NEWTON 25 



'* moment," and the mode of passing to the limit. 

 We quote : — 



* * Demonstratio 



44. **Nam sit o quantitas admodum parva et 

 sunto oz, oy, ox, quantitatum z, y, x, momenta id 

 est incrementa momentanea synchrona. Et si 

 quantitates fluentes jam sunt z, y et x, hae post 

 momentum temporis incrementis suis oz, oy, ox 

 auctae, evadent z-\-oz^ y-\-oy, x-\-ox, quae in 

 aequatione prima prò z^ y Qt x scriptae dant 

 aequationem ... 



'^xx'^ + ^xxox -\- i'^oo — xyy — 2xyy 



— 2xoyy — xoyy — xooyy + aaz = o. 



Minuatur quantitas in infinitum, et neglectis 

 terminis evanescentibus restabit ^xx"^ — xyy — 2xyy 

 -^aaò=:0. O.E.U." 



Translation by John Stewart : 



'' Demonstration 



45. " For let 6» be a very small quantity, and let 

 oz, oy, oxhe the moments, that is the momentaneous 

 synchronal increments of the quantities z, y, x. 

 And if the flowing quantities are just now z, y, x, 

 then after a moment of time, being increased by 

 their increments oz, oy, ox : these quantities shall 

 become z-\-oz, y-\-oy, x-\-ox: which being wrote 

 in the first equation for z, y and x, give this 

 equation . . . 



^xx^ + ^xxox + ,i^oo — xyy — 2xyy 



— 2xoyy — xoyy — xooyy + aaz — o. 



