Some time ago, I attended a lecture by a prominent computer scientist, a man of Chinese origin, who began with the words, 'Since there are very few Chinese people in the audience, I will give my talk in the universal language of Science: Broken English...'In the 18th Century, the universal language of Science was Latin, and it does no injustice to those (essentially all) scientific writers whose native language was not Latin to note that they probably wrote 'broken Latin' in many cases. For reasons of historical interest and personal curiosity, I have chosen to translate from Latin to English a work by Edward Waring. Can I then represent accurately what would have been found in Waring's English language draft (if one ever existed) by matching my broken Latin to his, with virtually no English language fragments to aid me?' -- from the Translator's forward. Waring's Formulas and Waring's Problems are well known to mathematicians. Those familiar with symmetric functions in algebra will likely know of the English mathematician Edward Waring, who treated this subject in his 1782 book, Meditationes algebraicae.Waring, born in 1734, was appointed Lucasian Professor at Cambridge University at the unusually young ago of twenty-five and was known in his time as a profound and accomplished researcher. However, his writings have been nearly inaccessible because of their numerous typographical and printing errors, corrigenda, and addenda, not to mention his own awkward, obscure, and poorly organized writing style. In the present volume, a translation from the Latin of the third and last edition of Meditationes algebraicae, the translator has produced what amounts to a fourth edition, not only making the work available in English but also incorporating many of the corrections and additions that had appeared separately. The translator has made judicious choices about when to use modern terminology if archaic usage would confuse the reader, and when to retain the original words to preserve the historic flavour of the book. Also included as an appendix is the only critical review of Meditationes ever published, written in 1923 by Franz X Mayer, a Cistercian monk who taught secondary school mathematics in Switzerland. Historians and mathematicians will likely find this volume of great interest.