Ego quoque in eadem culpa, 
si qua est fuerim, tua verba in respondendo seculus est. Sed res ipsa liquitur
sinus esse debere radiorum quadratis directe proportionales, ut sint reciproce
proportionales vicibe viribus rndiorum quae Cum vires radiorum ex
distantia sint _ radiorum quadratis recippoce. Vires radiorum
luminis
ut vis radii in curmm ut impressio radiorum in superficiem curvam sit ubigue
aequalis, debere sims esse viribus radiorum reciproce proportionales; et ideo
incidentiae
cum vires sint, reciproce ut quadrata radiorum
sinus fore directe ut quadrata
Rodeo ad figuram huam tantumque pono FH e
adictum itur si radii sint AF AH, AE, Af et HF, FF, elementa curvae ponan
radictum
N tur aequalia inter se; et ex H et F in radios AF, Af agan-
ex constructione,
0
tur normales HL, FL, erunt HfL, ut sinus angu-
pae
lorum AM AFH, AfF, itaque si effectus radiorum ubique
debent esse aequales, erunt sinus FL ut quadrata radio
sed potest esse aequalis ipsi AF, quae voletura
AN pro arbitrio quae sit a, et tentro
erit ded ded = de de +drdr. jam de: dv =Ya
et de: de = rr: aa ex hypothesi, posita deo constante
=rdr: Y(a- ) sit rr= _t fiet rar = t. Ergo fie
se cujus sumatio dependet ab
arcu cirudi sed jam V est arcus circuli Np arcus ciru
sed Cdt: (aa -H) est etiam arcus circuli, cujus ranus a,
dlegantem tnan constructionem deductam apparit.
Unde C, adeoque rr haberi potest absolute
sublata consideratione quadraturae circuli   Unde
simis complinenti est
de de = dodo rr: aa. Ergo deo ded = dudv aa: rr. ita
do eexistente media proportionali inter deo et de. quia
autem deo doo = dede + drdr. Hinc fiet ae
seu
dedr- dodo Y(a ) dudo = drar aarr: a
sinus
batur circumferentia, cujus pelementum interceptum siet
inter AF et AF, vocetur dv, FF elementum
carvae vocetur deo, Radius AF, Y et Cf erit dr,
adio e descri-
circumferensiae
dodvsaa: rr) = d do dv (rr: aa) + drdr
dv = dt: 2Y (aa - H)
e
rum AF. In A tangeate, cor e ad A ponatur Cumatur 
AK
a
olinensio
lui
Xlecans AF Af
in V et V, et
aV
1
A habeturus et angulascui
respondet