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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... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Strona 62
autor: John Playfair - 1819 - Liczba stron: 333
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...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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Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - Liczba stron: 186
...triangle the square of the side subtending an acute angle is less than the sum of the squares of the two sides containing that angle, by twice the rectangle contained by either of those sides and the distance between the acute angle and the perpendicular drawn from the opposite...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - Liczba stron: 272
...21 (б) In every triangle, the square of the side which is opposite to a given angle is greater or less than the squares of the sides containing that...rectangle contained by either of these sides, and that part of it which is intercepted between the perpendicular, let fall upon it from the opposite...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...See N. THEOR. — In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that...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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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...13.) In every triangle, the square of the side which is opposite to any given angle, is greater or less than the squares of the sides containing that...rectangle, contained by either of these sides, and that part of it, which is intercepted between the perpendicular let fall upon it from the opposite...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - Liczba stron: 472
...obtuse angle. XIII. In every triangle the square of the side subtending any of the acute angles, is less than the squares of the sides containing that...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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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - Liczba stron: 88
...PROPOSITION XIII. Theorem. In every triangle, the square of the side -btending any of the acute angles is less than the squares of the sides containing that...upon it from the opposite angle, and the acute angle. Fig. 1. Fig. 3. Steps of the Demonstration to Case 1st. (in which AD falls within the A.) 1. Prove...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - Liczba stron: 240
...is greater than the squares of BC, CA, by twice the rectangle BC • CD. PROPOSITION XIII. THEOREM. of these sides, and the straight line intercepted...from the opposite angle, and the acute angle. Let ABC he any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - Liczba stron: 215
...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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The Elements of Euclid

Euclid - 1838 - Liczba stron: 416
...PROP. XIII. THEOR. In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that...from the opposite angle and the acute angle.* Let BBC be any triangle, and the angle at B one of its acute angles, and upon BC one of the sides containing...
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