# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0459
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0459?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 425, page id 1041163592:0459
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=459
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000459.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.

11
PRINCIDIA MATHEMATICA.
42
Solis. FE ut radius est ad sinum anguli sic inventis ita 2. 25 LLBEn
Cune 2d A quationem ceneri Sccundam, adcendam si summa illa TeRxIOS.
sit minor Temicirculo, subducendam s major. Sic habebitur ejus
Longicudo in ipsis Luminarium Syzrsiis.
Si computatio accuratior delideretur, corrigendus cA lOcus
Lunae in Orbe ut supra inventus per Variationem duplicem. Dc
Variacione Prima et principali diximus Cupra, haec maxima est
in Octancibus Lunxe. Variacio alcera maxima est in Ouadrancibus,
ex oritur 2 raria Solis actione in Orbem Lunxe pro varia politione
Aposxi Lunxe ad Solem, computatur vero in hunc modum.
VE radius ad sinum versum diltancia APogXI LunX a PCrIGXO
Solis in consequentia, ita ansulus quidam P ad quartum propor-
cionalem. Et uc radius ad sinum dictantix Lunx a Solc, ita sum-
ma hujus quarti proxorcionalis et anguli cujusdam alcerius  ad
Variacionem Secundam, (ubducendam si Lunae lumen augetur, 2d-
dendam A diminuitur. Sic habebitur locus verus Lunxe in Orbe,
e per R eductionem loci hujus ad Eclipticam habebitur Y onoi
cudo Lunx. Anguli vero P et O ex Observationibus decermi-
nandi TUnE. Et interca _ PrO angulO P USUTDENEUF 2, ec PFO
angulo  i, non mulcum crrabitur.
Cum Aemosphaera Terrxe ad usque alcirudinem milliarium 35
vel 40 retrinsat lucem Solis, ec retringendo spargat candem in
Ombram Terrae, ec (pargendo lucem in continio Umbrae dilatac
Ombram: ad diametrum Umbrae quae per Parallaxim prodits
addo minutum unum primum in Eclipsibus Lunae, vel minutum
unum cum criente.
Theoria vero Lunxe primo in Sy2ygiis, deinde in Quadraturis,
ec ultimo in Octantibus per Phaenomena examinari ee Babiliri de-
bet. Ec opus hocce aggressurus motus medios Solis de Lunxe ad
cempus meridianum in Obserratorio Regio Grrenovicensi, dic ul-
timo mensis Decembris anni 1700. I. vec. non incommode sc-
quentes adhibebit: nempe motum medium Solis n 2081. 4.3. 40, et
Apogei ejus ∞ 781. 44. 30, ec motum medium Lunx in L5Ec.
20. 00 et Aporai ejus X 88r. 20.00, _ Nodi ascendentis
S 2751. 24. 20; ee differentiam meridianorum Observatorii hu-
us ee Oblerracorii Regii Parisiensis 9hor. 9 min. 20 lec.
PRC