1913-14.] Obituary Notices. 283 
circle, properties of symmedians and symmedian points, etc., were early 
discussed in the diaries. Dr Mackay made a close study of these journals, 
and the results of his labours were communicated to the French 
Association for the Advancement of Science at their Congress at Besangon 
in 1893, in a paper entitled “ Notice sur le journalisme mathematique en 
Angleterre.” 
Dr Mackay ’s original papers were practically all published in the 
Proceedings of the Edinburgh Mathematical Society, and they constitute 
the most valuable record in our language of the geometry of the triangle. 
It is quite impossible to give here even the titles of all his papers, but 
it may be stated that no earnest student of any branch of plane geo- 
metry can afford to neglect his writings.* They deal with the nine-point 
circle, the six scribed circles of a triangle, isogonals, symmedians, and 
isogonic centres of a triangle. Perhaps his most valuable contributions 
are “ The Triangle and its Six Scribed Circles,” published in vol. i, vol. ii, 
and vol. xi of the above Proceedings , and “ The Symmedians of a Triangle 
and their Concomitant Circles,” in vol. xiv. The first of these two occupied 
several years of his leisure, and to make it as complete as possible he enlisted 
the services of such well-known geometers as Tucker, Neuberg, Fuhrmann, 
and d’Ocagne. We may judge of the completeness of the work when we 
know that it occupied 1600 quarto pages of MS. His paper on the 
“ Symmedians of a Triangle ” made known for the first time in an English 
journal the remarkable properties of the K points and of the Tucker 
group of circles which have as particular cases the first and second 
Lemoine circles, the Taylor circle, and the Adams’s circle. 
Dr Mackay was also the author of the articles “ Calendar ” and 
“ Geometry ” in Chambers’s Encyclopaedia, and “ Euclid ” in Encyclopaedia 
Britannica. The interesting and learned article on “ Numeration ” in the 
jubilee volume of the Chartered Accountants’ Association of Scotland is 
also from his pen. 
Of his books the most important is his Elements of Euclid (W. & R. 
Chambers, Edinburgh, 1884). Like many others, it is based on the well- 
known edition of Robert Sim son, but it shows a vast improvement on 
any previous text-book. Every page of it shows evidence of ripe scholar- 
ship, and it possesses what no other text-book we know possesses, viz. 
references to original memoirs and authorities and full historical notes. 
Writers of mathematical text-books in general carefully avoid introducing 
such personal elements, and thereby in our view make a very great 
* A list of these papers will be found in the index volume of the Edinburgh Mathe- 
matical Society. 
