...motion, the space («) is the product (ct) of the velocity and the time, and in Geometry the area of a rectangle is equal to the product of the base by the altitude ; we can therefore represent the space described (s) by a rectangle ABCD, Fig. 52, whose base AB is...

...rectangle we mean the figure formed, and not the product of the lines. We will show hereafter that the area of the rectangle is equal to the product of the number of units in the two sides. 2. In every parallelogram the figure formed by either of the parallelograms...

...motion, the space («) is the product (ct) of the velocity and the time, and in Geometry the area of a rectangle is equal to the product of the base by the altitude ; we can there-fore represent the space described (s) by a rectangle ABCD, Fig. 52, whose base AB is...

...all such cases, as in the proposition above, and again, where it is demonstrated that the area of a rectangle is equal to the product of the base by the altitude, and elsewhere, the ancients had to resort every time to the reductio ad absurdum. It was something...

...with a strip of paper on the back. You have now changed the parallelogram into a rectangle, keeping the same base and altitude. As the area of the rectangle is the product of its base and altitude, this is also the area of the parallelogram. Draw the following...

...angles at E, F, and G are also rt. A. is a rectangle. Hence EFGH 6. Then, EFOH= GH x HE. (The area of a rectangle is equal to the product of the base by the altitude.) § 280. 7. GH= CD. (In any parallelogram the opposite sides are equal.) § 104. 8. Hence, QH=10. 9....

...formulas have been obtained : 1. The area of a square is equal to the square of one side. 2. The area of a rectangle is equal to the product of the base by the altitude. 3. The volume of a rectangular parallelopiped is equal to the product of the length by the height by...

...by 3, M = ab N~a'b'' But N is the unit of surface, then, — = M, and M = ab. That is, the area of a rectangle is equal to the product of the base by the altitude. 204. If two surfaces have the same area, they are equivalent THEOREM LII 205. Tlie area of a parallelogram...

...b the base, and h the altitude. In the form of a theorem this is stated as follows : The area of a rectangle is equal to the product of the base by the altitude. The formula, S = b • h, which was shown to hold for rational values of 6 and h, is also true when...

...(c) (d) (e) (f) (g) 83 36 69 21 . 57 73 86 By means of the theorem which states that the area of a rectangle is equal to the product of the base by the altitude. we may prove by a geometrical construction the truth of the above rule (141), and consequently of the...