! THE- COMPLETE MEASURER: OR, THЕ Whole Art of Measuring. IN TWO PARTS. The First PART teaching And also the Multiplication of Feet and Inches, commonly The Second PART teaching to And fome Practical QUESTIONS. The Fourteenth EDITION. To which is added, By WILLIAM HAWNEY, Philomath. LONDON: Printed for J. and F. RIVINGTON, L. HAWES and I Have perused this BOOK, and recommend it to the Publick as a very useful One. Lately published, the Second Edition of The Doctrine of PLAIN and SPHERICAL TRIGONOMETRY; with its Use in various Branches of the MATHEMATICKS. By W. Hawney, Author of this Book. Also, The Eighth Edition of Pardie's Short but yet Plain ELEMENTS of GEOMETRY; shewing by a brief and easy Method how most of what is Necessary and Useful in this Science, may be understood. Translated by the above-mentioned Dr. Harris, and referred to in the Preface of this Book. THE PREFACE. i H AVING perused several Books concerning the Mensuration of Superficies and Solids, and the Works of Artificers relating to Building; but not finding any one Book so perfect, as to give any tolerable Satisfaction to a Learner; and I having practised and taught Measuring for several Years, and thereby gained Experience and Knowledge in that Art, having learned some Things from one Author, and some Things from another, I began to think of digefting my Thoughts into some such Method as might give a Learner full Satisfaction, without being at the Charge of buying so many Books; and being importuned thereunto by some Friends, I fell to work, and at laft brought them to that Perfection you here find in the following Work. 1. As to the Decimal Arithmetick, I have been as plain as the Matter would well bear, to make it plain. 2. As to the Multiplying of Feet and Inches, commonly called Cross Multiplication, my Method differs from that which is usually taught in other Authors, as being (I think) much shorter and plainer. 3. In measuring of Superficies and Solids, I have given the Demonftration of the Rules, which I thought might be very acceptable to the Ingenious; for, indeed, I always look upon the Writing of a Rule without a Demonstration (in any Part of the Mathematicks) to be but lame and defective; and for want of knowing the Reafon of the Rule, a Learner may commit great Errors; befides, when a Learner knows the Reason of the Rules, he may retain them better in his Memory. The Rule for measuring a Prismoid and Cylindroid, I had out of Mr. Everard's Art of Gauging; but the Reason he does not shew, neither have I found it in any other Author; but that the Method is true, I have endeavoured to make plain. The Demonstration of the Rules for finding the Area of an Ellipfis and Parabola; also the Demonstration of the Rules for finding the solid Content of the Frustum of a Cone and Pyramid, the Solidity of a Globe of a Spheroid, a Parabolic Conoid, and of a Parabolic Spindle, and their Fruftums, I had from the ingenious Mr. Ward's Young Mathematician's Guide; where the curious and ingenious Reader may see many other Demonstrations algebraically performed. I have also demonstrated the Rule for finding the Solidity of a Globe, out of Pardie's Elements of Geometry (Book the 5th, Art. the 33d) published in English with many Additions, F Additions, by the Reverend Dr. Harris, F. R. S and the fame is also done out of Sturmius's Mathesis Enucleata; so that the ingenious Reader may ufe which of those Ways he likes beft. : The Scale supposed to be ufed in all the Operations, is the Line of Numbers, commonly called Gunter's Line, which is upon the ordinary TwoFeet or Eighteen-Inch Rules, commonly used by the Carpenters, Masons, &c. because I thought it needless, as well as impertinent, to write the Use of Sliding-Rules, or any other particular Scales, they being sufficiently treated of by several Authors; viz. by the above-named Mr. Everard, in his Art of Gauging above-mentioned, where you have the Use of a Sliding-Rule in Arithmetick, Geometry, in Measuring of Superficies and Solids, Gauging, &c. Likewise Mr. Hunt has written largely of the Uses of his Sliding-Rule, in Arithmetick, Geometry, Trigonometry, Gauging, Dialling, &c. There are several others who have explained the Use of their own Rules; so that the more curious Readers may find full Satisfaction in those Authors. One Thing I have omitted in the Book, which I think may not be very improperly inserted in this Place; that is, how to find a Number upon the Line. If the Number you would find confiftsonly of Units, then the Figures upon the Line represent the Number sought: Thus, if the Number be 1, 2, 3, &c. then 1, 2, 3, &c. upon the Line, represents the Number fought. But if the Number confifts of two Figures, that is, of Units and Tens, then the Figure upon the Rule stands for |