Page:The Kinematics of Machinery.djvu/190

 168 KINEMATICS OF MACHINERY.

systeme plan, the surfaces of the triangle being supposed to be caused to move always in the same planes, which are therefore such plans ine'branlable as are considered to be peculiar to this third system. We might look in this direction for the real essence of the system, but then the turning pair would also on these grounds have to be put in the same category, while it must be claimed on the other hand as distinctly belonging to systeme tour. So we lose our clue, and fail in discovering what the real difference between things varying so essentially is, the very thing which it was and must be the object of the " system " to point out. But I will stop : it is evident that Laboulaye's position is unten- able. The question here, too, is not one of criticism of Laboulaye himself; many other writers have followed him without putting his ideas sufficiently to the proof, and they would therefore be open to the same criticism. That I do not undervalue Laboulaye will be seen from the Introduction, where I have paid my tribute of recog- nition to him as an investigator. I do this the more freely, that he has not drawn any special deductions in the applied part of his work from his first propositions, deductions which would neces- sarily have led to error. I have been desirous only to show upon what insecure and feeble supports it has been attempted to build up a science of Kinematics, a science having ostensibly a logical basis of its own. I wished to place again before the reader, in a form that could be readily grasped, a proof that if anything what- ever is to be accomplished by means of axiomatic propositions, they must be subjected to, and be able to bear, the most inexorably strict, exact and penetrating examination.

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