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" The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides. "
Practical Arithmetic: Uniting the Inductive with the Synthetic Mode of ... - Σελίδα 318
των James Bates Thomson - 1846 - 336 σελίδες
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 σελίδες
...demonstrated. PROPOSITION XLVIII. THEOREM. — If the square described on one of the sides of a triangle, be equal to the sum of the squares described on the other two sides of it; the angle made by those two sides is a right angle. Let ABC be a triangle, which is such that...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1838 - 359 σελίδες
...PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on the other two sides. • Let the triangle ABC be right angled at A. Having described squares on the three sides, let fall...

First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - 1840 - 252 σελίδες
...degrees, and 4=90 degrees. 10. In every right angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a right angled triangle, right angled at C, then will the square D described on AB...

Proceedings

Scotland free church, gen. assembly - 1847
...it makes the alternate angles equal. 2. If the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained...

Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - 1844 - 96 σελίδες
...PROP. VII. THEOREM. The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides. Let the triangle be Fig. 64. KDI, right angled at I. Describe squares on KD, KI, DI ; then we have...

Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - 1844 - 237 σελίδες
...BC^AB'-f-AC". Therefore, The square described on the hypolhcnuse of a right-angled triangle, is equivalent to the sum of the squares described on the other two sides. Cor. 1. Hence, by transposition, the square of one of the sides of a right-angled triangle is equivalent...

Practical Arithmetic: Uniting the Inductive with the Synthetic ..., Βιβλίο 5

James Bates Thomson - 1846 - 348 σελίδες
...geometry, that the square described on the hypothenuse of a right-angled triangle, is equal to the sumo? the squares described on the other two sides. (Leg....square of 3 is equal to the square of the hypothenuse EC ; that is, (4)2-r~(:<)'2, or 16+9=25, the square of the hypothenuse j therefore the square root...

Elements of Drawing and Mensuration Applied to the Mechanic Arts: A Book for ...

Charles Davies - 1846 - 240 σελίδες
...right-angled triangle equal to ? In every right-angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a rightangled triangle, right-angled at C, then will the square D, described on AB,...

HIGHER ARITHMETIC; OR THE SCIENCE AND APPLICATION OF NUMBERS; COMBINING THE ...

JAMES B. THOMSON - 1847
...contains 25 sq. ft. Hence, the square described on the hypothenuse of any right-angled triangle^ is equal to the sum of the squares described on the other two sides. OBS. Since the square of the hypothenuse BC, is 25, it follows that the , or 5, must be the hypothenuse...

Higher Arithmetic: Or, The Science and Application of Numbers; Combining the ...

James Bates Thomson - 1847 - 422 σελίδες
...10342656. 30. 34967ft-. 371 578. The square described on the hypothenuse of a rightangled triangle, is equal to the sum of the squares described on the other two sides. (Thomson's Legendre, B. IV. 11, Euc. I. 47.) The truth of this principle may be seen from the following...




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