But every quaternion formula is a proposition in spherical (sometimes degrading to plane) trigonometry, and has the full advantage of the symmetry of the method.
If Meckel's proposition is so far qualified, that the comparison of adult with embryonic forms is restricted within the limits of one type of organization; and if it is further recollected, that the resemblance between the permanent lower form and the embryonic stage of a higher form is not special but general, it is in entire accordance with modern embryology; although there is no branch of biology which has grown so largely, and improved its methods so much since Meckel's time, as this.
The result of this conference was a secret session of the Transvaal volksraad and the proposition of a secret treaty with the Free State, by which each state should bind itself not to build railways to its frontier without the consent of the other, the eastern and northern frontiers of the Transvaal being excepted.
He holds that the true method of research is the analytic, rising from lower to higher notions; yet he sees clearly, and admits, that inductive reasoning, as conceived by Bacon, rests on a general proposition not itself proved by induction.
In 1895 the volksraad passed a resolution, in which they declared their readiness to entertain a proposition from the Transvaal in favour of some form of federal union.
By 1907 altogether 59 local authorities had examined the proposition of establishing telephone systems after 1899, and licences were granted to local authorities at Brighton, Belfast, Chard, Glasgow, Grantham, Huddersfield, Hull, Portsmouth, Swansea, Tunbridge Wells, Oldham, Scarborough and Hartle - pool, but only six municipalities proceeded with the business.
He re-defines analysis in the very opposite way to the ancients; whereas they defined it as a regressive process from consequence to ground, according to Wundt it is a progressive process of taking for granted a proposition and deducing a consequence, which being true verifies the proposition.
The statement only affects the proposition; and whenever we believe the existence of the thing, the belief in existence is part of the judgment thought, whether it is part of the proposition stated or not.
Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.
By the hypothetical he means the new-fangled analysis from a given proposition to more particular propositions, i.e.