ing been endeavoured, in the Diction, to avoid both Ambiguity, and Superfluity; and in the Operation, to use that Kind of Process, which appeared to be most conducive to render the Solution intelligible, elegant, and concife; but how well this has been performed, must be left to futerior Judgment. In the Divifion and Arrangement of the feveral Solutions, the Author has endeavoured to imitate the Manner he has obferved in the Papers of. the most excellent Mathematician William Jones, Efg.hl 24 bron Thus are Students furnished with a great Number of Examples, applicable to any Book of Theory, fo difpofed, that they may be gradually applied, and by that Means the Learner may be relieved, at proper Intervals, from the Fatigue of going through a whole Syftem of Operations, before he can have fo much as a Glimpse of their Application or Ule; a Difadvantage very common to Books of Theory. Thofe Perfons, also, whofe rapid Genius, carries them, almost as foon as they can solve an Equation, to the fublimer Speculations of Fluxions, Quadratures, &c. will paffibly find here, Something, even in Common Algebra worthy Notice; which they may have hitherto either neglected, or overlooked. And if what is here done, should meet with a favourable Reception, from thofe, who (having duly examined the feveral Parts of Mathematical Learning) are the proper Judges of Performances of this Kind, all the Purposes of this Publication will be answered; and Encouragement thereby given, for the farther Profecution of a Scheme which the Author, and fome of his Mathematical Friends have long fince projected; and which, when accomplished, will be truly (what this is but in Part) The MATHEMATICAL REPOSITORY. January, 1747. ERRATUM. Queft. II. line 2. for 16 read 18. THE MATHEMATICAL REPOSITOR Y. T QUESTION I. WO travellers fet out at the fame time from London and York, whofe diftance is 150 miles; one of them goes S, the other 7 miles a day : In what time will they meet? x = the time of their meeting; 8x= 7 the miles which the first travels; the miles which the fecond travels; (the distance of the two 15 * =150 cities) by queftion: x=10. { QUEST. II. One bought 12 yards of cloth at a certain price; and another time 18 yards thereof at the fame price; at which last time he paid 48 fhillings more than before: What did he pay a yard? QUEST. III. Four men A, B, C, and D, built a fhip, which cost 2607 1. whereof B paid twice as much as A; C paid as much as A and B; and D paid as much as C and B: What did each pay? 1 Whence (the whole fum paid) 11 x=2607 1. by quest. Therefore x=237. QUEST. IV. A charitable lady relieving four poor perfons, gave among them 6s. 8 d. to the fecond she gave, twice; to the third, thrice; and to the fourth, four times as much as to the firft: What did fhe give to each? And (the gave in all) 10 (=6s. 8d.=).80 by question; Therefore x=8. QUEST. V. Four days after a courier, who travels 30 miles a day, had been difpatched, a fecond was fent with orders to overtake him; in order to which, the latter goes 42 miles a day: In what time will he overtake the former ? the days in overtaking; 42 miles the fecond travelled, 30x= But (30X4=) 120 = { be 30x+120 miles the firft travelled in all: 120 12x by fubtraction. |