Professed and Taught by the AUTHOR. Arithmetick, Geometrie: Aftronomie : In Whole Numbers, and Fractions. Inftrumentally, by Decimal Scales, Napiers Bones: And to extract The Principles thereof Practice, with the Theorical and Practical. and Demonftration. The Description of the Circles of the Sphere. The Ufe of the Globes, Celeftial, and {Terrestrial, To project the Sphere in Plano upon any Circle, Right, or Oblique. And upon thefe Foundations, the following Superftructures. The Ufe of Geometrical Inftruments, in the Practice of Trigonometria : Stone, regular or irregular. Cask, commonly called Gaging. Geodefia, or the Measuring of Land divers ways, and by feveral Inftruments; to draw the Plot of a whole Mannor or Lordship; to caft up the Content thereof; and to beautify the fame with all neceffary Ornaments thereunto belonging. Ravigation: Inftrumentally, by the Sector, Quadrants, Scales, and other Inftruments accommodated with Lines for that purpose. BOOKS IS ARITHMETICK, in Four Parts, Or, the Mathematical Sciences fo methodically gebraical. 8vo. The Ufe of the Line of Proportion, made Eafy, and by it to measure Timber, Stone, Board, Glass, Pavement, Hangings, Wainscote, &c. 120. His COMPLEAT SURVETOR: Teaching the Whole Art of Surveying of Land, by the Plain Table, Theodolite, Circumferentor, and other Inftruments. In Five Books. Folio. His Arithmetical Recreations. 120. as Read by fuch as would attain to a competent proficiency in them by their own Industry. Folio. His RECREATIONS, Numerical, Geometrical, Mechanical, Statical, Aftronomical, Horometrical, Cryptographical, Magnetical, Automatical, Chymical, Hiftorical. Folio. His PANARITHMOLOGIA: A Book of Accounts ready caft up: Being a Mirror for Merchants, a Breviate for Bankers, a Treasure for His Geometrical EXERCISES for young Tradesmen, a Platform for Purchasers or MortgaSea-men. 4to. His Geometrical Dialling. 4to. His Platform for Purchafers, Guide for Buil ders, and Mate for Measurers. 8vo. ' His PANORGANON: Being the Defcription of a Univerfal Quadrant, and the Ufes of it in Geometry, Aftronomy, Dialling, &c. 4to. His Ufe of the GLOBES in Aftronomy and gers, &c. He hath now Preparing, and almost ready for the Prefs, Thefe Pieces following, viz. ography. His ASTROSCOPIUM: Being the De-A TRIGONOMETRIE, Plain and Sphefcription and Ufe of two Hemispheres, Projected upon the Poles of the World. 8vo. His DIALLING, Plain, Concave, Convex, Projective, Reflective and Refractive. Folio. His Second Part of the Rule of Proportion. 120. His CURSUS MATHEMATICUS: A Treatife GEOMETRICAL, of Aftronomie and Geography, wholly defigned for Navigation; wherein that Art will be rendred far more ealy than hitherto it hath been usually Taught or Practised. URANIA PRACTICA Rediviva. ADVERTISEMENT. HE Place of the Author's Refidence is about Ten miles from London Westward, at a Place called Southal, in the Road between Acton and Uxbridge, and Three miles from Brainford: Where he intends to Read the Mathematicks and Inftruct young Gentlemen, and others: And to Board upon reasonable Terms, all fuch as fhall be pleafed to make a more clofe Application to thofe Studies: Where fuch Boarders, and others, (during their time of Refidence with him) fhall have the Ufe of all Books, Maps, Globes, and other Mathematical Inftruments, as are neceffary for their Inftruction, till they provide themselves of fuch as they fhall have occafion for afterwards. You may hear of him, and have an Account of his Terms, and manner of Proceedings: By Mr. Robert Morden, at the Sign of the Atlas in Cornhill, near the Royal Exchange, Globe-maker. Mr. Henry Wyn, at the Sugar-loaf in Chancery-Lane, over against the Rolls, Mathematical Inftrument maker. Mr. John Thornton, near Goodman's Tard in the Minories; Hydographer. Mr. Henhaw, near the Hermitage-Bridge in St. Katherines. Numerical RECREATIONS. CHAP. I. Of Digit, Article, Mixt, Square and Cube Num bers; and fome Obfervations upon them. T O pafs by the Common Species and Rules of Arithmetick, both Vulgar and Decimal, in Whole Numbers and Fractions; as alfo the Extraction of the Square and Cube Roots; fuppofing my Reader to be already acquainted with them; Ifhall proceed to treat of fome other Numerical Practices, wherein the Properties and Pri vileges which fome particular Numbers have over others; as alfo in the refolving of feveral Enigmatical Questions, to recreate the Spirits of the Ingenious Student in the Art of Numbers: And I shall begin with the Nine Digits, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9. I. Of the Digit 1. The Digit 1 hath a Property which no other Number hath besides it felf; for it neither Multiplieth nor Divideth, but leaveth the Number to be fo Multiplied or Divided ftill the fame: As if it were required to Multiply 365 by 1, it will ftill be but 365: Alfo if you were to Divide 365 by 1, the Quotient will be the fame; for i may be had 365 times in 365; and 365 Unites that is multiplied by 1, maketh it no more than 