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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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Young Scientist: A Practical Journal for Amateurs, Τόμος 1

1851
...this proposition is known as the Pythagorean : the square described upon the hypothenuse is equivalent to the sum of the squares described on the other two sides. As the unit of measure for the determination of the superficial relations of figures, we use a square...

The University Arithmetic: Embracing the Science of Numbers, and Their ...

Charles Davies - 1852 - 408 σελίδες
...worthy of particular notice. 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 tria,ngle, right angled at C, then will the square D described on AB...

ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...right-angled triangle, right-angled at A : then will the square described on the hypothenuse BC be equivalent to the sum of the squares described on the other two sides, BA, AC. FGI H D Haying described a square on each of the three sides, let fall from A, on the hypothenuse,...

A Theoretical and Practical Arithmetic: Designed for Common Schools and ...

Daniel Leach - 1853
...sides the base and perpendicular. 293. The square described on the hypothenuse, or longest side, is equal to the sum of the squares described on the other two sides. Thus, suppose the longest side is 10 ft., the base 6 ft., and the perpendicular 8 ft. 10a=100. 6a=36....

The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New ..., Βιβλίο 1

Euclides - 1853
...described on the sides AB, AC, including the right angle. Which was to be proved. PEOP. XLVIII. THEOE. If the square described on one of the sides of a triangle he equal to the squares described on the other two sides : then the angle included by these two sides...

Elements of geometry and mensuration

Thomas Lund - 1854 - 192 σελίδες
...ofAB.' COB. The converse of this proposition is also true, viz. 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 between these two sides is a right angle.' Let ABC be a triangle,...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 432 σελίδες
...triangle, right•angled at A : then will the square described on the hypothenuse BC be equivalent to the sum of the squares described on the other two sides, BA, AC. 1 GEOMETRY. Having described a square on each of the three sides, let fall from A, on the hy•...

The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...BE is equal to the sum of the squares BG, C H. XLVII.— EUCLID I. 48. If the square described upon one of the sides of a triangle be equal to the sum of the squares described on the two other sides, the angle contained by these two sides is a right angle. Let ABC (Fig. 37) be a triangle...

Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...them into two equal parts. What distinction is there between a parallelogram and a rhomboid? 4. If a 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....

A Treatise on Arithmetic, Combining Analysis and Synthesis: Adapted to the ...

James Stewart Eaton - 1857 - 355 σελίδες
...or circumferences. FIG. 12. 6. 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. This will be seen by counting the small squares in the square of the hypothenuse and those in the squares...




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