 | W. Hilton - Science - 1797 - 308 pages
...AL.LB. qED PROP. 11. • .» PROP. 11. BV N. Sim. The rectangle of the segments of the diameter HD.D£ is equal to the difference of the squares of the segments of the base EK,EL. • DEMONS. HD.DF^rDCJ=EK!,butHD.DF=HD.DE -f HD.EF, therefore HD.DE=EK'-HD.EF=EK2-EL' T/iro/t.... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...perpendicular be drawn from any angle of a triangle to the opposite side, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. Book IT. Let ABC be a. triangle, having the side AB greater than AC, and AD a perpendicular from the... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...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. 30. In any triangle, if a line be drawn from the vertex bisecting the base ; the sum of the squares... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 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. S From A the vertex of the triangle ABC, let AD be drawn perpendicular to the base ; the difference... | |
 | Euclides - 1821 - 294 pages
...fall on the opposite side, the difference between the squares of the sides which contain that angle, is equal to the difference of the squares of the segments of the sides on which the perpendicular falls. For the Q2 of one side is = to n1 of adjacent seg. »nd Q«... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...said hypothenuse and other side (th. 33). Coral. 2. Hence also, if two right-angled triangles have two sides of the one equal to two corresponding sides...of the two Sides, is Equal to the Difference of the Squnres of the Segments of the Base, or of the two Lines, or Distances, included between the Extremes... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...the problem to determine the triangle is indeterminate, because the difference of the squares of the sides is equal to the difference of the squares of the segments of the base, and may, therefore, be inferred from the base and the point of section. The geometrical circumstances... | |
 | John Playfair - Geometry - 1829 - 210 pages
...drawn from any angle of a triangle to the opposite side, the difference of the squares of the other two sides is equal to the difference of the squares of the segments of the base made by the perpendicular. For, bv the dem. AB3 — AC3 = BD3 — DC3. J CoB. 2. If a perpendicular... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...that is, to a right angle.* Therefore, &c. Cor. 1. In a right-angled triangle, the square of either of the two sides is equal to the difference of the squares of the hypotenuse and the other side. Cor. 2. It appears, from the demonstration, that if a perpendicular... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...isosceles; BC2=2AB2=2AC2; therefore, BC=ABV2. COR. 3. Hence, also, if two right angled triangles have two sides of the one, equal to two corresponding sides...third sides will also be equal, and the triangles will if, identical. PROP. XXXVIII. THEOR. If the square described upon one of the sides of a triangle,... | |
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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. 
