The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne.
- Title
- The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne.
- Author
- Brown, John, philomath.
- Publication
- London, :: Printed by W.G. for William Fisher ...,
- 1667.
- Rights/Permissions
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- Subject terms
- Mensuration -- Early works to 1800.
- Mathematical instruments -- Early works to 1800.
- Navigation -- Early works to 1800.
- Link to this Item
-
https://name.umdl.umich.edu/A77649.0001.001
- Cite this Item
-
"The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A77649.0001.001. University of Michigan Library Digital Collections. Accessed May 19, 2024.
Contents
- frontispiece
- title page
- To the Reader.
-
The Description and Ʋse of the
Carpenters-Plain-Rule as it is now made. -
The Description and Ʋse of the Line of Numbers, (commonly called
Gun∣ter 's Line.) In Arith∣metick, and Geometry, and Gaging of Vessels, &c.- The definition and description of the Line of Numbers, and Numera∣tion thereon.
-
CHAP. II.
-
PROBLEME.
1. Two numbers being given, to find a third Geometrically propertional unto them, and to three a fourth, and to four a fifth, &c. -
PROB.
2. One number being given to be multi∣plyed by another number given, to find the product. -
PROBLEM
3. Of Division. -
PROB.
4. To three numbers given to find a fourth in a direct proportion, (or the rule of3. direct.) -
PROBL.
5. Three numbers being given to find a fourth in an inversed proportion, (or the back Rule of3. ) -
PROB.
6. To three numbers given to find a fourth in a doubled proportion. -
PROBL.
7. To three numbers given to find a fourth in a triplicated proportion. -
PROB.
8. Betwixt two numbers given to find a mean arithmetically proportional. -
PROB.
9. Betwixt two numbers given to find a mean musically proportional. -
PROB.
10. Betwixt two numbers given to find a mean Geometrically proportional. -
PROB.
11. Betwixt two numbers given to find two means Geometrically proportional. -
PROB.
12. To find the Square root of any number under1000000. -
PROB.
13. To find the Cubique Root of a Number under.
-
PROBLEME.
-
CHAP. III. The Ʋse of the Line of Numbers in measuring any Superficial measure, as Board, Glass, and the like.-
PROB.
1. The breadth of an Oblong superficies given in Foot-measute, to find how much in length makes a Foot. -
PROB.
2. Having the length and breadth of any Superficies given in Foot-measure, to find the content of that Superficies in Foot-measure. -
PROB.
3. Having the breadth and length of an Oblong Superficies given in Inches, to find the content in Inches. -
PROB.
4. Having the breadth and length of an Oblong superficies given in Inches, to find the Content in feet. -
PROB.
5. Having the breadth of an Oblong su∣perficies given in Inches, and the length in Feet and parts, to find the Content in Feet, and such like parts as the length was. -
PROB.
6. Having the breadth in Inches, to find how much makes a Foot in Inch-measure, (that is, how many Inches makes a Foot.) -
PROB.
7. Having the length and breadth of an Oblong superficies, to find the side of a square equal to it. -
PROB.
8. Of a Circle. Having the Diameter of a Circle, to find the side of a square equal to that circle. -
PROB.
9. Having the Circumference of a Cir∣cle, to find the side of a square equal to the same Circle. -
PROB.
10. Having the Diameter to find the Cir∣cumference. -
PROB.
11. Having the Circumference to find the Diameter. -
PROB.
12. To find the side of a square that may be inscribed within a Circle, by having the Diameter. -
PROB.
13. By having the Circumference, to find the side of the inscribed square. -
PROB.
14. Having the Diameter to find the Su∣perficial content of a Circle. -
PROB.
15. Having the Circumference to find the Superficial content of a Circle. -
PROB.
16. Having the content to find the Dia∣meter. -
PROB.
17. Having the content to find the Cir∣cumference. -
PROB.
18. Having the content of a Circle to find the side of a square equal to it. -
PROB.
19. To find the content of a Circle two ways. -
PROB.
20. How to measure a Circle, a Semicircle, or a quarter of a Circle, or any part that goeth to the Centre of the sup∣posed Circle. -
PROBL.
21. How to measure a Triangle. -
PROBL.
22. How to measure a Rhombus, or a Rhomboides. -
PROB.
23. How to measure a Trapezium. -
PROB.
24. How to measure a many-sided irregu∣lar figure or Polygon. -
PROB.
25. How to measure a many sided regular figure, commonly called a regular Po∣lygon. -
PROB.
26. How to reduce Feet into Yards, Ells, or other parts.
-
PROB.
