Many assumptions are made in treating of the flexure of a continuous structure which are not strictly true; no assumption is made in determining the stresses on a frame except that the joints are flexible, and that the frame shall be so stiff as not sensibly to alter in form under the load.
In finding the abutment reactions some principle such as the principle of least action must be used, and some assumptions of doubtful validity made.
The conclusions of such a work are of wider significance than the assumptions we attribute to the author would warrant.
His assumptions are based upon ordinary observation and experience, and are usually accurate in proportion to his practical shrewdness and sagacity, so that he is not interested in the speculative flights of philosophy, except in so far as they influence or have influenced conduct.
The application of Simpson's rule, for instance, to a plane figure implies certain assumptions as to the nature of the bounding curve.
On these assumptions his results are certainly right, and are confirmed by the independent method of Gauss, so that the objections raised against them by Poisson fall to the ground.
Though both assumptions were totally incorrect, neither combatant pointed this out.
The struggle with the Crown, which ended in independence, began at the foundation of the colony, with assumptions of power under the charter which the colonial government was always trying to maintain, and the crown was as assiduously endeavouring to counteract.
D'Epinay's Memoirs as coloured, if not actually dictated, by the malevolent attitude of Grimm and Diderot; and her study of the documents undoubtedly qualifies a good many of the assumptions that have been made on the strength of evidence which is at least tainted by contemporary prejudice, and leaves the way open for an interpretation of the facts which would reconcile Rousseau's character as a writer with his actions as a man.
But in such an undertaking one is always apt to take subjective assumptions or mere fancies for established data.