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" I label the two new points e and /." FIG. 2 With the help of this figure he then proceeds to the usual proof of the theorem that the area of a parallelogram is equal to the product of the base by the altitude, establishing the equality of certain lines... "
Principles of geometry, mensuration, trigonometry, land-surveying, and ... - Page 110
by Thomas Tate (mathematical master.) - 1848
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A Compendious Course of Mathematics, theoretical and practical

John Radford YOUNG - 1855 - 218 pages
...a parallelogram, and CE its altitude ; then, in the right-angled triangle AEC, we shall have _^* BO that the area of a parallelogram is equal to the product of any two adjacent sides multiplied by the sine of the angle between them. The trouble of finding the...
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Lessons on plane trigonometry

Edward Butler (A.M.) - 1862 - 154 pages
...sin C+cl.2— 20. The area of a parallelogram, whose sides and angles are known, will therefore be equal to the product of the two adjacent sides by the sine of the contained angle. 66. Given the three sides of a triangle, to find the area. From (65) T=Ja6 sin C,...
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New Practical Arithmetic in which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...TRIANGLES AND QUADRILATERALS. 416i By Geometry, may be proved, in relation to areas, the following 1. The area of a PARALLELOGRAM is equal to the product of the base by the altitude. MENSURATION. This has been shown to be the case with a rectangle (Art. 210),...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...denote the continued product of the number of linear units in each of the three lines. Thus, when we say that the area of a parallelogram is equal to the product of its base and altitude, we mean that the number of superficial units in the parallelogram is equal to...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...the continued product of the number of linear units in each of the three lines. Thus, -when we say that the area of a parallelogram is equal to the product of its base and altitude, we mean that the number of superficial units in the parallelogram is equal to...
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The Complete Arithmetic: Combining Oral and Written Exercises in a Natural ...

Albert Newton Raub - Arithmetic - 1877 - 348 pages
...following are the rules for the measurements of triangles: It was proved in Denominate Numbers (Art. 107) that the area of a parallelogram is equal to the product of its base and altitude, and since a triangle is half a parallelogram, we derive the following RULE....
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Complete Arithmetic: Theoretical and Practical

William Guy Peck - Arithmetic - 1877 - 430 pages
...what is its altitude ? Ans. 16 ft. AREA OF A PARALLELOGRAM. 285. It is shown in Geometry (B. 4, P. 3), that the area of a parallelogram is equal to the product of its base and altitude; that is, Area of parallelogram = Base x Altitude. EXAM PLE S. 1. The base of...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 348 pages
...two positions shown in the figure. Corollaries. — i. By combining this theorem with § 126, we see that the area of a parallelogram is equal to the product of its base by its altitude. 2. All parallelograms having equal bases and equal altitudes are equivalent....
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New Practical Arithmetic: In which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1880 - 370 pages
...QUADRILATERALS. 416. By Geometry may be proved, in relation to areas, the following PRINCIPLES. 1. The area of a PARALLELOGRAM is equal to the product of the base by the altitude. What is a Quadrilateral * A Parallelogram 1 A Rectangle 1 A Rhomboid 1 A Rhombus"...
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The Complete Arithmetic, Oral and Written, on the Basis of Works

Henry Bartlett Maglathlin - Arithmetic - 1882 - 398 pages
...rhombus ABCD is equal to the rectangle EEC F of the same base and altitude (Art. 218). I—A f D HenC6> The area of a parallelogram is equal to the product of the base and altitude. 9. What is the area of a parallelogram whose base is 36 feet and altitude 15 feet...
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