The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Results 1-5 of 14
Page 13
... perpendicular from the point of bisec- tion . From the point A , as centre , with the straight line AB , draw the circle GBH and from B with BA draw the circle AD . AG and AH are Join AG , BG , AH , BH and GH . equal to AB ( Def . 6 ) ...
... perpendicular from the point of bisec- tion . From the point A , as centre , with the straight line AB , draw the circle GBH and from B with BA draw the circle AD . AG and AH are Join AG , BG , AH , BH and GH . equal to AB ( Def . 6 ) ...
Page 14
... perpendicular to it from the point of bisection . Q. E. F. , Cor . 1. It is plain that a perpendicular can be drawn from any given point in a straight line ( E 1. 11 ) . Because , if AF be a straight line , then from F a given point in ...
... perpendicular to it from the point of bisection . Q. E. F. , Cor . 1. It is plain that a perpendicular can be drawn from any given point in a straight line ( E 1. 11 ) . Because , if AF be a straight line , then from F a given point in ...
Page 18
... perpendicular can be drawn to a straight line or to a straight line produced from a point either within or without the straight line . Because , a perpendicular can be drawn from the point ( 18 )
... perpendicular can be drawn to a straight line or to a straight line produced from a point either within or without the straight line . Because , a perpendicular can be drawn from the point ( 18 )
Page 19
Āryabhaṭa Jasoda Nauden Sircar. Because , a perpendicular can be drawn from the point of bisection ( P. 5 ) and a straight line parallel to it can be drawn from the given point ( P. 9 ) . The parallel straight line will be the perpendicular ...
Āryabhaṭa Jasoda Nauden Sircar. Because , a perpendicular can be drawn from the point of bisection ( P. 5 ) and a straight line parallel to it can be drawn from the given point ( P. 9 ) . The parallel straight line will be the perpendicular ...
Page 36
... base and between the same parallels , therefore the parallelo- gram is double of DFC ( P. 13 ) . Therefore the paral lelogram FE is equal to the triangle DBC ( Ax . 4 ) . Secondly , even if the perpendicular FD may not meet ( 36 )
... base and between the same parallels , therefore the parallelo- gram is double of DFC ( P. 13 ) . Therefore the paral lelogram FE is equal to the triangle DBC ( Ax . 4 ) . Secondly , even if the perpendicular FD may not meet ( 36 )
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.