It was found advisable, later, to dispense with the last two, and so, only the square, equilateral triangle, circle and right-angled triangle, it was decided should be made.

There, just above the representation of the right-angled triangle, shone out, clearly and distinctly, this striking figure:

We reply to you, and we show to you that we can reason by indicating that the square of the hypothenuse of a right-angled triangle is equivalent to the sum of the squares of the other two sides.

There was the right-angled triangle, its lines reproduced in unbroken brilliancy, and there were the added lines used in the familiar demonstration, broken at intervals to indicate their use.

Their mathematicians knew the rule for finding the area of a triangle from its sides, and also the celebrated proposition concerning the squares on the sides of the right-angled triangle.

Let a man of good parts know all the maxims generally made use of in mathematics ever so perfectly, and contemplate their extent and consequences as much as he pleases, he will, by their assistance, I suppose, scarce ever come to know that the square of the hypothenuse in a right-angled triangle is equal to the squares of the two other sides.

Another simile likens it to a right-angled triangle, with the Bitter Root Range as its base.

Having continued this examination for about half an hour, we proceeded to enter into particulars respecting triangles; and having discoursed on the difference between isosceles triangles and scalene triangles, I observed that an acute isosceles triangle had all its angles acute, and proceeded to observe that a right-angled scalene triangle had all its angles acute.

"Why," says the children, "you said a right-angled triangle had one right angle, and that all its angles are acute.

Yes, there are right-angled and obtuse-angled.

Yes, there is a right-angled scalene triangle, which has one right angle.

Two right-angled isoceles triangles.

For not only the color and size of the triangle are indifferent, but its other peculiarities as well; the question whether it is right-angled or obtuse-angled, whether it has equal sides, whether it has equal or unequal angles, is not mentioned in the demonstration, and has no influence upon it.

"The three angles of a right-angled triangle were equal to two right angles in the days of Moses, as well as now.

When Pythagoras discovered the theorem of the squares erected on the sides of a right-angled triangle, it had the effect on him of a most preposterous joke.

Experimentally this is shown to be the case, for when the same oblong jet, discharged under the same conditions, impinged vertically upon a smooth plate, and gave a pressure of 71 units, gave 87 units when discharged into a confined right-angled channel.

The symbol of the right-angled triangle was afterwards adopted by Pythagoras when he visited the banks of the Nile; and the discovery which he is said to have made in relation to the properties of this figure, but which he really learned from the Egyptian priests, is commemorated in Masonry by the introduction of the forty-seventh problem of Euclid's First Book among the symbols of the third degree.

The forty-seventh problem of the first book of Euclid is, that in any right-angled triangle the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle.

The right-angled triangle still has an hypotenuse, and quadratics do not simplify with distance, while Tamil classics throw Vergil and Cicero into the shade.

They are so afraid to do anything that isn't laid out in a right-angled triangle.

Quite at once, a right-angled turning opened into a small chamber not above eight feet high by fifteen square.

Right-angled tensile strength of small clear pieces of 25 woods in green condition IV.

= 0.003 Right-angled compression-large " Z = 0.007 Right-angled compression-small " Z = 0.015 Shearing parallel to the grain Z = 0.015 Example: At what speed should the crosshead move to give the required rate of fibre strain in testing a small beam 2" X 2" X 30".

= 0.003 Right-angled compression-large " Z = 0.007 Right-angled compression-small " Z = 0.015 Shearing parallel to the grain Z = 0.015 Example: At what speed should the crosshead move to give the required rate of fibre strain in testing a small beam 2" X 2" X 30".

Another method of testing by indentation involves the use of a right-angled cone instead of a ball.