The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página 10
... angle AFB and CFD coincide and are therefore equal ( Ax . 6 ) . In this way , it can be shown that the angles BFC ... DEF be two trianglès , which have the two A A B base BC is equal to the sides AB , AC equal to the two sides DE , DF , each ...
... angle AFB and CFD coincide and are therefore equal ( Ax . 6 ) . In this way , it can be shown that the angles BFC ... DEF be two trianglès , which have the two A A B base BC is equal to the sides AB , AC equal to the two sides DE , DF , each ...
Página 11
... DEF , and is , therefore equal to it . angles of the one coincide with the the other and are therefore equal to And the remaining remaining angles of them , each to each ; viz . , the angle ABC to the angle DEF , and the angle ACB to the ...
... DEF , and is , therefore equal to it . angles of the one coincide with the the other and are therefore equal to And the remaining remaining angles of them , each to each ; viz . , the angle ABC to the angle DEF , and the angle ACB to the ...
Página 12
... ( def . 6 ) , and the 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 ...
... ( def . 6 ) , and the 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 ...
Página 13
... ( Def . 6 ) . And also BG , ( Def . 6 ) . therefore AG , AH , BG , BH are equal to AB BH are all equal ( Ax . 1 ) . Because the side AG is equal to the side BG , therefore the angle GAB of the ... angles is called a right angle , and ( 13 )
... ( Def . 6 ) . And also BG , ( Def . 6 ) . therefore AG , AH , BG , BH are equal to AB BH are all equal ( Ax . 1 ) . Because the side AG is equal to the side BG , therefore the angle GAB of the ... angles is called a right angle , and ( 13 )
Página 15
... ( Def . 6 ) to BF . Join EC . ' G FB , are equal But the angle Because AF is equal / Const . ) to FC , and BF / Const ... angle CFE , because they are vertical angles . Therefore the base AB is equal ( P. 3 ) to the base CE , the triangle ...
... ( Def . 6 ) to BF . Join EC . ' G FB , are equal But the angle Because AF is equal / Const . ) to FC , and BF / Const ... angle CFE , because they are vertical angles . Therefore the base AB is equal ( P. 3 ) to the base CE , the triangle ...
Términos y frases comunes
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
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.