The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página 5
... greater than a right angle . And an acute angle is that which is less than a right angle . XVIII . Rectilineal ( or rectilinear ) figures are those which are bounded by straight lines . XIX . Triangles are rectilineal figures which are ...
... greater than a right angle . And an acute angle is that which is less than a right angle . XVIII . Rectilineal ( or rectilinear ) figures are those which are bounded by straight lines . XIX . Triangles are rectilineal figures which are ...
Página 5
... greater mag- nitude , when the less measures the greater ; that is , when the less is contained a certain number of times exactly in the greater . XXVIII . - A greater magnitude is said to be a multiple of a less , when the greater is ...
... greater mag- nitude , when the less measures the greater ; that is , when the less is contained a certain number of times exactly in the greater . XXVIII . - A greater magnitude is said to be a multiple of a less , when the greater is ...
Página 6
... of the same thing or of equal things are equal to one another . VI . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . VII . The whole is greater than its part . ( 6 )
... of the same thing or of equal things are equal to one another . VI . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . VII . The whole is greater than its part . ( 6 )
Página 7
Āryabhaṭa Jasoda Nauden Sircar. VII . The whole is greater than its part . VIII . The parts together are equal to the whole . IX . Two straight lines can not enclose a space . X. If two straight lines intersect one another they cannot be ...
Āryabhaṭa Jasoda Nauden Sircar. VII . The whole is greater than its part . VIII . The parts together are equal to the whole . IX . Two straight lines can not enclose a space . X. If two straight lines intersect one another they cannot be ...
Página 12
... greater , which is absurd . In similar way , it can be to proved , that no part of AC could be equal to AB . Therefore AB is not unequal to AC ; that is , AB is qual to AC . Wherefore , the angles at the base & c . Q.E.D. THEOREM . ( E ...
... greater , which is absurd . In similar way , it can be to proved , that no part of AC could be equal to AB . Therefore AB is not unequal to AC ; that is , AB is qual to AC . Wherefore , the angles at the base & c . Q.E.D. THEOREM . ( E ...
Términos y frases comunes
AC is equal alternate angle ABC angle ADB angle BAC angle DEF angles are equal arc BC base BC bisected centre circle circumference coincide conversely described diameter divided double draw drawn equal angles equal Ax equal to AC equiangular Euclid exterior extremities fall figure fore four fourth Geometry given straight lines greater interior angles Join less Let ABC magnitudes meet multiple opposite angles parallel parallelogram parallelogram AC pass perpendicular Place polygon produced PROP propositions proved Q.E.D. PROP radius reason rectangle contained rectilineal figure right angles sector segment semicircle shown side BC sides similar square stand straight line taken THEOREM third angle touches the circle triangle ABC twice Wherefore
Pasajes populares
Página 10 - If two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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.
Página 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.
Página 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.
Página 74 - Any two sides of a triangle are together greater than the third side.
Página 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...
Página 53 - ... figures are to one another in the duplicate ratio of their homologous sides.
Página 62 - ... in a segment less than a semicircle, is greater than a right angle...
Página 59 - The angles in the same segment of a circle are equal to one another.