...From formulas (85) and (86), or those derived from them, it is easy to show, that B=A, when 6= a, or that the angles at the base of an isosceles triangle are equal; as, by taking a and b equal, the values of cos A and cos B would become equal. FORMULAS OF THE FOUR...

...immediately; and that three is the half of six. This immediate perception is immediate and intuitive judgment. That the angles at the base of an isosceles triangle are equal, I perceive by a process of reasoning, in which it will be acknowledged there is judgment. Another way...

...is a fact which all future geometrical analysis can only confirm and illustrate, and thus the truth that " The angles at the base of an Isosceles triangle are equal " becomes a fundamental part of celestial dynamics, and the Eureka of Archimedes an essential portion...

...; and that three is the half of six. This immediate perception is immediate and intuitive judgment. That the angles at the base of an isosceles triangle are equal, I perceive by a process of reasoning, in which it will be acknowledged there is judgment. Another way...

...without stating what it is fit for, — an absurdity as great, says the objector, as it would be to say that ' the angles at the base of an isosceles triangle are equal without adding to one another, or to any other angle.' Dr. Brown also, in arguing against this doctrine...

...propositions, are subsequently employed as major premises. Such, for example, are the propositions that the angles at the base of an isosceles triangle are equal ; that the three angles of every triangle are together equal to two right angles ; and that all equilateral...

...Though your brother's genius was all but catholic — I say all but ; for he could never demonstrate that the angles at the base of an isosceles triangle are equal — yet to me he generally showed the bright and sunny side of his nature ; and I need not tell you...

...is a fact which all future geometrical analysis can only confirm and illustrate, and thus the truth that " The angles at the base of an Isosceles triangle are equal " becomes a fundamental part of celestial dynamics, and the Eureka of Archimedes an essential portion...

...shown that there is only one intelligible law, then that must be the actual law. Thus we may argue that the angles at the base of an isosceles triangle are equal (not because there is no reason why one should be greater than the other, but), because, if not, no...

...sum of the angles of a spherical triangle is greater than two right angles, and less than six. Show that the angles at the base of an isosceles triangle are equal. (9.) Express the cosine of an angle of a spherical triangle in terms of the cosines and sines of the...