Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

PROP. I. Any Number given under 10000, or 100000, to find the Logarithm corresponding thereunto.

1. If the number propounded consist of one place whose Logarithm is required to be found, as suppose (5,) look for 5, in the top of the left hand Column under the Letter* 1.1 N, and right against 5, and in the next Column under LOG.* 1.2 you will find this number or rank of figures, 0698970, which is the Logarithm of the number 5 required.

2. If the number consisteth of two places as if it were 57, look 57 under N, and opposite to it and under LOG. you will find this num∣ber 1. 755875, which is the Logarithm of 57, the number propounded.

3. If the number propounded consist of three places as 972, look for 972, under N, and opposite to 972, and under ••o) the Column, you shall find this number 2. 987666, which is the Logarithm of 972, the number which was propounded.

4. But if the number consist of four places as 685, look the three first figures 168, under the Column N, and opposite to that, and un∣••er 5 at the top of the page, you will find this number 3. 226599, which is the Logarithm of 1685, the number propounded.

5. But if the number* 1.3 given be above 10000, and under 100000, you may find its Logarithm by the Table of parts proportional, printed at the latter end of this Book. Thus if the Lo∣garithm of 35786, be sought, first seek the Log. of 3578, which will be 553649, and the com∣mon Difference under D is 121; with this dif∣ference 121, Enter the Table of parts propor∣tional, and finding 121 in the first Column un∣der D, you may then lineally under 6, find the number 72, which add to the Log. of 3578, that is 553649, it produceth, 553712, which is the Log. of 35786 the number propounded: now be∣cause the number propounded 35786, ariseth to the place of X. M. therefore there must be the figure 4 prefixed before its Logarithm, and then it will be thus 4, 553712, which 4, is cal∣led the Index, as shall be hereafter shewed.

Now before we proceed to find numbers cor∣responding to Logarithms, it will be necessary to explain the meaning of the first figure to the left hand of any Logarithm placed, Mr. Briggs calleth it a Cha∣racteristick* 1.4 or Index, which doth represent the distance of any the first figure of any whole number from Unity, whose Index is 0, a Cypher; so the Index o•• 10 is 1, and so to 100 whose Index is 2, and s•• to 1000 whose Index is 3, and so to 10000 whose Index is 4, and so if you persist furthe•• the Characteristick is always one less in dignity

than the places or figures os the number pro∣pounded.

Notes

• * 1.1

  Signifies the Num∣ber, or figure sought.
• * 1.2

  Signifies the Loga∣rithm answering to the number Opposite.
• * 1.3

  ☞ Note this Rule well, for this explains the use of the Table of proportional parts, printed at the end of this Book.
• * 1.4

  Definition. The Rule to find the Characteristick or Index appertaining to any Lo∣garithm.