for Gardeners, &c. 9 



AXIOM T. 



§ 6. Things equal to one and the J^me, are equal among ft 

 thcff^fdvi'S* 



Thus the Lines A C, A C, which are equal to A B, 

 are equal alfo between themfclvcs. 



' A X 1 O M IT. 

 If to equal Things one [hall add Things equals all nill lecome 

 equal. 



The Lines A C, A C, are equal. 

 The added C D, C D, are equal. 

 All of them A D, A D, are therefore equal. 

 AXIOM IP. 

 Jf from Things equal one tales equal Things, the Remainder 

 [hall he equal. 



Thus if from the cqml Lines A D, A D. 

 One take the equal Parts AC AC, 

 The remaining Parts C D, C D. 



faall be alfo equal. 



Axiom iv. 



// to Things unequal, one add Tkiugs equal, the r^hole mil he 



unequal. 



If to the unequal Lines D E, D E. 

 One adds the equal Lines A D, A D. 

 The whole A E, A E. 



fha]l be unequal. 



Thefe Axioms may, at firft Light, feem very flrange to a 

 young Learner, who may fuppofe them to be more diffi- 

 cult than they really are ; I Ihall therefore demonftrate 

 them by Lines number'd, which feemsto me the beft Way, 



For the firft 'tis no more, than that the Lines A C, tho* 

 never fo many Times repeated, or tranfpos'd to never fo 

 great a Diftance, as they all appear to be equal to A B, 

 fo they are alfo ever amongft themfelves: For Tnftance, be- 

 ing of fix Foot in Length, they all of them are fo, and equal 

 to the firft A B. The like may be faid of the id and 3d 

 Axiom. 



And for the 4th, nothing is more plain, that if one add 

 an equal Line,or Number of two Foot,to an unequal Line 

 ox Number of five Foot, the Produce muft be (even Foot, 

 which is fiill an unequal Number; and if, as in the 2d and 

 3d, you add or fubftra6l the equal Line, or Number of 

 four, from or to the equal Number of ten, the Product 

 will be the equal Number of fourteen by Additi^rn, or fix 

 by Si3b|lra£tion, 



