is no more but to find the Number in the first Column, and in the second Co∣lumn you shall have the Logerithme answering thereunto.
Example. Let the Number given be 415, and if it is required to find the Loga∣rithme thereof, in the Table of Logorithmes, in the first Column thereof, under the Letter N, I find the Number 415, and right against it in the next Column I find 618048, which is the Logarithme of 415. In the same manner you may find the Logarithme under 1000; as the Logarithme of 506 is 704151, and the Logarithme of 900 is 954243, &c.
But here is to be noted, That before every Logarithme must be placed his proper Characteristick; viz. If the Number consist but of one Figure, as all Numbers un∣der 10, then the Characteristick is 0; if the Number consist of two Figures, as all Numbers between 10 and 100, then the Characteristick is 1; if the Number consist of three Figures, as all Numbers betwixt 100 and 1000, then the Characteristick is 2; and if the Number consist of four Figures, as all between 1000 and 10000, the Characteristick must be 3. In brief, the Characteristick of any Logarithme must con∣sist of an Unit less than the given Number consisteth of Di••its or Places: And by ob∣serving this Rule, the Logarithme of 415 will be 2.618048, and the Logarithme of 506 is 2.704151, and the Logarithme of 900 is 2.954243, &c.
PROBL. II. A Logarithme being given, to find the Absolute Number thereunto belonging, by the former Observation; the Characteristick will declare of what Number of Places the Absolute Number consisteth.
Example. Let the Logarithme given be 2.164353; now because the Characteri∣stick is 2, I know by it the Absolute Number consisteth of three places, and therefore may be found in the second Column of the Logarithme Tables, having 0 at the top thereof, against which I find 146, which is the Absolute Number answering to the Logarithme of 2.164353.
PROBL. III. How to find the Logarithme of a Number that consisteth of four Places.
You must find the three first Figures of the given Number in the first Column, as before, and seek the last Figure thereof amongst the great Figures in the head of the Page; and in the common Area or meeting of these two Lines is the Logarithme you desire, if before it you add or prefix its proper Characteristick.
Example. Let it be required to find the Logarithme of 5745; I find 574, the three first Figures, in the first Column, and 5, the last Figure, in the head of the Table; then going down from 5 in the head of the Table, until I come against 574 in the first Column, there I find 759290, before which I place 3 for the Characte∣ristick, which is 3.759290, and that is the Logarithme sought for.
PROBL. IV. Any Number of Degrees and Minutes being given, to find the Artificial Sine and Tangent thereof.
Admit it were required to find the Sine of 21 deg. 24 min. I turn to the Sines in the Table, and in the head thereof I find Degrees 21; then in the first Column (under M) I find 24, and right against it is 9.562146 for the Sine, and 9.593170 for the Tangent of 21 deg. 24 min. But suppose it were required to find the Sine or Tan∣gent of 56 deg. 35 min. look for all else under 45 deg. are found in the head, and the odd min. in the left hand; and all above 45 deg. are found in the foot of the Table, and the min. in the last Column toward the right hand; as in this Example the Sine of 56 deg. 35 min. is 9.921524, and the Tangent is 16.180590.