The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page ii
... angle , and to allude as having found in a previous work , a straight line equal to a given arc . Moreover , when ... whole appears as a continued demonstration , as if , of a single proposi- tion . The chain is never lost and if lost ...
... angle , and to allude as having found in a previous work , a straight line equal to a given arc . Moreover , when ... whole appears as a continued demonstration , as if , of a single proposi- tion . The chain is never lost and if lost ...
Page iii
... angle are given , and has merely contented himself with publishing the original in Sanscrit . One proposition ... whole matter therefore deserves the best attention of the Geometers . The student will find in this edition all the useful ...
... angle are given , and has merely contented himself with publishing the original in Sanscrit . One proposition ... whole matter therefore deserves the best attention of the Geometers . The student will find in this edition all the useful ...
Page 7
Āryabhaṭa Jasoda Nauden Sircar. VII . The whole is ... whole . IX . Two straight lines can not enclose a space . X. If two straight lines intersect one another they cannot be both parallel to the same straight line . XI . All right angles ...
Āryabhaṭa Jasoda Nauden Sircar. VII . The whole is ... whole . IX . Two straight lines can not enclose a space . X. If two straight lines intersect one another they cannot be both parallel to the same straight line . XI . All right angles ...
Page 8
... whole , which is impossible ( Ax . 7 ) . Therefore ADC will coincide with ABC . Wherefore , if a straight line ... angles are equal . Let the straight lines AC and BD cut one another at the point F. The vertical or opposite angles AFB ...
... whole , which is impossible ( Ax . 7 ) . Therefore ADC will coincide with ABC . Wherefore , if a straight line ... angles are equal . Let the straight lines AC and BD cut one another at the point F. The vertical or opposite angles AFB ...
Page 11
... angle BAC is equal to the angle EDF . Also , the point C shall coincide with the point F , because AB is equal to DF ... whole triangle ABC coincides with the whole triangle DEF , and is , therefore equal to it . angles of the one ...
... angle BAC is equal to the angle EDF . Also , the point C shall coincide with the point F , because AB is equal to DF ... whole triangle ABC coincides with the whole triangle DEF , and is , therefore equal to it . angles of the one ...
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.