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" The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. "
Elementary Geometry - Page 111
by William Chauvenet - 1893
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Practical Mechanics

John Perry - Machinery, Kinematics of - 1883 - 486 pages
...no matter what scale of measurement you use, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Area of a triangle. — Any side multiplied by its perpendicular distance from the opposite angle and...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...Suggestion. Draw the chords AC and CB. (p. II., Proposition XIV., Corollary.) ADB PROPOSITION X.—THEOREM. 28. The square of the length of the hypotenuse of...angled at C; then For, by Proposition IX., we have A~U* = AB X AD, and ~Etf = AB X BD, the sum of which is ZZ7* + :BZ7* = AB X (AD + BD) = ABxAB = 29....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...diameter, the perpendicular is a mean proportional between the segments of the diameter. PROPOSITION X. The square of the length of the hypotenuse of a right...lengths being expressed in terms of the same unit. PROPOSITION XI. If two chords intersect within a circle, their segments are reciprocally proportional....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...diameter, the perpendicular is a mean proportional between the segments of the diameter. PROPOSITION X. The square of the length of the hypotenuse of a right...lengths being expressed in terms of the same unit. PROPOSITION XI. If two chords intersect within a circle, their segments are reciprocally proportional....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1889 - 338 pages
...of the diameter. Suggestion. Draw the chords AC and CB. (v. II., Proposition XIV., Corollary.) ADB PROPOSITION X.— THEOREM. 28. The square of the length...the same unit. Let ABC be right angled at C; then -fFor, by Proposition IX., we have ZC 2 = AB X AD, and 27C ' ' = AB X the sum of which is 3T7 2 + ~BC2...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1891 - 336 pages
...of the same unit, the results just obtained may be written (5, Corollary) A~V*=ABX 277' = AB X BD. 27. COROLLARY. If from any point in the circumference...angled at C ; then For, by Proposition IX., we have ZT7' = AB X AD, and 1SV' = AB X BD, the sum of which is TC"' + :B7?* = AB X (AD + BD)=ABXAB='A~B\ 29....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1891 - 344 pages
...of the diameter. Suggestion. Draw the chords AC and CB. (v. II., Proposition XIV., Corollary.) A XI B PROPOSITION X.— THEOREM. 28. The square of the...angled at C; then For, by Proposition IX., we have A~U* = AB X AD, and ~Etf = AB X BD, the sum of which is 3T7' + -&? = AB X (AD + BD} =AB X AB =TB\ 29....
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An Academic Arithmetic for Academies, High and Commercial Schools

Webster Wells - Arithmetic - 1893 - 390 pages
...all ex- jr pressed in terms of the same unit, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. It follows from the above that In a right triangle, the square of either side about the right angle...
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Applied Mechanics: A Treatise for the Use of Students who Have Time to Work ...

John Perry - Mechanical engineering - 1897 - 724 pages
...no matter what scale of measurement you use, the square of the length of the hypothenuse is equal to the sum of the squares of the lengths of the other two sides. Area of a triangle. — Any side multiplied iks perpendicular distance from the opposite corner and...
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Machinists' and Draftsmen's Handbook: Containing Tables, Rules, and Formulas ...

Peder Lobben - Mechanical engineering - 1899 - 460 pages
...sides are called the base and perpendicular. The square of the length of the hypothenuse is equal to the sum of the squares of the lengths of the other two sides. ( See Fig. 5). a2 + b2 = c2 From this law the third side of a right-angled triangle can always be found,...
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