The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page iv
... meet with encouragement , the condition of the print and figures will be improved and the original published in full . It is not unlikely , to quote the opinion of Colbroke , that Arya Bhatta flourished several centuries before Christ ...
... meet with encouragement , the condition of the print and figures will be improved and the original published in full . It is not unlikely , to quote the opinion of Colbroke , that Arya Bhatta flourished several centuries before Christ ...
Page 5
... meets the circumference , and being produced does not cut the circle , that is , does not intersect the circumference . [ This ... meet in any point , but do not cut one mother . XV . A plane rectilineal angle is the inclination of [ 2 ]
... meets the circumference , and being produced does not cut the circle , that is , does not intersect the circumference . [ This ... meet in any point , but do not cut one mother . XV . A plane rectilineal angle is the inclination of [ 2 ]
Page 5
... meet together , but are not in the same straight line . N. B. In the figure subjoined B is an angle and is thus expressed : " Angle A B C. " . A B XVI . C When a straight line standing on another straight line makes the adjacent angles ...
... meet together , but are not in the same straight line . N. B. In the figure subjoined B is an angle and is thus expressed : " Angle A B C. " . A B XVI . C When a straight line standing on another straight line makes the adjacent angles ...
Page 5
... meet . XXIV . A parallelogram is a four - sided figure of which the opposite sides are parallel , aud the diagonal is the straight line joining the vertices of two opposite angles . [ See figure Prop . XI . ] XXV . Every right - angled ...
... meet . XXIV . A parallelogram is a four - sided figure of which the opposite sides are parallel , aud the diagonal is the straight line joining the vertices of two opposite angles . [ See figure Prop . XI . ] XXV . Every right - angled ...
Page 16
... meet towards BD . In like manner , it may be prov → ed , that they do not meet when produced towards A , C. But those straight lines in the same plane , which do not meet either way , though produced ever so far , are paral lel ( Def ...
... meet towards BD . In like manner , it may be prov → ed , that they do not meet when produced towards A , C. But those straight lines in the same plane , which do not meet either way , though produced ever so far , are paral lel ( Def ...
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.