The manner of raising, ordering, and improving forrest-trees also, how to plant, make and keep woods, walks, avenues, lawns, hedges, &c. : with several figures proper for avenues and walks to end in, and convenient figures for lawns : also rules by M. Cook.

CHAP. XLVII. (Book 47)

Numeration on the Line, or to read a summe on the Line of Numbers. (Book 47)

YOu may observe, that the Figures on this line, as in the preceding Chapter, are, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 1, 2, 3, 4, 5, 6, 7, 8, 9, 10; Now the same poynt or Division on the Rule, which hath 1, 2, 3, 4, 5, &c. may be read 10, 20, 30, 40, 50, &c. or they may be called 100, 200, 300, 400, 500:

By this you may perceive, that the larger Numbers you have to number, any of those Figures will admit of a larger Denomination; so that if you be to read any summe from one to 10, you have it in the Second part, for then the first one is one tenth, the middle one is one, the End one is 10; but if you be to read a Number of three Figures, (as any is under 1000) then the first one is 10, the middle one 100, the End one 1000.

Example.

To find 144, I take the middle one for the 100, then 4 of the great Divisions forward for 40, then 4 Divisions (forward still to the Right hand) for 4, and that poynt is 144, which may also be called fourteen and 4/10, or 1450, or 14500; then must the middle one be 10000, and 4 tenths forward, 4000; and 5 tenths forward, 500; this poynt wants but five small Divisions of the long poynt, which is 15, or 150, or 1500, or may be 15000, according as your summe is in greatness.

Example.

To find the poynt 12; first I read the middle one 10, then 2 tenths forward for 2, that is the poynt 12, where (in many Rules) there is a Brass Pin, because it is a Poynt much used, as you will find hereaf∣ter; now this poynt 12, is also 120, or 1200; for the first one being one, then the middle one is 10, and two tenths forward is the poynt 12, &c. but if you read this poynt 120, then the first one is 10, the middle one 100, and two tenths forward 20, which is 120; and if it be read 1200, then the middle one is 1000, and two tenths forward 200, which is 1200, &c.

Example.

To find the Number 1728, being the Cube-Inches in a foot of Tim∣ber; the middle one is 1000, then 7 tenths forward is 700, and two tenths of them forward is 20: Now the Divisions on the Rule do not shew the 8 that remains, therefore you must estimate the place for 8, which is almost one tenth more; so having found that place, 'tis the poynt which is for 1728; so, in many great summes, you must esti∣mate or ghess at the Unite, but Decimal summes do shew themselves more plainly, as you may well perceive hereafter, especially when they end with a Cypher or Cyphers.

I hope you now plainly see the use in Reading, or numbering any summe, under 10000; and that you see also, that this is a Decimal Line, and is taken from that excellent Rule of Decimals, the Canon of Lo∣garithmes; and that you may read any Decimal Fraction, as one tenth, one of 100, or one of 1000, or 2/10, 3/10, 4/10, or 15/100, 26/100, 71/100, &c. that is, if the Integer be in 10 parts, you may find out any of these parts; or if in 100 parts, you may find out any part from one to 100 readily.

Ex. If the Integer be 10, that is if 10 make one foot, yard, pound, or the like, I would know the poynt of one and 5/10, or one and ½; take either the middle one, or the first one, extend the Compass poynt to 5, which is the longest Division between 1 and 2, that is, the poynt of one and 5 tenths, or one and a half.

Example.

If it were required to find the point of 100 50/100, or 100 and half, 'tis the same point, or it is 1000 and a half.

Example.

If it be to find the point of 60 of 100, then the middle one is the 100, and the figure 6 in the first part is the figure that is 60 of a 100, or, 60/100, or as decimal fractions commonly are writ. 60, the prick before, shewing it to be a decimal fraction.

Example.

To find 1560, take the middle one for 1000, and five tenths for 500, and 6 tenths of them tenths for 60, which is the point 1560 &c. Also if it be desired to find the fraction 1560, of 10000, that is the same point, and may thus be writ 1560/10000; or it is the point that represents the fra∣ction 156/1000 &c. Be perfect to read the Line well, then will the other Rules be easie.