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FOR THE USE OF STUDents.
DEMONSTRATIVE AND EXPLANATORY,
A SYNOPSIS OF BOOK V. OF EUCLID,
BY NICOLAS VILANT, A. M. F. R. S. ED.
PRINTED FOR BELL & BRADFUTE, J. FAIRBAIRN, AND ARCH. CONSTABLE
IN this fmall Treatife on Mathematical Analyfis, the most general Propofitions ONLY are given; and in the Notes at the bottom of the pages, are pointed out the principal authors to be confulted by ftudents. The whole to page 129, was printed in 1777; but owing to the Author's bad health, &c. it was not until 1783, that the fame with the addition of the quarter sheet from page 129 to page 133 (which fhould have come in after Propofition VII.), was used here as a Text Book. As now published, the Definitions formerly omitted, are placed properly before the Axioms; and in the NOTES Concluding the Analyfis, from page 133 to page 148, are given demonstrations of several propofitions, and corrections of feveral errata in the text; all other errata of confequence, being pointed out in the table following this preface.
Several Corollaries to Propofitions XV. XVII. having been omitted by mistake in the printing, the reader is referred to the truly learned and judicious Mr Baron Maferes Differtation on the Negative Sign, where the reduction of quadratic and cubic equations, &c. is given at great length, and in the most perspicuous and scientific manner,
The fecond Corollary (54) of Propofition XXI. being imperfect as PRINTED, may be corrected in manner following, viz. IN ́EVERY AFFECT
ED EQUATION, THE COEFFICIENTS OF THE INTERMEDIATE TERMS BF
TWEEN THE FIRST AND LAST, COMPREHEND ALWAYS divifors fimple or compound of the last term, in the component parts of their fums and dif ferences,
The rule of intereft (115), as now given (207), is general for all rates PER CENT. PER ANNUM. And the rule of intereft (210), is general also for all rates PER CENT. PER ANNUM, perfectly accurate, and more fimple and easy in appplication, than any rule hitherto given.
The prefent Treatise is an abridgment of part of a comprehensive System of the Elements of Mathematical Analyfis, common and fluxionary, now almost finished.
With regard to the Sign of Inequality, here introduced, the difcrimi nating letters r, s, fhould have been in a smaller character, and placed above the angular point of the fign; or more SPACE fhould have been taken by the printer, to prevent any ambiguity when the fymbols following are r, s or any powers of the fame.