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" The area of a triangle is equal to half the product of its base by its altitude. "
Elements of Geometry and Trigonometry - Page 100
by Adrien Marie Legendre - 1863 - 455 pages
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Library of Useful Knowledge: Natural philosophy, Volume 3

1834 - 578 pages
...Si t, being very small, differs insensibly from the straight line joining the points s, t ; and the area of a triangle is equal to half the product of its base, and the perpendicular from its vertex. Again, the angle t E s, being very small, the perpendicular...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...Schol.); therefore the area of the parallelogram ABCD is equal to AB X AF. PROPOSITION VI. THEOREM. The area of a triangle is equal to half the product of its base by its altitude. For, complete the parallelogram ABCE. The triangle ABC is half of the parallelo-...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 pages
...other, as A x C : BxC: that is, as A : B. GEOMETRY. Areta of Triangles and Trapezoids. THEOREM IX. The area of a triangle is equal to half the product of its base by its altitude. Let ABC be any triangle and CD its altitude : then will its area be equal to...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...altitude, then they will be to each other, as GEOMETRY. Areas of Triangles and Trapezoids. THEOREM IX. The area of a triangle is equal to half the product of its base by its altitude. Let AE C be any triangle and CD its altitude : then will its area be equal to...
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Elements of Analytical Geometry and of the Differential and Integral Calculus

Elias Loomis - Calculus - 1851 - 296 pages
...and the area equals fxy. If n=1, the figure becomes a triangle, and the area equals %xy; that is, the area of a triangle is equal to half the product of its base and perpendicular. Ex. 3. It is required to find the area of a circle. The equation of the circle,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...generally, are to each other- as the products of their bases and altitudes. PROPOSITION VI. THEOEEM. The area of a triangle is equal to half the product of its base and altitude. For, draw CE parallel to BA, and AE parallel to BC, completing the parallelogram...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...generally, are to each other as the products of their bases and altitudes. PROPOSITION VI. THEOREM. The area of a triangle is equal to half the product of its base and altitude. Let BAC be a triangle, and AD perpendicular to the base: then will its area be equal...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1855 - 340 pages
...each other, as AXC BxC: that is, as A : BGEOMETRYAreas of Triangles and Trapczoids1) THEOREM IX% The area of a triangle is equal to half the product of its base by its altitudeLet ABC be any triangle and CD its altitude : then will its area be equal to hall'...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...have the same ratio that their equimultiples have (Prop. VIII., B. II.). PROPOSITION VI. THEOREM. The area of a triangle is equal to half the product of its base by its altitude. Let ABC be any triangle, BC its base, and AD its altitude ; the area of the triangle...
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Elements of Analytic Geometry and of the Differential and Integral Calculus

Elias Loomis - Calculus - 1859 - 320 pages
...parabola, and the area equals \xy. If n=l, the figure becomes a triangle, and the area equals that is, the area of a triangle is equal to half the product of its base and perpendicular. Ex. 3. It is required to find the area of a circle. The equation of the circle,...
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