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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 of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...equal to the square of AH. Which was to be done. PROPOSITION XII. THEOREM. In obtuse angled triangles, the square of the side subtending the obtuse angle is greater than the squares, which are made by the sides containing the obtuse angle by twice the rectangle contained under one...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...twice the rectangle contained by the side upon which, vchen produced, the perpendicular Jails, and the straight line intercepted without the triangle between...

Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 σελίδες
...in all respects. In any obtuse-angled triangle, if a perpendicular be drawn from either of the two acute angles to the opposite side produced, the square...side subtending the obtuse angle is greater than the sum of the squares of the sides containing it by twice the rectangle under the base and the distance...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 σελίδες
...was to be done. 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 wit/tout the triangle between the perpendicular and the obtuse angle. Book II. 12. I. U4. 2. c 47....

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

Robert Simson - 1835 - 513 σελίδες
...ivan to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...side upon which, when produced, the perpendicular fulls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...

The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, tht square of the side subtending the obtuse angle, is...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle,...

A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 σελίδες
...AH*. PROPOSITION XII. Theorem. 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. Obs. This proposition is so short,...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...AH. PROPOSITION XII. THEOREM. Iii 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,...

Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 σελίδες
...containing the right angle. 10. 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. 11. In acute-angled triangles,...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 σελίδες
...was to be done. 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,...




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