 In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the...  The Element of Geometry - Page 29by John Playfair - 1836 - 114 pagesFull view - About this book
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square, of the side subtending the obtuse angle is...perpendicular falls, and the straight line intercepted between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle, having the obtuse... | |
 | Euclid - Geometry - 1838 - 470 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is...twice the rectangle contained by the side upon which, wnen produced, the perpendicular falls, and the straight line intercepted without the triangle between... | |
 | Euclides - 1840 - 82 pages
...In an obtuse-angled triangle, the square of the side subtending the obtuse angle exceeds the sum of the squares of the sides containing the obtuse angle, by twice the rectangle contained by either of those sides and the produced part of it intercepted between the perpendicular let fall on... | |
 | Euclides - Geometry - 1841 - 378 pages
...Mangles, if a perpendicular be dratcn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is...triangle between the perpendicular and the obtuse angle. obtuse angle ACB, and from the point A let AD be drawn* perpendicular to BC produced: the square of*... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is...perpendicular falls, and the straight line intercepted between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle, having the obtuse... | |
 | Euclides - 1842 - 316 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is...squares of the sides containing the obtuse angle, by twiee the rectangle contained by the side upon which, when produced, the perpendicular falls, and the... | |
 | Perry Fairfax Nursey - Industrial arts - 1843 - 538 pages
...also subtends the obtuse angle EPK of ihe triangle EPK, and by (12 Prop. 2 Book Eu.) it is.— " The square of the side subtending the obtuse angle is...obtuse angle, by twice the rectangle contained by one of the sides about the obtuse angle, and the line intercepted without by a perpendicular to it... | |
 | Education - 1844 - 688 pages
...angled-triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is...perpendicular falls, and the straight line intercepted between the perpendicular and the obtuse angle. 8. If two circles cut one another, they shall not have... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is...angle, by twice the rectangle contained by the side uponwhich, when produced, the perpendicular falls, and the straight line intercepted between the perpendicular... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...we find AB2=BC'+AC'+'^BCxCD). Hence, of the other two sides by twice the rectangle contained by that side upon which, when produced, the perpendicular falls, and the straight line intercepted between the perpendicular and the obtuse angle. Scholium. The right-angled triangle is the only one... | |
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