By G. H. Hardy
There will be few textbooks of arithmetic as famous as Hardy's natural arithmetic. considering the fact that its e-book in 1908, it's been a vintage paintings to which successive generations of budding mathematicians have grew to become initially in their undergraduate classes. In its pages, Hardy combines the keenness of a missionary with the rigor of a purist in his exposition of the basic rules of the differential and essential calculus, of the homes of endless sequence and of different issues related to the concept of restrict.
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8. Find the area of each of the right triangles whose sides are given as follows. The hypotenuse is represented by c and the legs are represented by a and b. (a) a = 4", b = 6.... (d) a = 15", c = 17". (g) a = 1", b = t". (b) a = 4", b = 5". (e) b = 4", c = 8t". (h) a = 41", b = 41". (c) b = 12", c = 13". (f) a = 20", c = 21". 9. The lengths of the parallel bases a and b and the altitude h of a trapezoid are given as indicated below. Find the area of the trapezoid. (a) a = 4", b = 6", h = 2". (d) a = 40 ft, b = 4 rods, h = 10yds.
D) a = 40 ft, b = 4 rods, h = 10yds. (b) a = 2', b = 16", h = 10". 9". (c) a = 3 ft, b = 10 ft, h = 5 ft. 01'. /2 ft, h = 3V2 ft. 12. Second Test for Congruence of Triangles. An alternate test for the congruence of two triangles is stated in the following theorem. THEOREM 5. Two triangles are congruent if the two angles and the included side of one are equal, respectively, to the I--.... CONGRUENCE OF TRIANGLES two angles and the included side of the other. ) The proof of this theorem follows by the method of superposition similar to that used in the proof of Theorem 3 and is left as an exercise for the student.
An angle can be bisected by one and only one line. 8. Through a given point there is only ·one line parallel to a given line not on the given point. ) 9. A geometric figure can be moved about freely without change in form or size. 10. Two circles having equal radii are equal. n. A diameter divides a circle into two equal parts. 12. Corresponding parts of congruent figures are equal. 6. Necessary and Sufficient Conditions. can be demonstrated that In algebra it I. if ~ = ~, then ad = be, b ~ 0, d ~ 0; and b d II.
A course of pure mathematics by G. H. Hardy