 | George Roberts Perkins - Geometry - 1847 - 326 pages
...hypothenuse and other side (B. II, Prop. vn). Cor. 2. Hence, also, if two right-angled triangles have two sides of the one equal to two corresponding sides of the other, their third sides will be equal, and the triangles themselves equal. Cor. 3. The square on the diagonal of a square is double... | |
 | Euclides - 1847 - 128 pages
...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... | |
 | Euclid, Robert Potts - Euclid's Elements - 1847 - 118 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... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...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,... | |
 | George Roberts Perkins - Geometry - 1850 - 332 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... | |
 | Horatio Nelson Robinson - Mathematics - 1851 - 96 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. Let ABC be any triangle. Take the longer side as a base, and from the opposite angle let fall the perpendicular... | |
 | Euclides - 1852 - 152 pages
...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... | |
 | Euclides - 1862 - 140 pages
...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... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 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... | |
 | John Playfair - Geometry - 1855 - 350 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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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. 
