THE RAMSDEN DIVIDING ENGINE. 727 



DECIMAL DIVISION OF THE CIRCLE ADVOCATED IN THE SIXTEENTH 



CENTURY. 



Whatever may have been the origin of the division of the circle 

 into 36(F the system has been condemned from time to time by many 

 eminent mathematicians, among them Stevinns (1548-1020), who, in 

 his "Cosmography" (lib. i, def. 6), states that "the decimal division 

 of the circle (which he contends for) prevailed in Sceculo sapientiJ^* 



Henry Briggs (1556-1630), Oiightred (1574-1660), and Sir Isaac 

 Kewton (1642-1727) constructed large tables of sines, the plan being to 

 divide each degree into 100 minutes of 100 seconds each. 



Dr. Charles Hutton, in the early part of this century, published 

 extensive tables giving real lengths of arcs of various decimal degrees 

 in terms of the radius. Some of the French mathematicians divided 

 the quadrant into 100 degrees and then into decimals of degrees. Wil- 

 liam Crabtree, Gascoigne,t and Jeremiah Horrocks | (1619-1641) pro- 

 jected tables with complete decimal divisions, the whole arc of the 

 circle being divided into 1,000,000 parts. (Philosophical Transactions, 

 vol. XXVII, p. 230.) 



DECI:MAL system frequently used by the HEBREWS. 



I have taken some pains to find, if possible, some trace of the employ- 

 ment of a sexagesimal numerical system by the Hebrews in the meas- 

 urement of straight lines. 



In the description of the city and temple seen by Ezekiel in his vision 

 and described in the fortieth and forty-second chapters, the measuring 

 reed (qana) § of 6 great cubits, corresponding somewhat with our 10-foot 

 rod, is mentioned in ten places. 



The decimal system however was more frequently used than the sexa- 

 gesimal in noting the dimensions of the walls and courts described in 

 these chapters. Thus the number 500 is found three times, 100 eleven 

 times, 90 one time, 70 one time, 60 one time, 50 nine times, 30 two times, 

 25 five times, 20 six times, 10 three times, 5 seven times. It would seem 

 reasonable to assume that in describing an imaginary structure the 



* The decimal method is in all respects comparable with our own and was used by 

 preference in the Assyrian period. In it words and signs were used which were pre- 

 cisely equivalent to our "hundreds" and "thousands." (Sayce and Bosanquet, vol. 

 40, Monthlt/ Notices, Eoyal Astronovncal Society.) 



t Gascoigne is said to have invented a micrometer about 1640. 



t Horrocks observed the first transit of Venus that was carefully noticed November 

 24, o. s. 1639, that predicted by Kepler in 1631 being invisible in Europe. 



§ Ezekiel 40: 3, revised version: "And he brought me thither, and behold there 

 was a man, whose appearance was like the appearance of brass with a line of flax iu 

 his hand, and a measuring reed." Same chapter, verse 5: "And behold, a wall on the 

 outside of the house round about, and in the man's hand a measuring reed of 6 cubits 

 long of a cubit and an handbreadth each ; so he measured the thickness of the building 

 one reed ; and the height one reed." 



