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A74684 The scales of commerce and trade: ballancing betwixt the buyer and seller, artificer and manufacture, debitor and creditor, the most general questions, artificiall rules, and usefull conclusions incident to traffique: comprehended in two books. The first states the ponderates to equity and custome, all usuall rules, legall bargains and contracts, in wholesale ot [sic] retaile, with factorage, returnes, and exchanges of forraign coyn, of interest-money, both simple and compounded, with solutions from naturall and artificiall arithmetick. The second book treats of geometricall problems and arithmeticall solutions, in dimensions of lines, superficies and bodies, both solid and concave, viz. land, wainscot, hangings, board, timber, stone, gaging of casks, military propositions, merchants accounts by debitor and creditor; architectonice, or the art of building. / By Thomas Willsford Gent. Willsford, Thomas. 1660 (1660) Wing W2876; Thomason E1748_1; Thomason E1748_2; ESTC R209647 103,352 283

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25   1665 Sunday VII July 2 9 16 23 30   1666 Monday VIII August 6 13 20 27   1667 Tuesday IX Septemb. 3 10 17 24 ✚ 1668 Wednesd X October 1 8 15 22 29   1669 Friday XI Novem. 5 12 19 26   1670 Saturday XII Decemb. 3 10 17 24 31 The Tables use explained This Table contains 6 Columes the first hath onely 3 Crosses to signifie those years against them to be greater then the rest being Bissextiles or Leap-years in the next are the years that shall be elapsed since the birth of Ch●ist from 1659 unto the year 1670. In the third Colume are placed the week dayes which begins each year respectively or the first day of January in the fourth and fifth stands the 13 moneths the last column shews the weekdaye in every moneth on which New-years day did fall upon in any of these years EXAMPLE I. It is required to know what day of the week shall be the fourth of December in the year 1659. against which I find Saturd for the first day of the year and likewise the third of Decemb. the next is Sunday the thing desired The Saturdayes in this moneth 1659 are upon 3 10 17 24 31. Saturday concluding both moneth and year and Sunday beginning the year 1660 as in the Table EXAMPLE II. Admit it were required in a Leap-year to know what dayes of any moneth shall be Sunday here you are to observe that in Bisextiles or Intercalary years there is one day added to February which then hath 29. so after that moneth take one from the day found as in the year 1660. the first Sunday in March in October and the last day of December is required New-years day I find to be upon a Sunday and in the Columns of Moneths against March stands 5 which should have been the same day of the week but being February had 29 dayes this year the 4 11 18 25 are the Sundayes in March this year Secondly against October I finde 1 which should have been the same with New-years day in a common year but now the last of September so the 7 day of October shall be the ●●rst Sunday likewise 14 21 28 and from any other number subtract 1. and then for December the last Lords day shall be 30 and the 31 to conclude the year shall be Monday A Gregorian KALENDER Bis New-years day   Moneths Dayes   1659 feria 4 ☿ I January 1 8 15 22 29 ✚ 1660 feria 5 ♃ II February 5 12 19 26   1661 feria 7 ♄ III March 5 12 19 26   1662 feria 1 ☉ IV April 2 9 16 23 30   1663 feria 2 ☽ V May 7 14 21 28 ✚ 1664 feria 3 ♂ VI June 4 11 18 25   1665 feria 5 ♃ VII July 2 9 16 23 30   1666 feria 6 ♀ VIII August 6 13 ●0 27   1667 feria 7 ♄ IX Septemb. 3 10 17 24 ✚ 1668 feria 1 ☉ X October 1 8 15 22 29   1669 feria 3 ♂ XI Novem. 5 12 19 26   1670 ●eria 4 ♀ XII Decemb. 3 10 17 24 31 This Kalendar of 12 years is made for the payment or receit of Money or Merchandizes assign'd upon a prefixt day of the month in Forreign parts to find on what day it will fall upon observe this Table does not essentially differ from the former in construction but in the dayes of the moneths the Reformed Account being 10 dayes before ours so that the 22 day of December according to the Old Style or computation is the first day of January in the New and so all the other moneth precedes our 10 dayes their Septimana or Week-dayes are diversly reckoned but most usually thus viz. Sunday Feria prima Dies Dominica or Dies Solis ☉ Monday Feria secunda or Dies Lunae ☽ Tuesday Feria tertia or Dies Ma t is ♂ Wednesday Feria quarta or Dies Mercurii ☿ Thursday Feria quinta o● Dies Jovis ♃ Friday Feria sexta or Dies Veneris ♀ Saturday Feria septima Sabbath or D●e● Saturni ♄ The f●r●t computation is an Arithmeticall progression from 1 to 7. the other ac●ording to the Planets denoted by their Characters as they are appro●riatod unto those peculiar dayes in other things this Table differs not from the former so I refer the Reader to those 2 Examples THE SECOND BOOK Demonstrating a Sympathetical affection between Arithmetick and Geometry by solution of several Problemes or Propositions of Magnitude with exactness by the assistance of Art and Numbers PROBLEME I. In any right-lin'd Triangle propounded with the Perpendicular and Basis to find the Area or content of it in square Inches Feet Yards Perches c in whole numbers or fractions The Theoreme The superficiall content of any right-lin'd Triangle is half the Square produced in multiplying of the Basis by the Perpendicular Lib. 1. Prop. 16. Trigon IN the Triangle A.C.D. from the Angle at A. let fall a Perpendicular as A. B. upon the Basis or ground-line C.D. This Perpendicular suppose to be measured in inches or feet c. but here in this admit 4 feet and the basis C. D. 5 feet the product of these is 20 square feet the half of this 10 feet superficial content of the Triangle A.C.D. the thing required All right-lin'd multiangular and irregular figures may be reduced into Triangles and thus measur'd a Probleme of great use to the Surveyer PROBLEME II. In all plain right-angled Triangles with either of the two sides known to find the third side from whence with any line how to describe or set out a perfect square for any Plat or Building c. The Theoreme In any lain right angled Triangle given the square made of the Hypothenusal or Subtendant side is equal to the square made of both the containing sides Lib. 1. Prop. 23. Trigon In the last Triangle A.C.D. having let fall a Perpendicular from the Angle at A as the line A. B. making 2 right angled triangles viz. A.B.C. and A. B. D. whereof A.B. is 4. and b. C. is 3. their squares 9 and 16 the summe of them 25. whose quadrat root is 5 as by the demonstration may be explained in the second book pag. 122. the true length of A.C. the Hypothenusal required and the squares of A. B. 16. and B.D. 4. will be 20. wh●●e root will be A.D. as 4 4 9 or 4 47 100. but neither of them exactly true as lib. 2. par 1. examp 5. but to return if the Subtendant side A. C. were known and one of the other two containing sides the third side will be discovered as admit A.C. 5 and A.B. 4. their squares 25. and 16. the difference 9. whose quadrat root is 3. for the side B.C. or if the square of 3 that is 9. were taken from 25. the remainder will be 16. the root 4. for the Perpendicular A.B. In all plain right angled triangles these numbers are onely rational to be found without fractions or their products and quotients