-
CHAP. IV. The use of the line of Numbers in mea∣suring of land by perches, and acres.-
PROB.
1. Having the breadth and length of an oblong Superficies given in perches, to find the content in perches. -
PROB.
2. Having the length and breadth in per∣ches, to find the content in square acres. -
PROB.
3. Having the length and breadth of an Oblong superficies given in Chains, to find the Content in Acres. -
PROB.
4. Having the Base and Perpendicular of a Triangle given in Perches, to find the Content in Acres. -
PROB.
5. Having the perpendicular and base given in chains, to find the content in acres. -
PROB.
6. Having the concent of a Superficies after one kind of perch, to find the con∣tent of the same Superficies according to another kind of perch. -
PROB.
7. Having the Plot of a field with the content in acres, to find the scale by which it was Plotted. -
PROB.
8. Having the length of the Oblong, to find the breadth of the acre.
-
PROB.
-
CHAP. V. The use of the line of numbers in mea∣suring of Solid measure such as Tim∣ber, Stone, or such like Solids.-
PROB.
1. By Foot-measure. A peice ofimber being to be mea∣sured and not just square, how to make it square. -
PROB.
2. Having the side of a square, equal to the base of any Solid given in Foot-measure, to find how much makes a Foot Solid in Foot-measure. -
PROB.
3. To find how much in length makes a Foot, any breadth and depth with∣out squaring. -
PROB.
4. Having the side of a square, equal to the Base of a Solid given, and the length thereof in Foot- measure, to find the content in Feet. -
PROB.
5. Having the length breadth and depth of a Square Solid given in Foot-measure, to find the content in Feet. -
PROB.
6. By Inches, (only) and Feet and Inches. Having the side of a Square, equal to the base of any Solid given in Inches, to find how many Inches in length will make one Foot. -
PROB.
7. Having the breadth and depth of a squared Solid given in inches, to find the length of a Foot in Feet and Inches. -
PROBL.
8. Having the side of the square and the length thereof given in Inch-mea∣measure, to find the content in Feet. -
PROB.
9. Having the side of a Square equal to the base of any solid given in Inch∣measure and the length in Foot-mea∣sure, to find the content in Feet. -
PROB.
10. Having the length, breadth and depth, of a Squared Solid given in Inches, to find the content in Inches. -
PROBL.
11. Having the length, breadth, and depth given in Inches, to find the content in Feet. -
PROB.
12. Having the breadth and depth of a squared solid given in Inches, and the length in Feet, to find the con∣tent.
-
PROB.
-
CHAP. VI. The Use of the Line of Numbers in measuring of Cylinders, by Foot-measure.-
PROB.
1. Having the Diameter of a Cylinder given in Foot-measure, to find the length of a Foot-solid in Foot mea∣sure. -
PROB.
2. Having the circumference given in Foot-measure to find the length of a Foot solid in Foot- measure. -
PROB.
3. Having the Diameter and length of a Cylinder given in Foot-measure, to find the content in Foot- measure. -
PROB.
4. Having the Circumference and length of a Cylinder given in Foot-measure, to find the content in Foot-measure. -
PROB.
5. By Inch-measure. Having the Diameter of a Cylinder given in Inches, to find how many Inches makes a Foot-solid. -
PROB.
6. Having the Circumference given in Inches, to find the length of a Foot-solid. -
PROB.
7. Having the Diameter and length given in Inches to find the content in Inches. -
PROB.
8. Having the Circumference and length given in Inches, to find the content in Inches. -
PROB.
9. By Feet and Inches. Having the Diameter given in Inches and the length in Feet to find the content in Feet. -
PROB.
10. Having the Circumference given in Inches, and the length in Feet-mea∣sure to find the content in Feet. -
PROB.
11. -
PROB.
12. Having the Circumference in Inches, to find the content in the abovesaid measure. -
PROB.
13. How to measure Taper Timber, that is bigger at one end than at the other. -
PROB.
14. To mensure a Cone, such as is a Spire of a Steeple, or the like by having the height and Diameter of Base. -
PROB.
15. To measure a Globe or Sphere arith∣metically.
-
PROB.
-
CHAP. VII. Of Gaging of Vessells. The Use of the Line of Numbers in Gaging of Vessels.- The Art of Gaging all manner of Ves∣sels either close or open.
- Example as before.
- To Gage any round Tun.
- Or else measure it by this Analogy.
- Example.
-
PROB.
1. The true content of aolid measure being known, to find the Gage point of the same measure. -
PROB.
2. To find the equated Dia∣meter two ways first by Arithmetick, as in Problem8 of the second Chapter. -
PROB.
3. Having the mean Diameter, and the longth of a Vessel, to find the content. -
PROB.
