the art of levelling, and a few astronomical problems, with the manner of using Hadley's quadrant and sextant; even here some suggestions will be found that are new and useful. I have now to name another gentleman, who has contributed to render this work more perfect than it would otherwise have been, and it is with pleasure I return my best thanks to Mr. Landman, Professor of Fortification and Artillery to the Royal Academy at Woolwich, for his communications, more particularly for the papers from which the course of practical geometry on the ground was extracted. If the professors of useful sciences would thus liberally co-operate for their advancement, the progress thereof would be rapid and extensive. This course will be found useful not only to the military officer, but would make a useful and entertaining part of every gentleman's education. I found it necessary to abridge the papers Mr. Landman lent me, and leave out the calculations, as the work had already swelled to a larger size than was originally intended, though printed on a page unusually full. The work finishes with a small tract on perspective, and a description of two instruments designed to promote and facilitate the practice of that useful art. It is hoped, that the publication of these will prevent the public from being imposed upon by men, who under the pretence of secresy, enhance the value of their contrivances. I knew an instance where 401. was paid for an instrument inferior to the most ordinary of the kind that are sold in the shops. Some pains have been taken, and no small expence incurred, to offer something to the public superior in construction, and easier in use, than any instrument of the kind that has been hitherto exhibited. I have been anxious and solicitous not to neglect any thing that might be useful to the practitioner, or acceptable to the intelligent. In a work which embraces so many subjects, notwithstanding all the b care that has been taken, many defects may still remain; I shall therefore be obliged to any one who will favour me with such hints or observations, as may tend toward its improvement. A list of the authors I have seen is subjoined to this preface. I beg leave to return my thanks to the following gentlemen for their hints and valuable communications, the Rev. Mr. Hawkins, J. Priestley, Esq. Mr. Gale, Mr. Milne, Dr. Rotherham, Mr. Heywood, Mr. Landman, and Mr. Beck, a very ingenious artist. * As the various authors are cited by name in the work, to save room, the list is now dispensed with in this edition. EDIT. ADVERTISEMENT BY THE EDITOR. IN the two preceding editions of this work, the editor made such corrections and additions, as, he is happy, gratefully, to state, have met with great share of public approbation and encouragement. To this fourth edition, he has further added occasional instrumental and exemplary articles, caused the engraving of the plates to be perfectly repaired, &c. all which, he humbly presumes, will render the work still more deserving of the notice of students and practitioners in the different professional branches of Geometry, Trigonometry, Surveying, Fortification, &c. &c. July 1, 1813. IV. JONES. Just published, by the same Author and Editor, Astronomical and Geographical Essays, in 8vo. with seventeen plates, sixth Edition, price 12s. boards. 169 186 GEOMETRICAL AND GRAPHICAL ESSAY S. NECESSARY DEFINITIONS, and first GEOMETRY originally signified, according to the etymology of the name, the art of measuring the earth; but is now the science that treats of, and considers the properties of magnitude in general. In other words, extension and figure arc the objects of geometry. It is a science, in which human reason has the most ample field, and can go deeper, and with more certainty, than in any other. It is divided into two parts, Theoretical and Practical. By Theoretical geometry considers and treats of first principles abstractedly. Practical geometry applies these considerations to the purposes of life. practical geometry many operations are performed of the utmost importance to society and the arts. "The effects thereof are extended through the principal operations of human skill: it conducts the B |