Rekhaganit

The book "Rekhaganit" by Atmaram Babu is a geometry textbook written in Hindi, intended for students in vernacular and normal schools. It is based on Euclid's Elements, with a focus on simplifying the language and providing clear explanations, especially for definitions.

Key features of the book include:

• Euclidean Basis: The text adheres to Euclid's foundational principles of geometry, acknowledging its enduring importance in academic curricula.
• Simplified Language: The author has strived to make the complex terminology of geometry accessible by simplifying the style and providing extensive explanations where technical terms are unavoidable.
• Multiple Proofs: For many propositions, additional proofs are offered, including direct methods where Euclid used indirect proofs (reductio ad absurdum). This aims to cater to different learning capacities.
• Added Content: The book includes new corollaries, exercises, and annotations to supplement Euclid's work, acting as a running commentary.
• Classified Index: A methodical index is provided to help students quickly find propositions related to specific topics, addressing a common criticism of the original Elements.
• Multilingual Terminology: A glossary is included, listing technical terms with their English, Hindi, and Urdu equivalents.
• Target Audience: The book is specifically designed for students preparing for the Normal School Certificate and the Middle Class Vernacular Examination in the North-Western Provinces and Oudh.
• Historical Context: The preface mentions Euclid as a renowned mathematician who established a school of mathematics and whose work became synonymous with geometry.
• Structure: The book is organized into chapters, starting with definitions and then moving on to propositions (Saadhya) and axioms (Avadhyopkram) and postulates (Swayamsiddhi). The propositions are classified as "Vastupadya" (constructive) and "Pramayopadya" (demonstrative).
• Practical Application: The text emphasizes the importance of geometry in measurement and understanding the relationships between geometric figures.
• Jain Connection: While the core content is Euclidean geometry, the publication is associated with the Shri Mahavir Jain Aradhana Kendra and Acharya Shri Kailassagarsuri Gyanmandir, indicating its use within the Jain educational framework.

The book covers fundamental geometric concepts like points, lines, surfaces, angles (right, obtuse, acute), circles, triangles (equilateral, isosceles, scalene, right-angled, obtuse-angled, acute-angled), quadrilaterals (square, oblong, rhombus, rhomboid, parallelogram, trapezium), and polygons. It meticulously defines each term and presents theorems and their proofs. The book also includes detailed exercises and questions at the end of chapters to test student comprehension.

The latter part of the text includes detailed proofs for numerous propositions and exercises, covering various geometric constructions and theorems, including those related to triangles, parallel lines, areas, and proportions, with a strong emphasis on the logical progression of geometric reasoning.