56 LETTERS ON SCIENTIFIC SUBJECTS. 



who brought your letter or by whom to returne my answere, 

 were the occasions, as I now remember, that you have beene 

 put to this second trouble. Now I shall indevoure to give 

 you suche satisfaction as I can, and seinge I do not know 

 who brought this letter, or by whom more conveniently to 

 sende, I purpose to sende mine answere to London, from 

 thence to be brought to Trinity College where I hope it will 

 finde you. 



1. For your first demande (seinge I do not know whose 

 lines you use, my answer wil be somewhat more uncertaine, 

 and it may be the author whom you followe would satisfie 

 you more fully,) 'tis well if I can satisfie for mine owne de- 

 fectes. These artificiall numbers (injuriously named sines) 

 are not made for degrees, minutes, &c., but for the true sinus 

 dati cujuscunque gradus et minuti : therefore if you first finde 

 the true sine of any arke, the Nothi may best be found by the 

 generall rule set downe in 14 cap. of my booke, Dato cuilibet 

 numero absolute, Logarithmum congruum invenire et contra. 

 But if this seeme too tedious, you may use the parte pro- 

 portionall. If 60 minutes or secondes rather (for the minutes 

 are expressed in the printed tables) give the whole difference 

 inter duos proximos ; what shal be the difference to be added 

 or subtracted for 27" or any other number; but in the parte 

 proportionall we muste not expect suche exact precisenes as 

 in the former, especially if there be any notable inequalitie in 

 the differences next adjoyninge : where we may not safely 

 trust proportion, as namely in the artificiall sines of the be- 

 ginninge and ende of the quadrant. But if you be willinge 

 to inlarge some parte of your table to secondes, I have ex- 

 pressed the maner in my booke cap. 12, and more easily 

 cap. 13, where first you may inlarge them to fiftes of minutes 

 or to 12"; and if you be at leisure afterwards to 24" or to 

 the 25 parte of a minute; then (the differences beinge brought 

 more nere to equalitie) you may somewhat more safely trust 

 the parte proportionall. 



2. Concerninge the logar. of all fractions proper or impro- 

 per, see my 10 cap. and for a generall rule take this, Diffe- 

 rentia logarithmorum numeratoris et denominators est loga- 

 rithmus datarum partium. As of f 017609125905568 of f 

 017609 etc. of y T 034678748622466 of T %% 034678 etc. 

 And contra, to finde the absolute number of any logarithme, 

 seeke the logarithme in the tables, and if it be there you shall 

 have the absolute number in the m argent; if it be not there, 

 then by the parte proportionall you may come nere it, so that 

 if neede be, you change the characteristica as is prescribed in 

 the 1 1 cap. de qua in 4 cap., for so there wil be lesse defect in 



