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" If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Σελίδα 120
των Thomas Perronet Thompson - 1833 - 150 σελίδες
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - 1878 - 209 σελίδες
...PYTHAGOREAN PROPOSITION. Theorem. The square described upon the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the other two sides. HYPOTH. In the triangle ABC ZB AC = R. To HE PROVED. BC- / \ n PROOF. On the sides of the triangle...

Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...of the triangle, and that nine times the square on DF is thirteen times the square on the hypo"nuse. PROPOSITION XLVIII. THEOREM. If the square described...on one of the sides of a triangle, be equal to the squares described on the other two sides of it ; the angle contained by these two sides is a right...

A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 σελίδες
...top of a wall on the opposite side 1 2 yards high ? • 48. Prove that if the square described upon one of the sides of a triangle be equal to the sum of the squares described upon the other two sides of it, the angle contained by these two sides is a right angle. Deductions....

Topographical Drawing and Sketching: Including Applications of ..., Τόμος 1

Henry Albert Reed - 1886 - 129 σελίδες
...the familiar principles 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 ; and that if a perpendicular be let fall from the vertex of the right angle to the hypothenuse, the...

The Bizarre Notes and Queries in History, Folk-lore, Mathematics ..., Τόμοι 3-4

1886
...them be found ? " 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." — Davics' Lfgeniire, Bk. iv, Prop. n. Was the Pythagorean harmony known as " The Music of the Spheres,"...

Elementary Psychology and Education

Joseph Baldwin - 1887 - 299 σελίδες
...President ; that the earth revolves around the sun ; that the square described on the hypotenuse is equal to the sum of the squares described on the other two sides of a right-angled triangle ; and we accept these conclusions as true. We assent to these conclusions ;...

Topographical Drawing and Sketching, Including Applications of ..., Τόμοι 1-2

Henry Albert Reed - 1888 - 26 σελίδες
...the familiar principles 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; and that if a perpendicular be let fall from the vertex of the right angle to the hypothenuse, the...

An Advanced Arithmetic, Theoretical and Practical

James William Nicholson - 1889 - 395 σελίδες
...to find the third side. THEOREM. — The square described on the hypothenuse of a right triangle is equal to the sum of the squares described on the other two sides. Hence, the square of cither side about the right angle is equal to the square of the hypothenuse diminished...

The Teachers' Psychology: A Treatise on the Intellectual Faculties, the ...

Adonijah Strong Welch - 1889 - 299 σελίδες
...and 8 inches long, the hypothenuse 10 inches; show that the square described on the hypothenuse is equal to the sum of the squares described on the other two sides, by dividing each of the three squares into small squares whose area is one inch each; then counting...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 σελίδες
...pieces of cardboard of the shapes, and arrange them in the several ways, here indicated. PROPOSITION 48. THEOREM. If the square described on one of the sides of a triangle be equal to the squares described on the other two sides, the angle contained by these two sides is a right angle....




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