...think, in the words, " He that walketh with wise men shall be wise." The boy that has learned to prove that the angles at the base of an isosceles triangle are equal to one another — especially if he has learned it after Euclid — has made a certain gain in mental...

...proposes a problem ; for it is possible to inscribe one that is not equilateral. But when anyone asserts that the angles at the base of an isosceles triangle are equal, he must affirm that he proposes a theorem ; for it is not possible that the angles at the base of an...

...plaiued by an In the fifth proposition of Playfair's Geometry, BI, it is proposed example. to prove that the angles at the base of an isosceles triangle are equal. The first step is to prepare the diagram by producing the two sides, AB, and AC, indefinitely towards...

...school. The Euclid in itself is not of much practical use — no one wants to prove in everyday life that the angles at the base of an isosceles triangle are equal to one another or that the three angles of a triangle are equal to two right angles, but you learn...

...should, of course, look for his demonstrations among the most awkward. We find it stated, for instance, that the angles at the base of an isosceles triangle are equal was first "set forth and said by" Thales. This is evidently a quotation from a poet and is supposed...

...their vacant time, — proceeded, one to perform a problem, and the other to demonstrate the theorem, that " the angles at the base of an isosceles triangle are equal." They had gone, it was remarked, about halfway through the first book of Playfair's Euclid, demonstrating...

...fifth proposition of Euclid for the sake of the] discipline, not for the sake of learning the mere fact that the angles at the base of an isosceles triangle are equal. She answered, ' Yes, that is quite true, and I often think that we are on the wrong track altogether...

...shown that there is only one intel. ligible 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...

...PONS ASINORUM Straight Latin for "bridge of asses," pons asinorum is the nickname for Euclid's theorem that the angles at the base of an isosceles triangle are equal. The theorem was considered hard for beginners to understand, and pons asinorum has come to mean any...

...; 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...