282 
Proceedings of the Royal Society of Edinburgh. [Sess. 
German commentator, published his three-volume edition of Pappus, and 
Dr Mackay took no further steps to bring his out. This is all the more 
regrettable as British scholarship could well have stood a native edition of 
Pappus ; and although Dr Mackay very magnanimously admitted that his 
Pappus was in no way superior to that of Hultsch, it is not to be doubted 
but that mathematical literature would have been greatly richer to-day if 
his book had been published. I understand that Sir T. L. Heath is soon 
to add Pappus’ “ Mathematical Collections ” to his excellent editions of 
Archimedes, Apollonius, Diophantos, and Euclid, and so remove the stigma 
that English mathematicians are no longer interested in Greek mathematics. 
Dr Mackay was unfortunate, too, in coming so soon after Allman, whose 
researches in Greek geometry appeared first in Hermathena and afterwards 
in book form. These circumstances to a certain extent robbed him of the 
full honour due to his original work, but, nevertheless, he was looked upon 
as one of the foremost living authorities on Greek mathematics. His 
reviews of Heath’s Diophantos and of Gow’s History of Greek Mathematics 
in the Academy give us an insight into his grasp of the subject, and 
make us regret all the more that we have not a work from his own pen 
dealing with the early history of geometry. He was par excellence the 
man to have done it. 
These studies naturally led on to the work of the Scottish geometers, 
Robert Simson and Matthew Stewart, who were more Euclid than Euclid 
himself in their methods of geometrical analysis, and Dr Mackay subjected 
their works to a most exhaustive examination. To mention only one of 
the results that followed from this, I might note that he finally settled the 
question as to who was the original discoverer of the so-called Simson Line, 
and he showed that Robert Simson has no claim to that honour, but that 
the theorem in question is due to William Wallace, who published it under 
a nom de plume in the Mathematical Repository (old series), ii, 111.* 
Popular periodicals of the type of the Repository , the Lady's and Gentle- 
man's Diary, etc., were forms of mathematical literature that flourished 
in our country from the middle of the eighteenth to the middle of the nine- 
teenth century, and were supported very greatly by non-academic mathe- 
maticians. These journals gave incontestable proof that mathematical 
science, and particularly geometry, was very widely studied in our country, 
and was a source of pleasure and amusement to many whose daily avoca- 
tions required physical rather than intellectual energy. Many of the 
problems dealt with were of a high order, and afterwards formed a 
prominent part of geometrical science. The existence of the nine-point 
* See Dr Mackay’s paper in Edin. Math . Soc. Proc ., vol. ix. 
