The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page 15
... alternate angles equal to each other ; these two straight lines are parallel , and conversely , if a straight line falls upon two parallel straight lines , it makes the alternate angles equal . Let the straight line EF , which falls ...
... alternate angles equal to each other ; these two straight lines are parallel , and conversely , if a straight line falls upon two parallel straight lines , it makes the alternate angles equal . Let the straight line EF , which falls ...
Page 16
... alternate angles AEF and EFD equal . Because it can be proved , that no angle either less or greater than EFD can be equal to AEF . For , if possible , let the angle EFH which is less than the angle EFD be equal to the angle AEF ...
... alternate angles AEF and EFD equal . Because it can be proved , that no angle either less or greater than EFD can be equal to AEF . For , if possible , let the angle EFH which is less than the angle EFD be equal to the angle AEF ...
Page 17
... alternate angle ; therefore AB , CD are parallel ( P. 7 ) . Lastly , let the two interior angles BGH and GHD be together equal to two right angles . But BGH and AGH are together equal to two right angles ( cor . 2 : 5 ) . Therefore the ...
... alternate angle ; therefore AB , CD are parallel ( P. 7 ) . Lastly , let the two interior angles BGH and GHD be together equal to two right angles . But BGH and AGH are together equal to two right angles ( cor . 2 : 5 ) . Therefore the ...
Page 18
... alternate angles CAD and ACG equal , therefore these two straight lines are parallel ( Prop . 7 ) . Wherefore , through the point A , AD is drawn parallel to the straight line GII . Q. E. F. Cor . Hence a perpendicular can be drawn to a ...
... alternate angles CAD and ACG equal , therefore these two straight lines are parallel ( Prop . 7 ) . Wherefore , through the point A , AD is drawn parallel to the straight line GII . Q. E. F. Cor . Hence a perpendicular can be drawn to a ...
Page 21
... alternate angle BDC . Because AD is parallel to BC , and BD meets them , the angle ADB is equal ( P. 7 ) to the alter- nate angle CBD . Because in the two triangles ABD , CBD , the two angles ABD , BDA , in the one , A D are equal to ...
... alternate angle BDC . Because AD is parallel to BC , and BD meets them , the angle ADB is equal ( P. 7 ) to the alter- nate angle CBD . Because in the two triangles ABD , CBD , the two angles ABD , BDA , in the one , A D are equal to ...
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.