Observationes Cyclometricae by Adam Adamandy Kocha\'nski - Latin text with annotated English translation

TL;DR

This paper provides an annotated Latin-English translation of Kochański's 1685 work, detailing his geometric methods for circle rectification and rational approximations of pi, preserving original layout and notation.

Contribution

It offers a faithful, annotated translation of Kochański's classic paper, including original mathematical notation, tables, and corrections, facilitating historical mathematical study.

Findings

Introduces approximate geometric methods for circle rectification.

Presents rational approximations of pi from the 17th century.

Includes detailed annotations and preservation of original layout.

Abstract

Annotated parallel text in Latin and English of the classic paper of Adam Adamandy Kocha\'nski "Observationes Cyclometricae", published in Acta Eruditorum 4:394--398 (1685), in which he presented approximate geometric method of rectification of the circle, as well as a series of rational approximations of \pi. The included Latin text of Observationes closely follows the original text published in Acta Eruditorum. Punctuation, capitalization, and mathematical notation have been preserved. Several misprints which appeared in the original are also reproduced unchanged, but with a footnote indicating correction. Every effort has been made to preserve the layout of original tables. The translation is as faithful as possible, often literal, and it is mainly intended to be of help to those who wish to study the original Latin text.