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" In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute... "
The Principles of Analytical Geometry ... - Page 1
by Henry Parr Hamilton - 1826 - 326 pages
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...angled triangles, úc. QED "4. S. •47. iS. l. b 7. 2. *7. i. * 16. i. ' it. t. PKOP. XIII. THEOR. IN every triangle, the square of the side subtending...contained by either of these sides, and the straight line intercopted between the perpendicular let fall upon it from the opposite angle, and the acute angle....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...than the squares of the fides containing that angle, by twice the rectangle contained by either ot these sides, and the straight line intercepted between the perpendicular let fall upon it from ttie opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...of the base of an isosceles triangle is the double of the rectangle contained by either side, and by the straight line intercepted between the perpendicular,...let fall upon it from the opposite angle, and the extremity of the base. (XIV.) If from any point, in the circumference of the greater of two given concentric...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...of the base of an isosceles triangle is the double of the rectangle contained by either side, and by the straight line intercepted between the perpendicular,...let fall upon it from the opposite angle, and the extremity of the base. If the vertical angle of the isosceles A be a right angle, the proof of the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...CA, by twice the rectangle BC, CD. Therefore, in obtuse angled triangles, &c. QED PROP. XIII. THEOR. IN every triangle, the square of the side subtending...sides, and the straight line intercepted between the perpendiculai let fall upon it from the opposite angle, and the acute angle.* Let ABC be any triangle,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...twice the rectangle BC, CD. Therefore, in obtuse angled triangles, &c. QED Proposition XIII. Theorem. In every triangle, the square of the side subtending...contained by either of these sides, and the straight line inteicepted between the perpendicular let fall upon it from the opposite angle, and the acute angle....
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...the base of an isosceles triangle, is equal to twice the rectangle contained by either side, and by the straight line intercepted between the perpendicular, let fall upon it from the opposite angle and the extremity of the base. 3. If the vertical angle of a triangle be two-thirds of a right angle, the square...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...D. PROPOSITION XIII. See N. THEOR. — In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the...of these sides, and the straight line intercepted bi-twecn the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...perpendicular falls, and the straight line intercepted between the perpendieu lar and the obtuse angle. XIII. In every triangle the square of the side subtending...sides, and the straight line intercepted between the perperdicular, let fall upon it from the opposite angle, and the acute angle. A. If one side of a triangle...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 254 pages
...the side subtending any of the acute angles is less than the squares of the sides containing the same angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular, drawn to it from the opposite angle, and the acute angle. SUBSTANCE OF SECTION VII. 1. Squares are...
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