By John Casey

**Read or Download A Sequel to the First Six Books of the Elements of Euclid, Fifth Edition PDF**

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**Extra resources for A Sequel to the First Six Books of the Elements of Euclid, Fifth Edition**

**Sample text**

KHIB is a quadri later al inscribed in a circle ; . . the L KIH = REA. in like manner, the L KJH = KAB ; . B; but FG il:) e vi dently greater than IJ ; much more is FG greater than AB . Hence AB is the minimum line th at can be drawn through E. 0 . I f i n the foregoing :tig. B A receive a n infinitely small change of position, namely, 13 along BC, and A along AC ; then A SE QUEL TO EUCLID . 40 it is plain the motions or ]3 and A would be the same as if the � ARB got an infinitely small turn round the point K, which remains fixed : on this account the point K is called the centre of instantaneous rotation for the line AB.

J oin JI{, lK, OK, KL. No w, since AE = DB, it is evident that EK = DL. Hence KL is 11 to AB ; . . the L KLO = ADC, an d is consequently a ri ght L ; . ' . K O is the d iam e t e r of the (:) ; . . the L KB O is right, and the L KHI is ri ght ; . . KHIB is a quadri later al inscribed in a circle ; . . the L KIH = REA. in like manner, the L KJH = KAB ; . B; but FG il:) e vi dently greater than IJ ; much more is FG greater than AB . Hence AB is the minimum line th at can be drawn through E. 0 .

On AB ; then, the rectangle AD . DB = area of the D. 36. The sides AB, AC of a D.. are bisected in D, E ; CD, inte rsect in F : pro ve 6 BFC = quadrilateral ADFE . BE 37. If lines be drawn from a fixed point to all the p oints of the circumference of a given 0 , the locus of all their points of bisec tion is a 0 . 38. Show by drawing 11 lines how to construct a D.. = to any given rectilineal figure . 39 . ABCD is a D : show that if B be j oine d to the middle point of CD, and D to the middle point of AB, the joining lines will trisect A C .