The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page 4
... square ) . अथप्रसङ्गात् त्रिधाच्छेदं दर्शयति योगस्य । क्षेत्रं प्राह प्रकारमाह । द्विकभूमिं द्विधाकृत्य भुजे लम्बं निपा- तयेत् ...
... square ) . अथप्रसङ्गात् त्रिधाच्छेदं दर्शयति योगस्य । क्षेत्रं प्राह प्रकारमाह । द्विकभूमिं द्विधाकृत्य भुजे लम्बं निपा- तयेत् ...
Page 5
... square is a four - sided figure , having all its sides equal and all its angles right angles . XXIII . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways do not meet . XXIV . A ...
... square is a four - sided figure , having all its sides equal and all its angles right angles . XXIII . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways do not meet . XXIV . A ...
Page 37
... square . If the perpendiculars drawn from the extremities of the side are equal to the side and the other extremities of the perpendicular be joined , the rectangle thus formed is a square ( 37 )
... square . If the perpendiculars drawn from the extremities of the side are equal to the side and the other extremities of the perpendicular be joined , the rectangle thus formed is a square ( 37 )
Page 44
... square BN ( 21. cor . 2 ) . From A , draw AD perpendicular to BC ( 9. cor . ) . Pro- duce AD to M. It may be shown ... square of AC ( P. 22 ) . For the same reason , the rectangle BC.BD is equal to the square of AB . But the rectangles ...
... square BN ( 21. cor . 2 ) . From A , draw AD perpendicular to BC ( 9. cor . ) . Pro- duce AD to M. It may be shown ... square of AC ( P. 22 ) . For the same reason , the rectangle BC.BD is equal to the square of AB . But the rectangles ...
Page 45
... square . Therefore the square of a whole line is equal to the rectangles contained by the whole line and each of its parts . PROP . XXVII . THEOREM . ( E. 2. 4. ) If a straight line be divided into any two parts , the square of the ...
... square . Therefore the square of a whole line is equal to the rectangles contained by the whole line and each of its parts . PROP . XXVII . THEOREM . ( E. 2. 4. ) If a straight line be divided into any two parts , the square of 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.