The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page 30
... divided straight line , that is , into parts proportional to the parts of the given divided straight line . ( E. 6. 10 ) . In the above figure , if AC be the straight line divided into parts at D and E , and AB to be divided similarly ...
... divided straight line , that is , into parts proportional to the parts of the given divided straight line . ( E. 6. 10 ) . In the above figure , if AC be the straight line divided into parts at D and E , and AB to be divided similarly ...
Page 31
... divided into parts at F , G similarly to AC . Cor . 3. To find a third proportional to two given straight lines . ( E. 6. 11 ) . In the above figure . If AF and AD be the two straight lines and if FG be made equal to AD . Then AF is to ...
... divided into parts at F , G similarly to AC . Cor . 3. To find a third proportional to two given straight lines . ( E. 6. 11 ) . In the above figure . If AF and AD be the two straight lines and if FG be made equal to AD . Then AF is to ...
Page 44
... divided int any two parts , the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and the parts of the divided line . In the above figure , let BC and BL be two straight lines . Let ...
... divided int any two parts , the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and the parts of the divided line . In the above figure , let BC and BL be two straight lines . Let ...
Page 45
... divided into any two parts , the square of the whole line is equal to the squares of the parts and twice the rectangle contained by the parts . Let AD be a straight line divided into any two parts at B. The square of AD is equal to the ...
... divided into any two parts , the square of the whole line is equal to the squares of the parts and twice the rectangle contained by the parts . Let AD be a straight line divided into any two parts at B. The square of AD is equal to 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.