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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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The Testimony of Reason

Samuel Louis Phillips - 1903 - 124 σελίδες
...nature and find that a square described on the hypothenuse of every right angle triangle is equivalent to the sum of the squares described on the other two sides ; that one of the functions of logarithms is that a high power of a number may be obtained by the multiplication...

Elements of Plane and Solid Geometry

Alan Sanders - 1903 - 392 σελίδες
...PROPOSITION XI. THEOREM 643. The square described on the hypotenuse of a rightangled triangle is equivalent to the sum of the squares described on the other two sides. Let ABC be a right-angled triangle. To Prove ~Bi? = AJ? + AC* Proof. Describe squares on the three...

A Text-book of Euclid's Elements for the Use of Schools, Βιβλίο 1

Euclid - 1904 - 488 σελίδες
...so as exactly to fill up the square DC. PROPOSITION 48. THEOREM. If the square described on one side of a triangle be equal to the sum of the squares described on the other two sides, then the angle contained by these two sides shall be a right angle. BC Let ABC be a triangle ; and...

Arithmetic for Business with Short Methods and Rapid Calculations in All ...

Jacob Henry Minick, Clement Carrington Gaines - 1904 - 412 σελίδες
...with the base. 438. To find the Hypotenuse. It is seen that the square described on the hypotenuse is equal to the sum of the squares described on the other two sides. Hence. RULE. — Add the square of the lose to the square of tJie perpendicular, and extract the square...

Exercises in Concrete Geometry: With Supplementary Discussions

David Sands Wright - 1906 - 104 σελίδες
...given triangles. 25. Theorem. The square described on the side of a triangle opposite an acute angle is equal to the sum of the squares described on the other two sides diminished by twice the product of one of those sides by the projection of the other side upon it....

Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - 1906 - 634 σελίδες
...Theorem or Pythagoras. — In any right triangle, the square described on the hypotenuse is equivalent to the sum of the squares described on the other two sides. Let ABC, Fig. 38, be a right triangle. Draw an equal triangle in the position C B' C', so that C B'...

Report of the Commissioner of Education Made to the Secretary of ..., Τόμος 1

United States. Bureau of Education - 1907 - 724 σελίδες
...another, and the diameter bisects the parallelogram — that is, divides it into two equal parts. 6. 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....

Annual Report, Τόμος 1

United States. Office of Education - 1907 - 720 σελίδες
...another, and the diameter bisects the parallelogram — that is, divides it into two equal parts. 6. 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....

Report of the Commissioner of Education Made to the Secretary of ..., Τόμος 1

United States. Bureau of Education - 1907 - 732 σελίδες
...another, and the diameter bisects the parallelogram — that is, divides it into two equal parte. 6. 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....

Woodworking for Beginners: A Manual for Amateurs

Charles Gardner Wheeler - 1907 - 594 σελίδες
...the squares of the two sides. (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.) You can measure the diagonal directly from a plan if you understand mechanical drawing well enough...




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