## 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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**angle**, and to allude as having found in a previous work , a straight line ...**third**, fourth and sixth books being not progressively founded upon each ...**3rd**book or the tenth in the fourth ) , but they rather contribute to puzzle the ... Page 10

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**angle**AFB and CFD coincide and are therefore equal ( Ax . 6 ) . In this way ...**third**sides are equal the two triangles are equal and their other**angles**are ...**angle**BAC equal to the**angle**EDF . Then the equal to the base EF ; the ... Page 19

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**third angle**of the one to the**third angle**of the other . Let ABC , DEF be two triangles which have the two angles ABC and BCA of the one equal to the two angles DEF , EFD of the other , each to each ; viz . , ABC to DEF and BCA to EFD ... Page 20

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**third angle**BAC is equal to the**third angle**EDF . Apply the triangle DEF to the triangle ABC ; so that the side DE may be on the side AB and the angle DEF coincide with the angle ABC . Therefore the side EF is placed on the base BC and ... Page 21

... angle ABD is equal ( P. 7 ) to the alternate angle BDC . Because AD is parallel to BC , and BD meets them , the ...

... angle ABD is equal ( P. 7 ) to the alternate angle BDC . Because AD is parallel to BC , and BD meets them , the ...

**third angle**of the one is equal to the**third angle**of the other ( P. 10 ) ; viz . , the side AB to the side CD , the side ...### 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.