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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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A Treatise on Special, Or Elementary Geometry

Edward Olney - 1872 - 239 σελίδες
...346. COR.. 3. — .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. DEM.— From Cor. 1, AC" = AB x AD and also CBa = AB x DB. Therefore, adding, AC4 + CB =AB (AD + DB)...

A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - 1872 - 84 σελίδες
...PYTHAGOREAN PROPOSITION. 668. 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. Fio. 372. 1st METHOD.—Let ABC be the given triangle, and ACED the square described on the hypotenuse....

A Treatise on Special Or Elementary Geometry, Τόμοι 1-2

Edward Olney - 1872
...compared? 346. COR. 3. — 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. DEM.— From Oar. 1, AC* = AB x AD and also CB* = AB x DB. Therefore, adding, AC* + CB* =AB (AD + DB)...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 368 σελίδες
...PROPOSITION X.— THEOREM. 25. The square described upon the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides. ia a Let the triangle ABC be right angled at C; then, the square AH, described upon the hypotenuse,...

New Elementary Geometry: With Practical Applications; a Shorter Course, Upon ...

Benjamin Greenleaf - 1873 - 176 σελίδες
...EQ THEOREM IX. 195. 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 ABC be a right-angled M triangle, having the right angle at A . then the square described on the...

The Bombay university calendar, Τόμος 1

Bombay city, univ - 1874
...unlimited length, from a given point without it. 2. Show that if the square described on one of the sides 8 of a triangle be equal to the sum of the squares described on the other two sides of it, the anglo contained by these two sides is a right angle. 3. In every triangle the square on the side subtending...

A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...that the area of the triangle on the hypotenuse is equal to the area of the other two. PROPOSITION 48. THEOREM. If the square described on one of the sides of a triangle be equal to the squares- described on the ether two sides of it, the angle contained by these two sides is a right...

Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...bisectors of two consecutive angles of a quadrilateral is half the sum of the two remaining angles. 5. 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....

Euclidian Geometry

Francis Cuthbertson - 1874 - 349 σελίδες
...the square on PR. Similarly it may be proved that the O QC is = the square on RQ; PROPOSITION XXXVI. 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 those sides is a right angle....

Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 455 σελίδες
...proved. c PROPOSITION XI. THEOREM. 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. , Let ABC be a triangle, right-angled at A : then will SO* = AS2 + AC2. Construct the square BG on...




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