Geometry with Trigonometry
xx Glossary oblong<Loblongus, longish. obtuse<Lobtusus, blunted (perf. partic. ofob- tundere, to blunt). orthogonal<Gko ...
1 Preliminaries 1.1 Historicalnote............................. This is one in a long line of textbooks on geometry. While all c ...
2 Preliminaries Ch. 1 between them were worked out. Among prominent countries,The Elementslasted longest in its original style i ...
Sec. 1.2 Note on deductive reasoning 3 mathematical words. 1.2 Noteondeductivereasoning...................... The basic idea of ...
4 Preliminaries Ch. 1 vice versa. But we must havesomeaxioms to get an approach under way. 1.3 Euclid’sThe Elements............. ...
Sec. 1.3 Euclid’sThe Elements 5 AnOBTUSE ANGLEis that which is greater than a right angle. AnACUTE ANGLEis that which is less t ...
6 Preliminaries Ch. 1 ARHOMBUSis that which has all its sides equal, but its angles are not right angles. ARHOMBOIDis that whic ...
Sec. 1.3 Euclid’sThe Elements 7 If equals be added to equals the wholes are equals. If equals be taken from equals the remainde ...
8 Preliminaries Ch. 1 1.3.6 Quantities or magnitudes The Elementsspoke of one segment (then called a line) being equal to or gre ...
Sec. 1.4 Our approach 9 1.4 Ourapproach 1.4.1 Typeofcourse............................. Very scholarly courses in geometry assum ...
10 Preliminaries Ch. 1 1.5 Revisionofgeometricalconcepts 1.5.1 As part of the preliminary programme, we now include a review of ...
Sec. 1.5 Revision of geometrical concepts 11 A B Figure 1.3. A half-line[A,B. A B C Opposite half-lines. If the pointsB,Ca ...
12 Preliminaries Ch. 1 A B C Figure 1.6. An interior region. A B C The corresponding exterior region. If|BACis a non-stra ...
Sec. 1.5 Revision of geometrical concepts 13 in triangles, we could take|BAC=[A,B∪[A,C. However whenAis betweenBand C, this woul ...
14 Preliminaries Ch. 1 H 5 is called atriangle. The pointsA,B,Care called itsverticesand the segments [B,C],[C,A],[A,B]itssides. ...
Sec. 1.5 Revision of geometrical concepts 15 A B D C Figure 1.12. A convex quadrilateral. 1.5.3 Distance; degree-measure of an a ...
16 Preliminaries Ch. 1 With each wedge-angle∠BACwe associate a non-negative number, called its degree-measure, denoted by|∠BAC| ...
Sec. 1.5 Revision of geometrical concepts 17 A B C P D Figure 1.17. Mid-line of an angle-support. C A B P D Any angle∠BA ...
18 Preliminaries Ch. 1 then[A,B,C]is congruent to[A′,B′,C′]. This is known as the ASA (angle, side, angle) condition for congrue ...
Sec. 1.6 Pre-requisites 19 A B C D T Figure 1.22. A parallelogram. A B C D T A rectangle. 1.6 Pre-requisites Although this book ...
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