The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página 5
... ABC Prop . 3. is a triangle . ] XX . A right - angled triangle is that which has a right angle . XXI . An isosceles triangle is that which has two sides equal . XXII . A square is a four - sided figure , having all its sides equal and all ...
... ABC Prop . 3. is a triangle . ] XX . A right - angled triangle is that which has a right angle . XXI . An isosceles triangle is that which has two sides equal . XXII . A square is a four - sided figure , having all its sides equal and all ...
Página 10
... angle AFB and CFD coincide and are therefore equal ( Ax . 6 ) . In this way , it can be shown that the angles BFC ... ABC , DEF be two trianglès , which have the two A A sides AB , AC equal to the two sides DE , DF , each to each ; that is , ...
... angle AFB and CFD coincide and are therefore equal ( Ax . 6 ) . In this way , it can be shown that the angles BFC ... ABC , DEF be two trianglès , which have the two A A sides AB , AC equal to the two sides DE , DF , each to each ; that is , ...
Página 11
... triangle ABC coincides with the whole triangle DEF , and is , therefore equal to it . And the remaining angles of the one coincide with the remaining angles of the other and are therefore equal to them , each to each ; viz . , the angle ABC ...
... triangle ABC coincides with the whole triangle DEF , and is , therefore equal to it . And the remaining angles of the one coincide with the remaining angles of the other and are therefore equal to them , each to each ; viz . , the angle ABC ...
Página 12
... angle BAC contained by the sides AB , AC is equal to the angle FAD ( Prop . 2 ) contained by the sides AD , AF , therefore the triangles ABC and ADF are equal ( Prop . 3 ) , and the angles at B and C are equal to the angles at D and F ...
... angle BAC contained by the sides AB , AC is equal to the angle FAD ( Prop . 2 ) contained by the sides AD , AF , therefore the triangles ABC and ADF are equal ( Prop . 3 ) , and the angles at B and C are equal to the angles at D and F ...
Página 14
Āryabhaṭa Jasoda Nauden Sircar. of these angles is called a right angle , and the straight line which stands on the ... ABC be a triangle , and its side BC be produced to D. The exterior angle ACD is greater than either of the morior ...
Āryabhaṭa Jasoda Nauden Sircar. of these angles is called a right angle , and the straight line which stands on the ... ABC be a triangle , and its side BC be produced to D. The exterior angle ACD is greater than either of the morior ...
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.