With their Application to the SOLUTIONS of a 1 BY BENJAMIN DONN, Teacher of the Mathematics, and Lecturer in experimental Philofophy, Author of the Essays on Arithmetic, Book-keeping, the British The SECOND EDΙΤΙΟΝ. Quicquid in astronomicis, geographicis, vel nauticis, efficiendum, LONDON: Sold by J. JOHNSON, in ST. PAUL'S CHURCH-YARD. M.DCC.LXXV. 1 。 Thorp 2-11-43 46901. TO THE TUTORS IN THE UNIVERSITIES, MASTERS OF ACADEMIES, AND OTHER TEACHERS OF GEOMETRY, IN GREAT-BRITAIN. GENTLEMEN, T is probable that many of you, as well as myself, have found it frequently difficult to initiate young Gentlemen into a necessary Acquaintance with Geometry by the Elements of Euclid, and therefore have wished for a more easy Introduction to that valuable Science, which, at the same time as it facilitated the Attainment of Geometry, might not depart (as many do) too much from the geometrical Spirit of the Ancients, which is so necessary for acquiring a Habit of reasoning with Propriety and Judgement. Such a Treatise, with its Application to Trigonometry, I have now attempted, and beg Leave to offer to the Public, under your Protection; and, if it should be so far approved of, by you, as to be put into the Hands of your Pupils, I flatter myself you will find the Science will be acquired by them in much less Time than is usual, and with greater Eafe to yourselves. If this meets with your Encouragement, it will induce me to pursue my original Design, of presenting the Public with other Essays, for rendering the several Branches of mathematical Literature, both ancient and modern, more pleasant in the Study, and more easily to be attained, than by any other Course, hitherto published, in our Language. Kington, near Taunton, I am, Gentlemen, Your humble Servant, B. DONN. THE PREFACE. IN the general Preface to the Essays on Arithmetic, I published in the Year 1758, the Public were acquainted with our Design of presenting them with a new Course of mathematical Learning, a Thing generally allowed to be much wanted: * For the great and numerous Improvements, which have been made since any Course has been published in the English Language, make a new Course absolutely necessary. For, as those Sciences, with their Improvements, are dispersed in a Multitude of Authors, the young Student knows not how to proceed; and, even to a Master, it is no easy Task to direct: Whereas, if these Sciences are brought into a regular Course, as they depend on each other, the Student will learn with more Eafe, Pleasure, and Dispatch. As * " Mathematical Learning, during the last and present " Centuries, has made a most surprizing Progress; and Truth, "assisted by the uncontroverted Principles of this Science, has "banished hypothetical Chicanery from the Regions of Philo"sophy. It is, therefore, no Wonder that a great Variety of " Authors, defirous of extending so valuable a Branch of Sci"ence, should have written on every Part of mathematical "Learning. But still a Course of Mathematics and Natural" Philosophy, tracing the Science from its first Principles, and " exhibiting the Demonstrations on which each Rule or Problem " is founded, is still wanting; there being none, in our own " Language, that can, with any Show of Justice, be called a " Course of Mathematics and Natural-Philofophy, according " to the modern Improvements, and properly adapted to Learn"ers. This Defect Mr. Donn has undertaken to supply." MONTHLY REVIEW for JULY, 1758. |