## 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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**fore**the angles at B and C which are equal to the same thing D or F , are equal . Conversely , let the angles at B and C be equal , then the sides BA and AC are equal . Because it can be proved , that no part of AB can be equal to AC ... Page 20

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**fore**, if two triangles , & c . Q. E. D. PROP . XI . THEOREM . ( E. I. 34 ) The opposite sides and angles of a parallelogram are equal to one another , and the diagonal bisects it , that is , divides it into two equal parts . Let AC be ... Page 23

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**fore**GBCA is a parallelogram and AB being the diagonal , the parallelogram is double of the triangle ABC ( P. 11 ) . But the parallelogram BF is equal to the parallelogram GBCA ( P. 12 ) , and is therefore double of ABC . Where-**fore**if ... Page 32

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**fore**alternately BA to CA as EA to DA ( 16 , cor . 1 ) . Because DG is parallel to AB . Therefore CD to DA as CG to GB ( P. 17 ) . And , by composition , CD , DA together are to DA ; as CG , GB together are to GB ( 16 , cor . 2 ) , that ... Page 33

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**fore**the triangles AGC and AEC are equiangular ( P. 3 ) : viz . , the angle GAC is equal to the angle CAE , the angle AGC to the angle AEC and the angle ACG to the angle ACE . But it has been shown that the angles GAC , AGC and ACG are ...### 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.