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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. "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 18
by Euclides - 1858
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Robinson's New Practical Arithmetic for Common Schools and Academies

Horatio Nelson Robinson - Arithmetic - 1892 - 428 pages
...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...
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Robinson's New Practical Arithmetic for Common Schools and Academies

Horatio Nelson Robinson - Arithmetic - 1892 - 428 pages
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...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...
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Wiseman Review, Volume 110

1892 - 520 pages
...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...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 486 pages
...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...
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Letters on a Regicide Peace: Letters I. and II.

Edmund Burke - 1893 - 224 pages
...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...
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Exercises in Stewart's Plane and Solid Geometry: With Solutions for Teachers

Seth Thayer Stewart - Geometry - 1893 - 262 pages
...(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...
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The Principles of Argumentation

George Pierce Baker - Debates and debating - 1895 - 436 pages
...argumentation 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...
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The Principles of Argumentation

George Pierce Baker - Debates and debating - 1895 - 438 pages
...of argumentation that is pure 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...
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Robinson's New Higher Arithmetic: For High Schools, Academies, and ...

Horatio Nelson Robinson - Arithmetic - 1895 - 526 pages
...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...
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