By G. H. Hardy
There could be few textbooks of arithmetic as recognized as Hardy's natural arithmetic. considering the fact that its booklet in 1908, it's been a vintage paintings to which successive generations of budding mathematicians have became before everything 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 elemental principles of the differential and crucial calculus, of the homes of limitless sequence and of alternative themes regarding the thought of restrict.
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2-2, AB does not seem to equal CD although it actually does. Fig. 2-2 Measurement cannot serve as proof. Measurement applies only to the limited number of cases involved. The conclusion it provides is not exact but approximate, depending on the precision of the measuring instrument and the care of the observer. In measurement, allowance should be made for possible error equal to half the smallest unit of measurement used. Thus if an angle is measured to the nearest degree, an allowance of half a degree of error should be made.
BD bisects /B. To Prove: /A Х /C Fig. 6) / 1 > / 2, BF > DE BF bisects /B. DE bisects /D. /B and /D are rt. To Prove: AB > CD (c) In Fig. 3-27: Given: BC > AD E is midpoint of BC. F is midpoint of AD. AB > CD, BF > DE To Prove: /A Х /C (d) In Fig. 3-27: Given: Fig. 3-27 45 CHAPTER 3 Congruent Triangles Given: (g) In Fig. 3-29: Given: CD > CЈDЈ, AD > AЈDЈ CD is altitude to AB. CЈDЈ is altitude to AЈBЈ. To Prove: /A Х /Ar ( f ) In Fig. 3-28: Given: BF and CE bisect each other. To Prove: BC > EF (h) In Fig.
2-4. POSTULATE 13: The length of a segment is the shortest distance between two points. Thus, AB is shorter than the curved or broken line segment between A and B in Fig. 2-5. Fig. 2-5 POSTULATE 14: Fig. 2-6 One and only one circle can be drawn with any given point as center and a given line segment as a radius. Thus, only circle A in Fig. 2-6 can be drawn with A as center and AB as a radius. POSTULATE 15: Any geometric figure can be moved without change in size or shape. Thus, ^ I in Fig. 2-7 can be moved to a new position without changing its size or shape.