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" 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. "
A Complete Epitome of Practical Navigation, and Nautical Astronomy ... - Σελίδα 37
των John William Norie, J. W. Saul - 1917 - 595 σελίδες
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A Course of Mathematics in Two Volumes for the Use of Academies, as ..., Τόμος 1

Charles Hutton - 1816
...Is any Right-angled Triangle, the square of the Hypothcnuse, is equal to the Sum of the Squares of the other two Sides Let ABC be a right-angled triangle, having the right angle c ; then will the square of the hypoihenu^e AB,be equal to the sum of the squares of the...

A Supplement to the Elements of Euclid

Daniel Cresswell - 1825 - 582 σελίδες
...is cut harmonically by that side, and the straight line so drawn, which is •within the triangle. Let ABC be a right-angled triangle, having the angle BAC a right angle; and let AD and AE, cutting CB in D, and CB produced in E, make equal angles with AB: CE is rut harmonically...

Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 σελίδες
...Prop. 47. 1. In any right angled triangle the square described on the hypothenuse is equal to both the squares described on the other two sides. Let ABC be a right angled triangle, having the right angle ACB, and let the squares AE, FC, Cl be described on the...

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 from A,...

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 to prove...

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 Mode of ...

James Bates Thomson - 1846 - 336 σελίδες
...principle in geometry, that the square described on the hypothenuse of a right-angled triangle, is equal to the sum of the squares described on the other two sides. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle ABC is 4 feet, and the perpendicular 3...




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