## The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar |

### From inside the book

Page 5

I. A point is

I. A point is

**that**which has**no**parts , or magnitude . II . ... A straight line is the shortest distance between**two points**. ... A**circle**is a plane figure bounded by one line , which is called the**circumference**, and is such**that all**... Page 7

Ivet ABCD be a

Ivet ABCD be a

**circle**and F its centre . Let AC a straight line pass through the centre and be terminated both ways by the**circumference**at the**points**A and C. AC divides the**circle**ABCD into**two**equal parts ABC and ADO . Page 8

Join FD , and produce FD to B. Because a

Join FD , and produce FD to B. Because a

**circle**is a plane figure bounded by one line and is such**that all**straight ... 6 ) , therefore**all**the straight lines drawn from F to the different**points**in the**circumference**ABCD are equal ... Page 66

... if not , let L be without the

... if not , let L be without the

**circle**.**Take any point**D in the arc intercepted between AL and CL . ... Therefore the**circumference**will pass through the**point**L. And a**circle**can be described about the quadrilateral figure ABCL . Page 75

In the same manner it may be demonstrated ,

In the same manner it may be demonstrated ,

**that**the**two**sides AB , BC are greater than CA , and the**two**sides BC ... If from**any point**without a**circle**, straight lines be drawn to the**circumference**; of those which fall upon the ...### What people are saying - Write a review

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### Common terms and phrases

AC is equal alternate angle ABC angle ADB angle BAC angles are equal arc BC base BC bisected centre circle circumference coincide conversely described diameter divided double draw drawn equal angles equal Ax equal to AC equiangular equimultiples Euclid exterior angle extremities fall figure fore fourth Geometry given straight line greater homologous interior Join less Let ABC magnitudes meet multiple opposite angles parallel parallelogram parallelogram AC pass perpendicular Place polygon produced PROP propositions proved Q.E.D. PROP radius reason rectangle contained rectilineal figure right angles sector segment semicircle shown side BC sides similar square stand straight line taken THEOREM thing third angle touches the circle triangle ABC twice Wherefore

### Popular passages

Page 12 - If two triangles have two sides of the one equal to two sides of the...

Page 41 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 5 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Page 42 - ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.

Page 76 - Any two sides of a triangle are together greater than the third side.

Page 49 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Page 57 - ... figures are to one another in the duplicate ratio of their homologous sides.

Page 64 - ... in a segment less than a semicircle, is greater than a right angle...

Page 61 - The angles in the same segment of a circle are equal to one another.