Books Books 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... Elements of geometry, containing the first two (third and fourth) books of ... - Page 90
by Euclides - 1871 ## The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Mathematical Association of America - Mathematics - 2003 - 572 pages
...geometrical way, of course. Proposition 12 deals with the obtuse-angled triangle: In obtuse-angled triangles, the square on the side subtending the obtuse angle...the obtuse angle by twice the rectangle contained 207 by one of the sides about the obtuse angle, namely that on which the perpendicular falls, and the... ## Dedomena: Euclid's Data, Or, The Importance of Being Given

Euclid - Mathematics - 2003 - 276 pages
...a given ratio to the triangle. 165 Dt 64 If a triangle have a given obtuse angle, the area by which the square on the side subtending the obtuse angle is greater than [the sum oil the squares on the sides containing the given angle, [that area] will have a given ratio to... ## Euclid's Elements in Greek: Vol. I: Books 1-4

Richard Fitzpatrick - Mathematics - 2005 - 298 pages
...squares on С A and AB by twice the rectangle contained by С A and AD. Thus, in obtuse-angled triangles, the square on the side subtending the obtuse angle is greater than the (sum of the) squares on the sides containing the obtuse angle by twice the (rectangle) contained by... ## Annual Report of the Public Schools of the Province of British Columbia

British Columbia. Superintendent of Education - 1897 - 710 pages
...rectangle contained by the parts. 3. In obtuse-angled triangles, if a perpendicular lie drawn from either of the acute angles to the opposite side produced,...angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted, without the triangle,... ## The Thirteen Books of Euclib's Elements.

Euclid - 454 pages
...cutting a given straight line in extreme and mean ratio. PROPOSITION 1 2. In obtuse-angled triangles the square on the side subtending the obtuse angle...the obtuse angle by twice the rectangle contained by one of the sides about 'he obtuse angle, namely that on which the 26 — 2 perpendicular falls, and... ## Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - Mathematics - 1998 - 516 pages
...ie cannot be expressed in whole numbers (OM I, p. 369)." 12. =&mftm Heath In obtuse-angled triangles the square on the side subtending the obtuse angle...the obtuse angle by twice the rectangle contained by one of the sides about the obtuse angle, namely that on which the perpendicular falls, and the straight... ## Annual Report - Dept. of Education

Saskatchewan. Department of Education - Education - 1913 - 202 pages
...EFG are equal. 4-. (a) Prove that in an obtuse-angled triangle if a perpendicular be drawn from one of the acute angles to the opposite side produced,...side subtending the obtuse angle is greater than the sum of the squares on the other sides by twice the rectangle contained by the side on which, when produced,... ## The Surveyor, Volumes 21-22

Surveying - 1908 - 608 pages
...i у" - 4.x2 = 4.-K + 1 4. Show that in an obtuse angled triangle, if a perpendicular be drawn from either of the acute angles to the opposite side produced the square on the side opposite the obtuse angle is greater than the sum of the squares on the sides forming the obtuse angle... ## Examination,Midsummer,1879

Education Department - 1879 - 1136 pages
...angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite aide produced, the square on the side subtending the obtuse Angle is greater than the sum of the squares on the sides containing the obtu=e angle, by twice the rectangle contained by the... 