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" In obtuse-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 greater than the squares of the sides containing the obtuse angle, by twice the... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 62
των John Playfair - 1819 - 333 σελίδες
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...to be done. PROP. XII. THEOR. In an obtuseangledtriangle, if a perpendicular be drawnfrom either of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle,...

The Elements of Euclid

Euclid - 1838 - 416 σελίδες
...square of AH : CKD PROP. Xn. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...twice the rectangle contained by the side upon which, wnen produced, the perpendicular falls, and the straight line intercepted without the triangle between...

The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...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...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...to be done. PROP. XII. THEOR. In obtuse-angled Mangles, if a perpendicular be dratcn from either of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. obtuse angle ACB, and from the...

Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...square of AH. QEF PROP. XII. THEOR. IN obtuse-angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...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...

Iron: An Illustrated Weekly Journal for Iron and Steel ..., Τόμος 38

Perry Fairfax Nursey - 1843
...EK 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...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...

Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 σελίδες
...done. PROPOSITION XII. THEOR. — In obtuse-angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle,...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...the squares of the sides containing the right angle ; but in an obtuse-angled triangle (Euc. n. 12), the square of the side subtending the obtuse angle is greater than the square of the side containing the obtuse angle ; and in an acute-angled triangle (Euc. n. 13), the...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...AH. « . E. v. PROP. XII. THEOR. In obtuse-angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted, without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle,...

The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...PROP. XLVII. THEOR. 12. 2 Eu . In obtuse angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. A Y str. line BD is divided into...




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