 | Horatio Nelson Robinson - 1892 - 428 σελίδες
...principles, which are demonstrated in geometry, afford applications of square root. PRINCIPLES. — I. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides; therefore, II. The hypotenuse is equal to the square root of the... | |
 | Euclid - 1892 - 460 σελίδες
...equal to one of the angles of the given triangle. 8. Pro.ve that the equilateral triangle described on the hypotenuse of a right.angled triangle is equal to the sum of the equilateral triangles described on the sides containing the right angle. [Let ABC be the triangle... | |
 | 1892 - 520 σελίδες
...selfintrospection will- make this clear. When, for example, the student has learnt that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides, he knows implicitly that he knows this truth, and he knows implicitly... | |
 | Henry Martyn Taylor - 1893 - 486 σελίδες
...the second part the ratio which the whole has to the second part. 406 PROPOSITION 31. A polygon on the hypotenuse of a right-angled triangle is equal to the sum of the polygons similarly described on the other sides. Let ABC be a right-angled triangle having the... | |
 | Seth Thayer Stewart - 1893 - 262 σελίδες
...(В. п., Р. п.), as GE = FH, and being | make = alternate Zs; ie, EO = OF. 4. Prove that five times the square of the hypotenuse of a right-angled triangle is equal to four times the sum of the squares of the medians from its extremities. Let A, B, C, be the three sides... | |
 | Edmund Burke - 1893 - 224 σελίδες
...the propositions that the triangle inscribed in a semicircle is right-angled, and that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides. ll. 25-26, Goitre . . . countenance, all being equally afflicted with the... | |
 | Adelia Roberts Hornbrook - 1895 - 222 σελίδες
...Demonstrative geometry will show the truth in all cases of the following principle : PRINCIPLE 54. — The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. 57. Measure off 6 inches on one side of a square surface and 8... | |
 | George Pierce Baker - 1895 - 436 σελίδες
...that is pure \ t , conviction is the proof of some theorem of Geometry, as, .;' for instance, that the square of the hypotenuse of a rightangled triangle is equal to the sum of the squares of the other two sides. All the proof adduced appeals solely to the intellect, and rests... | |
 | Horatio Nelson Robinson - 1895 - 526 σελίδες
...principles, which are demonstrated in geometry, afford applications of square root: PRINCIPLES. — I. The square of the hypotenuse of a rightangled triangle is equal to the sum of the squares of the other two sides ; therefore, II. T7'e hypotenuse is equal to the square root of... | |
 | Adelia Roberts Hornbrook - 1895 - 222 σελίδες
...Demonstrative geometry will show the truth in all cases of the following principle : PRINCIPLE 54. — The square of the hypotenuse of a right-angled triangle is equal to the sujn of the squares of the other two sides. 57. Measure off 6 inches on one side of a square surface... | |
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Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. 
