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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 209r, page id 00067993:0419
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est qradrapla rationis Circuli ad Oradratum. Archimedes quidem, Po-
Irgona Circulo inscribens ec circumscribens, groniam major est in-
Ccripeis e minor circum (criptis, modum octedie, exhibendi limites intra
quos circulos cadac, sire exhibendi appropingrationes: esse Scilicet rati-
onem circumterentia ad diametrum, majorem qramz ad i, seu quam et
2d7; de minorem quam 22 ad 7. Hlanc Mechodu alii sunt prosecuri, Pro-
lemaeus, Vieca, Mecius, Sed maxime Ludolphus Colonientis, qui ostendie
esle circumferenciam uc 3. 24 259265358979323846 ec.
ad diametrum,
ad 1, 00000000000000000000
Verum hujusmodi Appropingrationes, etEi in Geomerria practica
utiles, nihil camen exhibene, qrod menti Paristaciat, aridae veritatis, nis
progretocalium numerorum in infinitum continuandoru reperiatur.
Mulci quidem perfectum Tecragonilmum professi sune, ue Coedinalis
Cusanus, Oroncius Finaeus, solephus Scaliper, Thomas Gephrrander,
ThomasHlobbes, Sed omnes Falso; calculis enim Archimedis relhodio
Ludolphis refellebantur.
Sed qroniam rideo, mulcos non Paris percepisse, quid desidere.
tur: Sciendum est, Petragonismum sire conrertionem circuli in aequa-
le gradracum, aliamre rectilineam fixuram (qrae pendet à ratione
circuli ad gradratum diametri, vel circumferentiae ad diametrum)
posse incellisi gradruplicem, nempe rel per calculum, vel per constru.
ctionem linearem; ucrum q: vel accurate, vel propemodum. Qvadratu-
ram per calculum acCuTaTUM rOCO Analyticam; CaM VerO, qua Per
Constructionem accuracam fC, voco Geomerricam: per calculum
Prope verum, habetur appropinqu acio; per constructionem prope re.
ram, Mechanismus. Appropingracionem longissime produxic Ludol.
phus; Mechanismos corcoios Vieca, Flugenius, aliiqre dedere.
Constructio Geometrica accuraca haberi porest, qua non tantum
Circulum incegrum, sed de gremlibet sectorem sire arcum metiri li
ceac, motu exacto aegre ordinato, sed qri curris cranscendencibus
competati qra per errorem alioqri Mechanicae censentur, cum ta-
men aegre sine Geomecricae, ac vulgares: licet Algebraicae non sint, noc
ad aegrationes Algebraicas, seu certi gradiis, reduci greant; suasenim
proprias, etEi non Algebraicas, camen analycicas habent. Sed icta hic
prodionitate exponi non pollune. Quadracura Analyrica, (Eu quae per
calculum accuracum fic, iterum incres pocest dispelei; in Analyticam
transcendencem, Alsebraicam, ee Arichmericam. Analytica trans-
cendens,