4. Having the Diameter and Content, to find the length. -
PROB.
5. Having the length and content, to find the Diameter of a Vessel. -
PROB.
6. Having measured a Vessel according to Wine measure to know what it holds in Ale measure, without knowing the Gage-point. -
PROB.
7. To measure any vessel a more easie way. - To measure a Taper, round Tun by Arithmatick.
-
Example of this way. Diam. Head,
18 Bung,32 length,40 Inches. -
Another way more exact but yet more tedious to work.
Note the foregoing Example. - The use of several Gaging-lines.
- First, for the Diagonal line.
- Example.
- Example.
- The Use of the Rule to find the empti∣ness of Buts, Barrels or Kilderkins.
- Example.
- The use of the Rule for Corn, and for Sea-Cole measures.
- Two Examples of every measure.
- An Instrumental way to find the emp∣tiness of any Vessel, by the Line of Numbers, Close-Cask.
- Example.
-
CHAP. VIII. The use of the line of numbers in Que∣stions that concern Military Orders.-
PROB.
1. Any Number of Souldiers being pro∣pounded, to order them into a Square Battle of Men. -
PROB.
2. Any Number of Souldiers being pro∣pounded, to order them into a double Battle of men: that is, which may have twice as many in ranck as file. -
PROB.
3. Any number of Souldiers being pro∣pounded, to order them into a quadru∣ple batail of men; that is, four times so many in Ranck as File. -
PROB.
4. Any number of Souldiers being given, together with their distances in Rank and File, to order them into a Squareattail of ground. -
PROB.
5. Any number of Souldiers being pro∣pounded to order them in rank and file, according to the reason of any two numbers given.
-
PROB.
-
CHAP. IX. The use of the Line in Questions of Interest and Annuities.-
PROB.
1. A sum of money put out to Use, and the Interest forborn for a certain time, to know what it comes to at the end of that times, counting Interest upon In∣terest at any rate propounded. -
PROB.
2. A sum of money being due at any time to come, to find what it is worth in ready money. -
PROB.
3. A yearly Rent, Pension, or Annuity being forborn for a certain term of years, to find what the Arrears come to at any rate propounded. -
PROB.
4. A yearly Rent or Annuity being pro∣pounded, to find the worth in ready money. -
PROB.
5. A sum of money being propounded, to find what Annuity to continue any number of years, at any rate pro∣pounded, that sum of money will pur∣chase.
-
PROB.
-
CHAP. X. The application of the Line of Num∣bers to use in domestick affairs, as in Coals, Cheese, Butter, and the like. -
CHAP. XI. To measure any Superficies, or Solid by Inches only, (or by Foot-measure) without the help of the line, by Mul∣tiplication of the two sides.
-
An Appendix.
-
CHAP. I. The Description and use of a general and particular Sun-dial made for the Latitude of51. 30. North or the like for any other Lati∣tude. -
CHAP. II. The use of the Dial.-
PROB.
1. How to hold the Dial in time of Ob∣servation. -
PROB.
2. To find the Suns Altitude. -
PROB.
3. To find the perpendicular height of any thing by its shadow, by the line of shadows. -
PROB.
4. The Use of the Quadrat. -
PROB.
5. How to find unaccessable heights by the quadrat at two Observations. - The Ʋse of the Almanack.
-
PROB.
-
CHAP. III. The Description of a Universal Dial, for all Latitudes, from0 to66. 30, of North or South Latitude. -
CHAP. IV. The Description and Use of the NOCTURNAL.
-
- title page
-
The Use of the LINE OF NUMBERS ON A SLIDING-RULE, For the measuring of
Superficial orSolid-measures. - CHAP. 1.
-
CHAP. II. To measure Board or Glass by the Sliding rule, the length and breadth being given. -
CHAP. III. To measure Timber by the Sliding-rule. -
CHAP. IV. The description of the Line of Num∣bers on a Sliding-rule, to measure Solid measure onely, according to Mr.White 's first contrivance, but much augmented byJ. B. -
PROB.
1. A piece of Timber being not square, to make it square. -
PROB.
2. The side of the square given, to find how much makes a foot. -
PROB.
3. The side of the square and length given to find the Content. -
PROB.
4. The square of a small piece of Tim∣ber given, to find how much makes a Foot. -
PROB.
5. Under1 Inch square to find the length of a Foot. -
PROB.
6. A great piece above3 Foot½ square, to find the length of a Foot.
-
PROB.
-
CHAP. V. For round Timber. -
CHAP. VI. To measure Timber, having the Dia∣meter and the length given.
- The TABLE.