## 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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**sector**of a circle is the figure contained by two radii and the arc , or part of the circumference , between them . [ ABF in figure : Prop . 2. is a**sector**. ] XII . A segment of a circle is the figure contained by a straight line or ... Page 9

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**sector**AFB coincides with the**sector**CFD . 1 For , if , AFB do not coincide with CFD , first , let a part of the radius FA fall beyond the arc CD . But that is impos- sible . Because ...**sector**AFB coincides with the**sector**CFD and ( 9 ) Page 10

Āryabhaṭa Jasoda Nauden Sircar. Therefore the

Āryabhaṭa Jasoda Nauden Sircar. Therefore the

**sector**AFB coincides with the**sector**CFD and the angle AFB and CFD coincide and are therefore equal ( Ax . 6 ) . In this way , it can be shown that the angles BFC and AFD are equal ... Page 72

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**sectors**. Let ABC , DEF be equal circles ; and at their centres the angles BGC , EHF , and the angles BAC , EDF at ...**sector**EHF . Take any number of arcs CX and XE , each A equal to BC ; and any number FM and MN , each equal to EF ... Page 73

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**sector**EHF . Place the circle DEN upon the circle ABE so that the radius HE may be on the radius GB and the arc EF ...**sector**BGE of the**sector**BGC . For the same reason , whatever multiple the arc EN is of the arc EF , the same multiple ...### 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.