The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page 9
... shown in the first proposition . Secondly , let the radius FA remain within the arc CD but the arc BA ( i.e. CGA ) fall beyond the arc CD . Join FG . In this case also , FH which is a part of the radius FG is equal to the whole radius ...
... shown in the first proposition . Secondly , let the radius FA remain within the arc CD but the arc BA ( i.e. CGA ) fall beyond the arc CD . Join FG . In this case also , FH which is a part of the radius FG is equal to the whole radius ...
Page 10
... shown that the angles BFC and AFD are equal . Wherefore , if two angles , & c . Q.E.D. PROP . III . THEOREM . ( Prop 4. Book I. E. ) If two triangles have two sides of the one equal to two sides of the other , each to each ; and have ...
... shown that the angles BFC and AFD are equal . Wherefore , if two angles , & c . Q.E.D. PROP . III . THEOREM . ( Prop 4. Book I. E. ) If two triangles have two sides of the one equal to two sides of the other , each to each ; and have ...
Page 20
... shown that they wholly coincide . Therefore the angles EDF and BAC coincide . Wherefore the sides DE , DF and AB , AC are equal and so are the angles EDF and BAC . Next , let those sides which are opposite to the equal angles in each ...
... shown that they wholly coincide . Therefore the angles EDF and BAC coincide . Wherefore the sides DE , DF and AB , AC are equal and so are the angles EDF and BAC . Next , let those sides which are opposite to the equal angles in each ...
Page 26
... shown , that if the base HC be greater than the base CL , the triangle AHC is greater than the triangle ALC ; if equal , equal ; and if less , less . Therefore , as the base BC is to the base CD , so is the triangle ABC to the triangle ...
... shown , that if the base HC be greater than the base CL , the triangle AHC is greater than the triangle ALC ; if equal , equal ; and if less , less . Therefore , as the base BC is to the base CD , so is the triangle ABC to the triangle ...
Page 30
... shown ; as in the first case , that BD to DA a CE to EA . Thirdly , let GE and FD be drawn paral- lel to BC , and through D , draw DK parallel to BF . It may be shown that FD and GE are parallel to one another ( 8. cor . ) , and that GF ...
... shown ; as in the first case , that BD to DA a CE to EA . Thirdly , let GE and FD be drawn paral- lel to BC , and through D , draw DK parallel to BF . It may be shown that FD and GE are parallel to one another ( 8. cor . ) , and that GF ...
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.