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THE

DOCTRINE OF PROPORTION

CLEARLY DEVELOPED,

ON A COMPREHENSIVE, ORIGINAL, AND
VERY EASY SYSTEM;

OR,

THE FIFTH BOOK OF EUCLID

SIMPLIFIED.

BY

OLIVER BYRNE,

PROFESSOR OF MATHEMATICS, COLLEGE FOR CIVIL ENGINEERS; CONSULTING
ACTUARY TO THE PHILANTHROPIC LIFE ASSURANCE SOCIETY.

AUTHOR OF

THE NEW AND IMPROVED SYSTEM OF LOGARITHMS;" "THE PRACTICAL, COMPLETE,
AND CORRECT GAGER;" "A TREATISe on spherICAL TRIGONOMETRY ;'
ELEMENTS OF EUCLID, BY COLOURS;" "HOW TO MEASURE THE
LENGTH OF A DEGREE ON THE EARTH'S SURFACE, WITH
THE ASSISTANCE OF RAILROADS;" ETC., ETC.

"THE

INVENTOR OF

"THE GAGER'S PATENT CALCULATING INSTRUMENTS;" "THE SYSTEM OF FACILITATING THE
ACQUIREMENT OF GEOMETRY, AND OTHER LINEAL ARTS AND SCIENCES,
BY COLOURED DIAGRAMS;" ETC., ETC., ETC.

no
London:

J. WILLIAMS, LIBRARY OF ARTS,

No. 106, GREAT RUSSELL STREET, BLOOMSBURY.

MDCCCXLI.

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