|Author:||Leybourn, William, 1626-1700?|
|Title:||The line of proportion or numbers, commonly called Gunters line, made easie by the which may be measured all manner of superficies and solids, as board, glass, pavement, timber, stone, &c. : also, how to perform the same by a line of equal parts ... : whereunto is added, the use of the line of proportion improved ... / by William Leybourn.|
|Publication info:||Ann Arbor, Michigan: University of Michigan, Digital Library Production Service
2011 April (TCP phase 2)
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The line of proportion or numbers, commonly called Gunters line, made easie by the which may be measured all manner of superficies and solids, as board, glass, pavement, timber, stone, &c. : also, how to perform the same by a line of equal parts ... : whereunto is added, the use of the line of proportion improved ... / by William Leybourn.
Leybourn, William, 1626-1700?
London: Printed by J.S. for G. Sawbridge ..., 1667.
First ed. Cf. BM.
Reproduction of original in British Library.
Mathematical instruments -- Early works to 1800.
Mensuration -- Early works to 1800.
license to print
TO THE READER.
How to Measure Board and Timber BY THE Carpenters PLAIN RULE.
I. Of the FORE-SIDE.
II. Of the BACK-SIDE.
I. Of the Fore-side, or Side of Inches.
II. Of the Backside.
I. Of the Line of Board-measure.
PROB. 1. The breadth of any Board being given, to finde how much there∣of in length will make a Foot square.
PROB. 2. The length and breadth of a Super∣ficies being given, to finde how many Square Feet are therein contained?
II. Of the Line of Timber-measure.
PROBL. 1. The Square of any piece of Timber at the end thereof being given, to finde how much of that piece in length shall make a Foot solid?
Concerning the Tables at the be∣ginning of the Lines of Board and Timber-Measure.
instruction to printer
THE Line of Proportion (or Numbers,) Commonly called Gunters Line; Made Easie.
CHAP. I. NUMERATION upon the Line.
PROP. I. A whole number consisting of two, three, or four places, being given; to finde the point upon the Line, which representeth the same:
PROP. 2. Having two numbers given, to finde as many more as, you please, which shall be in continual proportion one to the other, as the two numbers given were.
CHAP. II. MULTIPLICATION by the Line.
CHAP. III. DIVISION by the Line.
CHAP. IV. The GOLDEN-RULE Direct by the Line.
CHAP. V. The GOLDEN-RULE Reverse by the Line.
CHAP. VI. Of DUPLICATE PRO∣PORTION by the Line.
1. Of the proportion of LINES to SUPERFICIES.
II. Of the Proportion of SUPER∣FICIES to LINES.
CHAP. VII. OF TRIPLICATE PRO∣POTION by the Line.
1. Of the Proportion between LINES and SOLIDS
II. Of the proportion of SOLIDS to LINES.
CHAP. VIII. The Extraction of the SQARE-ROOT By the Line.
CHAP. IX. The Extraction of the CƲBE-ROOT By the Line.
CHAP. X. The Use of the Line, applied to SUPERFICIAL-MEASURE, Such as Board, Glass, Wainscot, Pavement, Hangings, Paintings, &c. of what kind soever.
I. Examples in Inch-Measure only.
II. Examples in Foot-Measure only.
CHAP. XI. OF YARD-MEASƲRE By the Line.
PROBLEM. The length and breadth of any Su∣perficies being given in Feet, in finde the content thereof in Yards.
CHAP. XII. OF LAND-MEASƲRE By the Line.
CHAP. XIII. Of the Mensuration of divers Regular SUPERFICIAL-FIGƲRES by the Line.
I. Of the Circle.
CHAP. XIV. II. Of the Triangle.
III. Of the Trapezia.
IIII. Of Regular Figures of 5, 6, 8, 10, or 20 equal sides.
CHAP. XV. The Use of the Line applied to SOLID-MEASƲRE Such as Timber, Stone, &c.
1. In Inch-Measure only.
II. In Foot-Measure only.
CHAP. XVI. How to measure Stone or Timber by the Line, by having the Square of the Base, and the Length of the Piece given, both in Foot and Inch Mea∣sure.
CHAP. XVII. Concerning Timber that is bigger at one end than at the other, either Round or Square; and how to measure it.
I. For SQUARED-TIMBER.
II. For ROUND-TIMBER.
CHAP. XVIII. Concerning the measuring of Re∣gular Solids, as Cylinders, Globes, Cones, and such like.
I. Of the CYLINDER.
II. By having the Circumference given.
III. By having the Side of a Square, equal to the Base or End of a Cylinder.
II. Of the CONE.
III. Of SPHERICAL BODIES.
CHAP. XIX. Concerning the Gauging of Ʋessels By the Line.
I. For the two third parts of the Circle at the Bung.
II. For one third part of the Circle at the Head.
III. For the number of Square Inches in the Vessel.
IV. For the Content in Wine or Ale Gallons.
How to Measure Board, Glass, Tim∣ber, Stone, &c.
I. For SUPERFICIAL MEA∣SURE, as Board, Glass, &c.
I. In INCH-MEASURE.
PROP. I. A Plank being 27 Inches broad, and 263 Inches long, how many Square Inches are contained therein?
PROP. 2. If a Board, or Plank, or piece of Pavement, or of Glass, be 20 Inches broad, how much thereof in length shall make a Foot square?
II. In FOOT-MEASURE.
PROP. 3. A Room is 52 Foot broad, and 110.5 Foot long; how many Square Foot are there in that Room?
PROP. 4. A Plank being 2 Foot 25 parts broad, how much in length there∣of shall make a Foot Square?
III. In YARD-MEASURE.
PROP. 5. A Room is hung with Tapestry, containing 130 Yards 25 parts in compass, and in depth 5 Yards 20 parts; how many Yards of Tapestry is in that Room?
II. For SOLID-MEASURE, as Timber, Stone, &c. By the Line of Equal parts.
I. In INCH-MEASURE.
PROP. I. A piece of Timber being 30 Inches broad, 21 Inches 6 parts deep, and 183 Inches long; how many Foot is contained in that piece of Timber?
PROP. 2. If a Stone be 30 Inches broad, and 21 Inches 6 parts deep; how much in length of that Stone will make a Foot square?
II. In FOOT-MEASURE.
PROP. 3. If a Stone or piece of Timber be 2 Foot 50 parts broad, 1 Foot 80 parts deep, and 15 Foot 25 parts long; how many solid Feet doth that piece contain?
PROP. 4. The breadth being 2 Foot 50 parts, the depth 1 Foot 80 parts; how much in length thereof will make a solid Foot?
PROP. 5. To divide a Right Line into any number of Equal Parts, at the first opening of the Compasse.
The Use of the LINE of PROPORTION IMPROVED.
CHAP. I. OF SUPERFICIAL MEASURE,
I. Of FOOT-MEASURE.
II. Of YARD-MEASURE.
III. Of MEASURE by the ELL.
IV. Of MEASURE by the ROD.
V. Of MEASƲRING by the SQUARE.
CHAP. II. OF SOLID MEASURE.
CHAP. III. OF CIRCULAR MEASURE.