The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page 5
... semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . [ ACB in figure : Prop . 1. is a semicircle ] XI . A sector of a circle is the figure contained by two radii and the arc , or ...
... semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . [ ACB in figure : Prop . 1. is a semicircle ] XI . A sector of a circle is the figure contained by two radii and the arc , or ...
Page 42
... semicircle is a right angle . PROP . XXV . THEOREM . ( E. 6. 8 ) . In a right angled triangle if a perpendicular be drawn from the right angle to the opposite side , the triangles on each side of the perpendicular are similar to the ...
... semicircle is a right angle . PROP . XXV . THEOREM . ( E. 6. 8 ) . In a right angled triangle if a perpendicular be drawn from the right angle to the opposite side , the triangles on each side of the perpendicular are similar to the ...
Page 45
... semicircle ADC , draw BC per- pendicular from B. Join CA , CB . Because the square of AD is equal to the squares of AC and CD ( P. 26 ) , but the square of AC is equal to the squares of AB and BC , and the square of CD is equal to the ...
... semicircle ADC , draw BC per- pendicular from B. Join CA , CB . Because the square of AD is equal to the squares of AC and CD ( P. 26 ) , but the square of AC is equal to the squares of AB and BC , and the square of CD is equal to the ...
Page 50
... semicircle AEB . From the centre B with BD draw the circle DE . Join BE and from E draw EC perpendicular to AB . Because AB to BE as BE to BC ( 25. cor . ) . But BE BD . Therefore AB to BD as BD to BC . And BC is the third proportional ...
... semicircle AEB . From the centre B with BD draw the circle DE . Join BE and from E draw EC perpendicular to AB . Because AB to BE as BE to BC ( 25. cor . ) . But BE BD . Therefore AB to BD as BD to BC . And BC is the third proportional ...
Page 51
... semicircle ACD . From B draw BC perpendicular to AD . Join CA , CD . Because ACD is a right angle and CB is perpen- dicular from it , therefore AB to BC as BC to BD ( P. 25 ) , Therefore BC is the mean proportional required . Secondly ...
... semicircle ACD . From B draw BC perpendicular to AD . Join CA , CD . Because ACD is a right angle and CB is perpen- dicular from it , therefore AB to BC as BC to BD ( P. 25 ) , Therefore BC is the mean proportional required . Secondly ...
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.