A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

From EDWARD J. ROUTH, M.A., F.R.S., &c., Cambridge.
" It seems to me that so excellent a treatise will soon make its
way to the front, even against the severe competition which all
books on Conics now meet with. I fancy that many of the
theorems cannot be elsewhere found so conveniently explained."
From the " FREEMAN'S JOURNAL."
"This treatise exhibits in a marked degree the qualities which
distinguish the author's other works. It is at once compact and
comprehensive... Dr. Casey's treatise, indeed, may well
accomplish for this generation what Dr. Salmon's did for their
fathers, namely, to introduce the young mathematician to the
latest developments in the highest departments of the Science.... Scarcely any important step is there in the work which
he has not simplified, giving one, and sometimes several, original
methods.... The method of projection is treated of in an
entirely original manner, not requiring the consideration of space
of three dimensions, the projection being performed in one plane,
and the equation of the curve obtained by a simple transformation.
The properties of the M'Cay, Neuberg, and Brocard Circles are
considered at some length: indeed the latter has now a literature
of its own, to which Dr. Casey has largely contributed.
There are considerably over a thousand examples, graduated
from easy applications of the formulæe to exercises of the highest
class of difficulty. Many of these are original, and many are
historically interesting."
From the " DUBLIN EVENING MAIL."
"This work will give a new impulse to the study of Analytic
Geometry, introduce the student to new and more powerful
methods, and greatly enlarge his mathematical horizon. It has
been known for some time that Dr. Casey was engaged on a
'Conic Sections,' and people expected that notwithstanding the
many works in the field, Dr. Casey's would present a good many
valuable novelties; but the work has, we venture to think, excelled all anticipation.... Dr. Casey makes a large use of
determinants. He introduces them in the very first chapter, and
employs them to the end. In the first chapter we find a section
devoted to complex variables, and Gauss's geometrical representation of them; and from Clebsch he takes the comparison of
' point' and ' line' co-ordinates. He gives a great development
to trilinear co-ordinates and tangential equations, discusses the
new circles (Tucker's, Brocard's, Neuberg's, M'Cay's), applies
Aronhold's notation to the discussion of the general equation of
the second degree, and reproduces from his own Papers in the
Transactions of learned societies many important theorems and
problems relating to inscribed and circumscribed figures, orthogonal conics, and the tact-invariant of two-conics.... The
work is a noble monument to Dr. Casey's genius, and his mastering of all the resources of Modern Analytic Geometry."
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