365: And from hence it also followeth, that if any Number be divided by 1, there will nothing remain, whereas Numbers divided by any other Digit are liable to. II. Of the Digit 2. If you would multiply readily any number by the Digit 2, it is but doubling of that number; fo 365 being doubled makes 730, which is equal to the Product of 365 multiplied by 2. Alfo, if you would divide any number by 2, it is but taking the half of that number; fo if 730 were to be divided by 2, the Quotient will be 365, for the half of 730 is 365. - But this Digit number 2 hath another Property or Privilege above any other Digit, Article, or Mixt Number; for there is no other whole Number to be found, which being added to it felf, or mul A multiplied in it felf, that fhall produce the fame number; but 2 added to 2, maketh 4 for the Sum; and 2 multiplied by 2, produceth 4 for the Product, which is alfo the Rectangle or Square of 2. And it is moreover worth the taking notice of, That no Square Number, how large foever, can terminate or end with the Digit 2. III. Of the Digit 3. If you would multiply any number by 3, to the given number add the double thereof, and the Sum fhall be equal to the Product; so 365 multiplied by 3, will be 1095; for the double of 365 is 730, to which 365 being added, the Sum is 1095; and fo much would 365 multiplied by 3 produce. Alfo, to divide any number by 3, take one third part thereof; fo one third part of 1095 is 365, which is equal to the Quotient. And with this Digit 3, no Square Number can terminate. If you would multiply any number by 4, you must double the duplication thereof, and the Sum is the Product; fo the double of 365 is 730, which doubled is 1460, and that is the Product of 365 multiplied 'by 4. -And if you would divide any number by 4, one fourth part thereof is the Quotient; fo one fourth part of 1460 is 365, equal to the Quotient. V. Of the Digit 5. If you would multiply any number by 5, add a Cypher to the given number, then the half of that number will be equal to the Product; fo 365 multiplied by 5, will produce 1825; for if to 365 you add a Cypher, it makes it 3650, the half whereof is 1825, equal to the Product. On the contrary, if you would divide any number by 5, double the number, and cut off the laft figure towards the right hand, (which will always be either a 5 or a Cypher) and the remainder fhall be the Quotient. So if you would divide 1825 by 5, the double of 1825 is 3650, from which cut off the o towards the right hand, and it leaves 365, equal to the Quotient, VI. Of the Digit 6. If you would multiply any number by 6, add a Cypher to the given number, and take the half thereof, to which add the given number, the Sum fhall be equal to the Product of that number multiplied by 6: So if you would multiply 365 by 6, a Cypher added to the given number makes it 3650, the half whereof is 1825, to which 365 added, it makes 2190, equal to the Product of 365 multiplied by 6. On the con trary, To divide any number by 6, take half the number, one third part of that half fhall be the Quotient: So if you would divide 2190 by 6, the half of 2190 is 1095, one third part whereof is 365, equal to the Quotient. I. Obfervation. I Between these two laft mentioned Digits 5 and 6, there is a fecret Property; for if you multiply either of them in themselves, the numbers produced by fuch multiplications fhall terminate in themfelves; fo5 multiplied in 5, produceth 25; and 6 multiplied in 6 produceth 36, terminating in themselves 5 and 6. Alfo, if any greater numbers be multiplied by 5 or 6, they will continually terminate or end in 5 and 6; fo 365 multiplied by 5, produceth 1825, terminating in 5; and 186 multiplied by 6, produceth 1116, terminating in 6. If II. Obfervation. The number 6 hath another eminent Property, for all its aliquot every of the Odd Places, as the I, -- VII. Of the Digit 7. I 6 28 II III 486 IX 8589869056 X 137438691328 you would multiply any number by 7, add a Cypher to the given number, and take the half thereof, to which half add the double of the number given, the Sum of them fhall be the Product of the given number multiplied by 7. So if you would multiply 365 by 7, add a Cypher to it, and it makes 3650, the half whereof is 1825, to which add 730, the double of 365 the given number, and the Sum will be 2555, which is the Product of 365 multiplied by 7. On the con trary, if you would divide any number by 7. Double the number given, and cut off the laft figure to the right hand; then take the feventh part of that number and double it, and fubftract it from the former number, the remainder fhall be the Quotient. So if you would divide 2555 by 7, that,number doubled is 5110, from which cut off the Cypher to the right hand, and it is 511, one feventh part whereof is 73, the double whereof is 146, which fubftracted from 511, the remainder is 365, and that will be the Quotient of 2555 being divided And with this Digit 7, no Square Number can terminate. by 7. A 2 VIII. Of |