...figure and have an angle equal to a given angle. 46. To construct a square on a given straight line. 47. In a right.angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. 48. If the square on one side of a triangle be equal to the...

...intersection of the diagonals of the square constructed on the outer side of the hypotenuse. PROPOSITION 47. In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other sides. Let ABC be a right-angled triangle, having the right angle BAC:...

...intersection of the diagonals of the square constructed on the outer side of the hypotenuse. PROPOSITION 47. In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other sides. Let ABC be a right-angled triangle, having the right angle BAC:...

...numbers. Your ordinary Englishman, indeed, is never quite satisfied by Euclid's demonstration that in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the two opposite sides; he honestly believes it when he sees it tried a hundred and...

...his 47th proposition, viz. that in a right-angled triangle the square on the hypothenuse is equal to the sum of the squares on the sides containing the right angle. Pursuing his labours in collecting, arranging, and formulating, Euclid so systematized the subject...

...proprium ; whilst, that ' the square on the hypothenuse of a right-angled triangle is equal in area to the sum of the squares on the sides containing the right angle ' is a proprium ; for it is an attribute common to all right-angled triangles, and which can be shown,...

...opposite two are parallel. (3) The square on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the sides containing the right angle. (4) The swallow is a migratory bird. (5) Axioms are self-evident truths. 5. Classify the following...

...numbers.. Your ordinary Englishman, indeed, is never quite satisfied by Euclid's demonstration that in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the two opposite sides; he honestly believes it when he sees it tried a hundred and...

...frequently used formula? are those applying to right.angled triangles (Euclid, book i., prop. 47), in which the sum of the squares on the sides containing the right angle is equal to that of hypothenuse which is opposite to it. For example, let the length of a bracing bar...

...ABF; their vertices pointing outwards. Prove that AD=BE=CF. THEOREM 6. [THE THEOREM OF PYTHAGORAS.] In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle. H Data ABC is a triangle, right.angled at A....