...general system of mathematical truth. If, for example, it be alleged, that it is needless to demonstrate that any two sides of a triangle are greater than the third, it may be replied that this is no doubt a truth, which, without proof, most men will be inclined to...

...as of the geometrical theorem that one circle cannot cut another circle in more than two points, or that any two sides of a triangle are greater than the third side. Indeed we think Mr. Gambier inconsistent when he affirms, of the former propositions that no doubt...

...the earth, M the moon in the horizon, and M' the same in the zenith, and draw MA, MC ; then because any two sides of a triangle are greater than the third side, MA and AC are greater than MC or M'C ; and therefore, if from each AC be subtracted, there will remain...

...general system of mathematical truth. If, for example, it be alleged, that it is needless to demonstrate that any two sides of a triangle are greater than the third ; it may be replied, that this is no doubt a truth, which, without proof, most men will be inclined...

...which of these two suppositions is the more philosophical. Having treated, at considerable length, of those habits in which both mind and body are concerned,...to quantity, considered abstractly, (to some, for exampie, in the fifth book of Euclid,) which almost every student would be ready to admit without a...

...Having treated, at considerable length, of those habits in which both mind and body are concerned, 1 proceed to make a few remarks on some phenomena which...to quantity, considered abstractly, (to some, for exampie, in the fifth book of Euclid,) which almost every student would be ready to admit without a...

...given time, will have arrived at the point D. Now I presume that Kinclaven does not require to be told, that any two sides of a triangle, are greater than the third side; and therefore, I suppose he will admit that the line AD, which the body under the action of the two...

...a scholar, who, at the threshold, should refuse to admit that two parallel lines can never meet, or that any two sides of a triangle are greater than the third. The powerful reasoning of Adam Smith, the clear demonstrations of Say, and the forcible and able expositions...

...consequently in the Terms, which are the exact representatives of those Definitions. • B. iv. c. 2. § 1. KG That any two sides of a Triangle are greater than the third — in other words that it is impossible to construct a triangle, one of whose sides shall be equal...

...HZ— KZ. Zp common to the triangles HZp, HZp, and angle WLp= angle KZjo, .-. pK = />H. But, since any two sides of a triangle are greater than the third side, Sp + pK > SK > SP + PK > SP + PH v PK=PH by construction> Sv + »H, by definition 1, But we have just...