The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página 14
... greater than either of the interior opposite angles , Let ABC be a triangle , and its side BC be produced to D. The exterior angle ACD is greater than either of the rior opposite angles CBA , BAC , Bisect ( P. 5 ) AC in F , join ( 14 )
... greater than either of the interior opposite angles , Let ABC be a triangle , and its side BC be produced to D. The exterior angle ACD is greater than either of the rior opposite angles CBA , BAC , Bisect ( P. 5 ) AC in F , join ( 14 )
Página 16
... line & c . Q.E.D. PROP . VIII . THEOREM . ( E. 1 , 28-29 . ) If a straight line fall upon two parallel straight lines ; it makes the exterior angle equal to the interior and opposite angle upon the same side of the straight line and ( 16 )
... line & c . Q.E.D. PROP . VIII . THEOREM . ( E. 1 , 28-29 . ) If a straight line fall upon two parallel straight lines ; it makes the exterior angle equal to the interior and opposite angle upon the same side of the straight line and ( 16 )
Página 17
... interior apposite angle or the two interior angles are together equal to two right angles ; the two straight lines are parallel . Let EF fall upon AB , CD which are parallel . The exterior angle EGB is equal to the interior and opposite ...
... interior apposite angle or the two interior angles are together equal to two right angles ; the two straight lines are parallel . Let EF fall upon AB , CD which are parallel . The exterior angle EGB is equal to the interior and opposite ...
Página 20
... interior opposite angle ACF ( P. 6 ) , while they have been shown to be equal ( hyp . ) Wherefore the two triangles coincide and are therefore equal ( Ax . 6 ) . Therefore the two sides AC , BC are equal to the two sides DF , EF , each ...
... interior opposite angle ACF ( P. 6 ) , while they have been shown to be equal ( hyp . ) Wherefore the two triangles coincide and are therefore equal ( Ax . 6 ) . Therefore the two sides AC , BC are equal to the two sides DF , EF , each ...
Página 22
... interior and opposite angle EAB . Therefore the base FC is equal ( P. 3 ) to the base EB , and the triangle FDC to the triangle EAB . From the figure ABCF , take the tri- angle FDC , and the remainder is the parallelogram AC . From the ...
... interior and opposite angle EAB . Therefore the base FC is equal ( P. 3 ) to the base EB , and the triangle FDC to the triangle EAB . From the figure ABCF , take the tri- angle FDC , and the remainder is the parallelogram AC . From the ...
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.