## The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |

### From inside the book

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**equal**parts . Let 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 ADC . A ... Page 8

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**equal**( Ax . VI ) . But if ADC do not coincide with ABC , let them stand as indicated . Join FD , and produce FD to ...**AC**and BD cut one another at the point F. The vertical or opposite angles AFB and CFD are**equal**to one another , and ... Page 9

Āryabhaṭa Jasoda Nauden Sircar. Because

Āryabhaṭa Jasoda Nauden Sircar. Because

**AC**is a diameter , therefore it divides the circle ABCD into two**equal**parts ...**the same**thing are**equal**( Ax . 5. ) Therefore ABC and BCD are**equal**. Take away the common part BFC and the ... Page 10

... equal ( Ax . 6 ) . In this way , it can be shown that the angles BFC and AFD are equal . Wherefore , if two angles ...

... equal ( Ax . 6 ) . In this way , it can be shown that the angles BFC and AFD are equal . Wherefore , if two angles ...

**AC equal**to the two sides DE , DF , each to each ; that is , AB to DE , and AC to DF ; and the angle BAC equal to the ... Page 11

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**equal**to DE . And AB coinciding with DE ,**AC**shall coincide with DF , because the angle BAC is**equal**to the angle EDF . Also , the point C shall coincide with the point F , because AB is**equal**to DF . But the point B was proved to coin ...### Common terms and phrases

AB is equal AC is equal angle ABC angle ADB angle BAC angle DEF angle EDF angles are equal arc BC base BC base CD bisected centre circle ABCD circumference coincide conversely diameter draw duplicate ratio equal angles equal Ax equal to AC equiangular equimultiples Euclid exterior angle figure described fore given straight lines greater Hindoo Geometry homologous isosceles triangle Join Let ABC mean proportionals multiple opposite angles parallel parallelogram AC perpendicular point F polygon produced Q. E. D. Cor Q.E.D. PROP rectangle contained rectilineal figure regular polygon remaining angle right angles sector BGC sector EHF segment semicircle side BC square of BC straight line &c THEOREM third angle touches the circle triangle ABC Wherefore whole angle

### Popular passages

Page 10 - If two triangles have two sides of the one equal to two sides of the...

Page 39 - 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 40 - ... 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 79 - THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD ; the.

Page 74 - Any two sides of a triangle are together greater than the third side.

Page 47 - 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 53 - ... figures are to one another in the duplicate ratio of their homologous sides.

Page 62 - ... in a segment less than a semicircle, is greater than a right angle...

Page 59 - The angles in the same segment of a circle are equal to one another.