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Books Books 21 - 30 of 52 on In any triangle, the difference of the squares of the two sides w equal to the difference....
" In any triangle, the difference of the squares of the two sides w equal to the difference of the squares of the segments of the base, or of the two lines or distances included between the extremes of the base and the perpendicular. "
A Course of Mathematics: For the Use of Academies as Well as Private Tuition - Page 301
by Charles Hutton - 1812
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847
...if a line be drawn from the vertex perpendicular to the base, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. PART. ENUN. — Let ABC be any A ; from the vertex A draw AD X to the base BC; then the difference...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ...

Euclid, Robert Potts - Euclid's Elements - 1847 - 478 pages
...true; then by Euc. vi. 16, it follows that the difference of the squares of the sides of the triangle, is equal to the difference of the squares of the segments of the base ; and therefore the difference of the squares of one side and the adjacent segment of the base, is...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides - 1849
...if a line be drawn from the vertex at right angles to the base, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. 6. If from one of the acute angles of a right-angled triangle, a line be drawn to the opposite side,...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 320 pages
...Geometry, conducting as it does to the solution of so many important problems. PROPOSITION IX. THEOREM. In any triangle, the difference of the squares of...of the two lines or distances included between the extremities of the base and the perpendicular, drawn from the vertical angle to the base, or to the...
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MATHEMATICAL RECREATIONS: CONTAINIG SOLUTIONS OF MANY VERY DIFFUCULT AND ...

H.N. ROBINSON - 1851
...be drawn from the vertical angle of any triangle to the base, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. Let ABC be any triangle. Take the longer side as a base, and from the opposite angle let fall the perpendicular...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852
...if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. In any triangle, if a line be drawn from the vertex bisecting the base; the sum of the squares of the...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...to the difference of two given squares. 49. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular from the opposite angle. 50. The three straight lines bisecting the three angles...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Conic sections - 1865 - 444 pages
...be drawn from the vertical angle of any triangle to the base, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. 27. The square described on the side of an equilateral triangle, is equal to three times the square...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair, Euclid - Geometry - 1855 - 317 pages
...isosceles; BC2=2AB2=2AC2 ; therefore, BC = ABv/2. COR. 3. Hence, also, if two right angled triangles have two sides of the one, equal to two corresponding sides of the other ; their third side* will also be equal, and the triangles will be identical. PROP. XLVIII. THEOR. If tfie square...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 283 pages
...said hypothenuse and other side (th. 33). Corol. 2. Hence, also, if two right-angled triangles have two sides of the one equal to two corresponding sides...triangle, the difference of the squares of the two sides w equal to the difference of the squares of the segments of the base, or of the two lines or distances...
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