"The history of the mathematical theory of Elasticity shows clearly that the development of the theory has not been guided exclusively by considerations of its utility for technical Mechanics. Most of the men by whose researches it has been founded and shaped have been more interested in Natural Philosophy than in material progress, in trying to understand the world than in trying to make it more comfortable."

"[D]iscussions... concerning the number and meaning of the elastic constants have thrown light on most recondite questions concerning the nature of molecules and the mode of their interaction."

"Even in the more technical problems, such as the transmission of force and the resistance of bars and plates, attention has been directed, for the most part, rather to theoretical than to practical aspects of the questions. To get insight into what goes on in impact, to bring the theory of the behaviour of thin bars and plates into accord with the general equations—these and such-like aims have been more attractive... than endeavours to devise means for effecting economies in engineering constructions or to ascertain the conditions in which structures become unsafe."

"The... fact that most great advances in Natural Philosophy have been made by men who had a first-hand acquaintance with practical needs and experimental methods has often been emphasized; and, although the names of Green, Poisson, Cauchy show that the rule is not without important exceptions, yet it is exemplified well in the history of our science."

"Whenever, owing to any cause, changes take place in the relative positions of the parts of a body the body is said to be "strained." A very simple example of a strained body is a stretched bar."

"Let l_0 be the length before stretching, and l the length when stretched. Then (l - l_0)/l_0is a number (generally a very small fraction) which is called the extension..."

"Let e denote the extension of the bar, so that its length is increased in the ratio 1 + e : 1 ...[V]olume is increased by stretching the bar, but not in the ratio 1 + e : 1. When the bar is stretched longitudinally it contracts laterally... If the linear lateral contraction is e^\prime, the sectional area is diminished in the ratio (1 - e^\prime)^2 : 1, and the volume in question is increased in the ratio (1 + e) (1 - e^\prime)^2 : 1. In... a bar under tension e^\prime is a certain multiple of e, say \sigma e... [with] \sigma... about \frac{1}{3} or \frac{1}{4} for very many materials. If e is very small and e^2 is neglected, the areal contraction is 2\sigma e, and the cubical dilatation is (1 - 2\sigma)e."

"[M]easure the coordinate z along the length of the [vertical] bar. Any particle of the bar which has the coordinates x, y, z when the weight is not attached will move after the attachment of the weight into a new position. Let the particle which was at the origin move through a distance z_0, then the particle which was at (x, y, z) moves to the point of which the coordinates arex(1 - \sigma e), \qquad y(1 - \sigma e), \qquad z_0 + (z - z_0)(1 + e)."

"Love was the first investigator to present a successful approximation shell theory based on classical elasticity. To simplify the strain-displacement relationships and, consequently, the constitutive relations, Love [in this Treatise] introduced the following assumptions, known as the first approximations and commonly termed the Kirchoff-Love hypotheses..."

"[Love's] early books on elasticity, theoretical mechanics, and calculus have been used by many generations of students, whilst the much enlarged edition of his Treatise on Elasticity is a monumental work."

"History of science"

"A History of the Theory of Elasticity and of the Strength of Materials"

"Engineering"

"The theory of elastic crystals adopted is that which has been elaborated by the researches of F. E. Neumann and W. Voigt."

"The discussion of the stress-strain relations rests upon as an axiom generally verified in experience, and on Sir W. Thomson['s] thermodynamical investigation of the existence of the energy-function."

"In the analysis of strain I have thought it best to follow Thomson and Tait's Natural Philosophy, beginning with the geometrical or rather algebraical theory of finite homogeneous strain, and passing to the physically most important case of infinitesimal strain."

"At Mr Webb's suggestion, the exposition of the theory is preceded by an historical sketch of its origin and development. Anything like an exhaustive history has been rendered unnecessary by the work of the late Dr Todhunter as edited by Prof. Karl Pearson, but it is hoped that the brief account given will at once facilitate the comprehension of the theory and add to its interest."

"The division of the subject adopted is that... by Clebsch in his classical treatise, where a clear distinction is drawn between exact solutions for bodies all whose dimensions are finite and approximate solutions for bodies some of whose dimensions can be regarded as infinitesimal. The present volume contains the general mathematical theory of the elastic properties of the first class of bodies, and I propose to treat the second class in another volume."

"The present treatise is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity. He has unfortunately found himself unable to proceed... and I have therefore been obliged to take upon myself the whole of the... responsibility. I wish to acknowledge... the debt that I owe to him as a teacher of the subject, as well as... for many valuable suggestions..."

"In most of the problems considered in the text Saint-Venant's "greatest strain" theory has been provisionally adopted. In connexion with this theory I have endeavoured to give precision to the term ""."

"The conditions of rupture or rather of safety of materials are as yet so little under stood that it seemed best to give a statement of the various theories that have been advanced without definitely adopting any of them."