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.

SECT. I. The Explication of the Tables of the Lo∣garithms, and of parts proportional.

THE Logarithms, were first inven∣ted,* 1.1 found out and framed, by that never to be forgotten and thrice Honourable Lord, the Lord Nepeir: which Numbers, so found out and framed by his diligent industry he was pleased to call Logarithms; which in the Greek signifies the Speech of Numbers, I shall not here trouble you with the manner or the Construction of those Tables of Logarithms but shall first lay down some brief and ge∣neral Rules, that thereby the better you ma•• Understand those Tables, and then I shall e••∣plain their manifold uses, in sundry Exam∣ples Arithmetical, &c.

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* 1.2 N, and right against 5, and in the next Column under LOG.* 1.3 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* 1.4 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* 1.5 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.

PROP. II.

To find the Logarithm belonging to a Vulgar Fraction, and a Mixt number.

First as is before shewed if it be a Vulgar Fraction, find the Log. of the Numerator, and the Log: of the Denominator, then substract the Log: of the Numerator, from the Log: of the Denominator, the remainder* 1.6 is the Log: of the Fraction propounded: Now if you would find the Logarithm of 5/7, do as is prescribed whose Log. I find to be 0. 146121, Now to find the Log. of a Mixt Number, reduce it into an Improper Fraction, and then do as before, so the Log of 15 ⅖, Improper 77/5;, is 1, 187, 52, and so do for any other Mixt number.

PROP III. A Logarithm propounded to find the whole, or Mixt number, corresponding thereunto.

For the more speedy finding the number, answering unto the Logarithm propounded, ob∣serve that if the Index be 0, then the Number sought may be found between 1 and 10; If 1,

between 10 and 100; if 2, between 100, and 1000; if 3 between 1000 and 10000, and so on still observing the Rules of the Characteris∣tick, or Index, therefore loo, in the Table un∣till you find the Logarithm proposed, and a∣gainst it in the Margent according to the afore∣going directions under N, you shall find the number belonging thereunto. This Rule holds in force in Mixt Numbers also.

Thus.

0. 845098

1. 556302

2. 130334

3. 980276

Are the Lo∣garithms of,

7

36

135

9556

NOTE.

But if you cannot find the Logarithm exact∣ly in the Table, as in many operations it so hapneth, you must then take the nearest Lo∣garithm Number to the Logarithm propoun∣ded, and so take the number belonging thereto ••or the desired number.

Notes

• * 1.1

  Defin.
• * 1.2

  Signifies the Num∣ber, or figure sought.
• * 1.3

  Signifies the Loga∣rithm answering to the number Opposite.
• * 1.4

  ☞ Note this Rule well, for this explains the use of the Table of proportional parts, printed at the end of this Book.
• * 1.5

  Definition. The Rule to find the Characteristick or Index appertaining to any Lo∣garithm.
• * 1.6

  〈 math 〉〈 math 〉