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" ... any two triangles are to each other as the products of their bases by their altitudes. "
An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in ... - Page 80
by Francis Joseph Grund - 1834 - 190 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...Now, &ABC= \EHASEC. 220 But ED ABEC = axb. 229 Hence &.ABC = I a X b. QED 232. COR. 1. — Two triangles are to each other as the products of their bases by their altitudes. COR. 2.— Two triangles having equal bases are to each other as their altitudes. COR. 3....
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 228 pages
...area of a triangle Is half the product of the base multiplied by the height. Consequently airy two triangles are to each other as the products of their bases by their heights. 161. If we designate the height of a rectangle by #, and the base by 6, the area will be expressed...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...CG is the product of the base of the rectangle CEFG by its height. Therefore — Two rectangles are to each other as the products of their bases by their heights. 159. It is usual to estimate areas by square feet, square yards, square rods, &c. By a square foot,...
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...the same parallels are equal; because if they are between the same parallels their heights must be equal; and we have the same case as in the last query;...areas of triangles are to each other as the products obtained by multiplying the length of their bases by their heights; for these products are the areas...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 542 pages
...weight can be supported by 2J pounds acting at the end of an arm 4 inches long ? Ans. 2/j pounds. (5) Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 and 18, and their altitudes as 21 and...
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New Elementary Algebra: in which the First Principles of Analysis are ...

Benjamin Greenleaf - 1863 - 338 pages
...x ? Ans. x = 57. 5. If a -f- x : a — x : : 11 : 7, what is the ratio of a to x '! Ans. 9 : 2. 6. Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 to 18, and their altitudes as 21 to 23...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...other as their bases ; triangles having equal bases are to each other as their altitudes ; and any two triangles are to each other as the products of their bases by their altitudes. PROPOSITION VI.— THEOREM. 17. The area of a trapezoid is equal to the produet of its altitude...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...other as their bases; triangles having equal bases are to each other as their altitudes; and any two triangles are to each other as the products of their bases by their altitudes. PROPOSITION VI.—THEOREM. 17. The area of a trapezoid is equal to the product of its altitude...
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Mensuration of lines, surfaces, and volumes

David Munn - 1873 - 160 pages
...each other as their bases ; triangles having equal bases are toeach other as their altitudes, and two triangles are to each other as the products of their bases by their altitudes. PROP. IV. — To find the area of a triangle, -when the three sides are given. In the triangle...
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New Elementary Algebra: Designed for the Use of High Schools and ..., Book 1

Benjamin Greenleaf - Algebra - 1879 - 348 pages
...of x ? Ans. x = 57. 5. If a -f- x : a — x : : 11 : 7, what is the ratio of a to x ? Ans. 9 : 2. 6. Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 to 18, and their altitudes as 21 to 23...
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