## 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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Āryabhaṭa Jasoda Nauden Sircar. of these angles is called a right angle , and the straight line which stands on the ...

Āryabhaṭa Jasoda Nauden Sircar. of these angles is called a right angle , and the straight line which stands on the ...

**exterior angle**is greater than either of the interior opposite angles , Let ABC be a triangle , and its side BC ... Page 16

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**exterior angle**AEF is greater ( P. 6 ) than its in- terior and opposite angle EFG . But the angle AEF is equal ( Hyp . ) to the angle EFG . Therfore the angle AEF is both greater than , and equal to the angle EFG ; which is impossible ... Page 17

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**exterior angle**is equal to the interior apposite angle or the two interior angles are together equal to two right angles ; the two straight lines are parallel . Let EF fall upon AB , CD which are parallel . The**exterior angle**EGB is ... Page 22

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**exterior angle**FDC is equal ( I. 8 ) to the interior and opposite angle EAB . Therefore the base FC is equal ( P. 3 ) to the base EB , and the triangle FDC to the triangle EAB . From the figure ABCF , take the tri- angle FDC , and ... Page 39

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**exterior angle**is equal to the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles . Let ABC be a triangle , and let one of its sides BC be produced to D. Then the ...### 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.