...easy of comprehension. What should we think of a mathematician who should say I will not believe that the square of the hypothenuse is equal to the squares of the sides of a right-angled triangle unless I have ocular demonstration of the facts ? And what do we think...

...having discovered the demonstration of the 47th proposition of the first book of Euclid, viz. that in n right angled triangle the square of the hypothenuse is equal to the sum of the squares of the two other sides. Julius Capito/ linus relates, that when an Hecatomb was...

...opinions that there must necessarily be hostile mathematical sects; some affirming, and some denying that the square of the hypothenuse is equal to the squares of the sides. But we do not think either the one analogy or the other of the smallest value. Our way of ascertaining...

...by the Square Root, without finding the Angles ; according to the following PROPOSITION : In every Right Angled Triangle, the Square of the Hypothenuse is equal to the Sum of the Squares of the two Legs. Hence, The Square of the given Leg being subtracted from the Square...

...by the Square Root, without Finding the Angles ; according to the following PROPOSITION : In every Right Angled Triangle, the Square of the Hypothenuse is equal to the Sum of the Squares of the two Legs. Hence, The Square of the given Leg being subtracted from the Square...

...demonstrate geometrical truths, I asked whether they were perfectly convinced that in a rightangled triangle the square of the hypothenuse is equal to...certain of this fact ? and, in reply, he demonstrated very clearly. Having drawn a figure with a pair of compasses, on paper, he cut out the three squares,...

...which subtends the right angle. Euclid, lib. i. proposition 47, demonstrates, that in every rectilmear right angled triangle, the square of the hypothenuse is equal to the squares of both the other sides. This celebrated problem was discovered by Pythagoras, who is said to have sacrificed...

...schools is of the CANINE SPECIES , and not very intelligible. (3) The discovery of Pythagoras , that the square of the hypothenuse is equal to the squares of the other two sides of a right angled triangle. Whose daring revels shock the sight, When vice and infamy combine ; When...

...right angle, as BC in the annexed diagram. According to the 47th Proposition ' of Euclid's Elements, the square of the hypothenuse is equal to the squares of the other two sides, as B C1 = BA* -f AC* ie the square BE equal to the squares BGandCH. HYPOTHESIS (Rltet.) vxltte-u, a...

...demonstrate geometrical truths, I asked whether they were perfectly convinced that in a right-angled triangle the square of the hypothenuse is equal to...three squares, folded the squares of the two short sides into a number of triangles, and also cut out these triangles ; then laying the several triangles...