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" ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse... "
Woolwich Mathematical Papers for Admission Into the Royal Military Academy ... - Σελίδα 2
επεξεργασία από - 1901
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 σελίδες
...AB.BH is equal to the square of AH. Which was to be done, Book II. PROP. XII. THEOR. IN obtuse angled triangles if a perpendicular be drawn from either...acute angles to the opposite side produced, the square of the side subtending the obtuse aigle is greater than the squares of the sides contain ng the obtuse...

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

Robert Simson - 1827 - 546 σελίδες
...rectangle AB, BH is equal to the square of AH. Which was to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from either...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...

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

Euclides - 1834 - 518 σελίδες
...the rectangle AB, BH is equal to the square of AH. Which was to be done. PROPOSITION XII. THEOR. — In obtuse-angled triangles, if a perpendicular be...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...

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

Euclides - 1837 - 112 σελίδες
...ie, fig FK = AB% ie, fig. AD, 4. that FH = HD, 3. that .'. AS x BH = AH*. PROPOSITION XII. Theorem. In obtuse-angled triangles, if a perpendicular be...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...

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

Charles Reiner - 1837 - 254 σελίδες
...subtending the right angle is equal to the sum of the squares of the sides containing the right angle. 10. In obtuse-angled triangles, if a perpendicular be...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...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 σελίδες
...Which was 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 square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse...

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

Euclides - 1841 - 378 σελίδες
...AH. Which was 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 square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse...

The British Annals of Education for ...: Being The Scholastic ..., Τόμοι 1-2

1844 - 688 σελίδες
...between the points of section, is equal to the square of half the line. 7. 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...

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

Euclides - 1845 - 546 σελίδες
...divided in H, so that the rectangle AB, BH is equal to the square of AH. QE r. PROPOSITION XII. THEOREM. In obtuse-angled triangles, if a perpendicular be...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...

The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846 - 128 σελίδες
...2a(a+ &) + £". Or(rt -|- b)" + b t =2b(a + b+ a 8 . PROP. XLVII. THEOR. 12. 2 Eu . In obtuse angled triangles, if a perpendicular be drawn from either...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...




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