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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 Columbian Cyclopedia, Τόμος 15

1897
...side opposite the right angle. The well-known property of the H., that the square described on it is equal to the sum of the squares described on the other two sides, is proved in the famous 47th proposition of the first book of Euclid's Elements, and has, in the sixth...

The Standard American Encyclopedia of Arts, Sciences, History ..., Τόμος 4

John Clark Ridpath - 1897
...opposite to the right angle. The well-known property of the II., that the square described on it is equal to the sum of the squares described on the other two sides, is proved in the famous 47th proposition of the first book of Euclid's Element». Hypothecation, the...

The People's Standard History of the United States: From the ..., Τόμος 4

Edward Sylvester Ellis - 1897
...problem of Euclid, or pans asiuomm (the square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides). ':;' PERIOD VII THE NEw UNITED STATEs 1865 The President's Cabinet Assassination of the President Garfield...

Report of the Superintendent of Public Instruction

Michigan. Department of Public Instruction - 1898
...the proposition in geometry: "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." The reasoning powers are not applied in reaching a conclusion here; and, as a general rule, the proposition...

Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898
...times the given triangle. 4. The square described on the hypothenuse of a right triangle is equivalent to the sum of the squares described on the other two sides. 5. Of all triangles having the same base and equal perimeters, the isosceles triangle is the maximum....

Yale University Entrance Examinations in Mathematics: 1884 to 1898

1898 - 208 σελίδες
...times the given triangle. 4. The square described on the hypothenuse of a right triangle is equivalent to the sum of the squares described on the other two sides. 5. Of all triangles having the same base and equal perimeters, the isosceles triangle is the maximum....

Report of the Committee of Council on Education in Scotland...[without Appendix]

1899
...POJt, QOS are equal in area, prove that PS is parallel toBQ. 4. If the square described on one side of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by these sides is a right angle. Hence show that if the lengths of the three sides...

Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 340 σελίδες
...rightangled triangle, two of whose sides are OC and CD ; that is, AB and BC. Lesson No. 22 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 of it, the angle contained by these two sides is a right angle....

SYLLABUS OF PROPOSITIONS IN GEOMETRY

1899
...perimeters. THEOREM VIII. The square described on the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides. BOOK V. REGULAR POLYGONS AND THE MEASURE OF THE CIRCLE. THEOREM I. An equilateral polygon inscribed...

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

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 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...




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