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In the preceding table, each number in the column of fegments is the area of the circular fegment, whofe height, or verfed fine of its half arc, is the number immediately on the left of it, the diameter of the circle being 1, and the whole area 78539816; and therefore all the numbers in the table are to be accounted decimals.

This table is here extended to ten times the length which it had ufually been, the diameter being divided into ten thousand equal parts, inftead of one thousand: And this fize of it alfo allowed me to carry each number out to eight places of figures, inftead of fix; for when the diameter is divided only into one thoufand parts, the proportional part for the figures in the verfed fine, beyond the third, will not give the area true beyond the 6th figure; but in this table it is always found true in the 8th place.

Rule the 9th to the circular fegiment in page 143 explains the use of it; to which it may be only neceffary to add there, when a fegment greater than a femicircle is to be found, fubtract the quotient of its verfed fine, divided by its diameter, from 1; then fubtract the tabular fegment which correfponds to the remainder, from 78539816, the whole tabular circle, and the remainder will be the tabular circle correfponding to the fegment required; and which muft. then be multiplied by the fquare of the diameter..

FINIS.

BOOKS by the fame AUTHOR, lately published.

1. MATHEMATICAL TABLES, containing the Common, Lo giftic, and Hyperbolic Logarithms. Alfo Sines, Tangents, Secants, and Verfed Sines, &c. 8vo. Price 14s in Boards.

2. A SYSTEM OF PRACTICAL ARITHMETIC, AND BOOK. KEEPING, both by Single and Double Entry, for the Ufe of 2s 6d.

Schools.

3. A KEY TO THE ARITHMETIC, containing the Solutions, at full Length, of all the Queftions propofed in the Arithmetic. For the Ufe of Preceptors and others.

4. THE MATHEMATICAL PARTS OF THE LADIES DIARIES. 3 vols. 155.

9s.

5. THE POETICAL PARTS OF THE LADIES DIARIES. 2 vols.

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7. TRACTS, MATHEMATICAL AND PHILOSOPHICAL. 4to. 15s. half bound.

8. THE COMPENDIOUS MEASURER, being a brief, yet com prehenfive Treatife on Menfuration and Practical Geometry; for the Ufe of Schools.

3s 6d.

9. THE PRINCIPLES OF BRIDGES.

28 68.

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