The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página 6
... thing or of equal things are equal to one another . V. Equal parts 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 ...
... thing or of equal things are equal to one another . V. Equal parts 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 ...
Página 8
... things which coincide , that is , exactly fill the same space are equal ( Ax . VI ) . But if ADC do not coincide with ABC , let them stand as indicated . Join FD , and produce FD to B. Because a circle is a plane figure bounded by one ...
... things which coincide , that is , exactly fill the same space are equal ( Ax . VI ) . But if ADC do not coincide with ABC , let them stand as indicated . Join FD , and produce FD to B. Because a circle is a plane figure bounded by one ...
Página 9
... thing are equal ( Ax . 5. ) Therefore ABC and BCD are equal . Take away the common part BFC and the remainders AFB and CFD are equal ( Ax . 3 ) . Apply AFB to CFD , so that the point F of the radius FB may be on the point F of the ...
... thing are equal ( Ax . 5. ) Therefore ABC and BCD are equal . Take away the common part BFC and the remainders AFB and CFD are equal ( Ax . 3 ) . Apply AFB to CFD , so that the point F of the radius FB may be on the point F of the ...
Página 12
... things which are equal to the same thing are equal to one another , there- fore the angles at B and C which are equal to the same thing D or F , are equal . Conversely , let the angles at B and C be equal , then the sides BA and AC are ...
... things which are equal to the same thing are equal to one another , there- fore the angles at B and C which are equal to the same thing D or F , are equal . Conversely , let the angles at B and C be equal , then the sides BA and AC are ...
Página 34
... things AC and DF ( P. 13 ) , therefore they are equal ( Ax : 5 ) . But they have their angles at B and E equal . Therefore according to the first case AB to DE as EF to BC . That is , the parallelograms AC , DF have their sides AB , BC ...
... things AC and DF ( P. 13 ) , therefore they are equal ( Ax : 5 ) . But they have their angles at B and E equal . Therefore according to the first case AB to DE as EF to BC . That is , the parallelograms AC , DF have their sides AB , BC ...
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.