| W. Hilton - Science - 1797 - 5 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 - Euclid's Elements - 1806 - 311 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 - 377 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
...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 - 618 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 - 324 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 - 186 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 - 316 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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