The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página 21
... angle BDC . Because AD is parallel to BC , and BD meets them , the angle ADB is equal ( P. 7 ) to the alter- nate angle CBD . Because in the two triangles ABD , CBD , the two angles ABD , BDA , in the one , A D are equal to the two ...
... angle BDC . Because AD is parallel to BC , and BD meets them , the angle ADB is equal ( P. 7 ) to the alter- nate angle CBD . Because in the two triangles ABD , CBD , the two angles ABD , BDA , in the one , A D are equal to the two ...
Página 34
... angle BDE stand opposite to the angle ADC . Join AB . Because the triangles ADC and EDB are equal , therefore they have the same ratio to the triangle ABD ( 16 , cor . 6 ) . B E D But ADC to ADB as DC to BD ( P. 16 ) . And EDB to ADB as ...
... angle BDE stand opposite to the angle ADC . Join AB . Because the triangles ADC and EDB are equal , therefore they have the same ratio to the triangle ABD ( 16 , cor . 6 ) . B E D But ADC to ADB as DC to BD ( P. 16 ) . And EDB to ADB as ...
Página 37
... angle ADB . And the two rectangles LMNP and DFCE are together equal to the figure ABCD . NP Of the two rectangles DFCE and LMNP place one of the sides NP of the one on DE of the other , so that , CE and PM may be in the same straight ...
... angle ADB . And the two rectangles LMNP and DFCE are together equal to the figure ABCD . NP Of the two rectangles DFCE and LMNP place one of the sides NP of the one on DE of the other , so that , CE and PM may be in the same straight ...
Página 41
... angles ADB , DAB and DBA are equal to two right angles ( P. 23 ) . And because the angle ADB is half of the sum , i.e. , two right angles , therefore is equal to one right angle . Conversely , if ADB is a right angle , the ( 41 )
... angles ADB , DAB and DBA are equal to two right angles ( P. 23 ) . And because the angle ADB is half of the sum , i.e. , two right angles , therefore is equal to one right angle . Conversely , if ADB is a right angle , the ( 41 )
Página 42
Āryabhaṭa Jasoda Nauden Sircar. Conversely , if ADB is a right angle , the straight line DC drawn from ADB bisecting the base AB at C is equal to AC or CB . For if not , let make CE equal to AC or CB . CD be produced to E and Join EA ...
Āryabhaṭa Jasoda Nauden Sircar. Conversely , if ADB is a right angle , the straight line DC drawn from ADB bisecting the base AB at C is equal to AC or CB . For if not , let make CE equal to AC or CB . CD be produced to E and Join EA ...
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.