The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page 31
... equiangular triangles are proportionals and those which are opposite to the equal angles are homologous . Conversely , if the sides about each of their angles be proportionals , the triangles are equiangular , i.e. , have these angles ...
... equiangular triangles are proportionals and those which are opposite to the equal angles are homologous . Conversely , if the sides about each of their angles be proportionals , the triangles are equiangular , i.e. , have these angles ...
Page 32
... on C and the side DA on the side CA Draw AG parallel to AB . Join EG . It can be shown that the triangle ABC and AGC are equiangular and therefore have their sides about the equal angles proportionals , i.e. , AB to BC as ( 32 )
... on C and the side DA on the side CA Draw AG parallel to AB . Join EG . It can be shown that the triangle ABC and AGC are equiangular and therefore have their sides about the equal angles proportionals , i.e. , AB to BC as ( 32 )
Page 33
... equiangular ( P. 3 ) : viz . , the angle GAC is equal to the angle CAE , the angle AGC to the angle AEC and the angle ACG to the angle ACE . But it has been shown that the angles GAC , AGC and ACG are respectively equal to the angles ...
... equiangular ( P. 3 ) : viz . , the angle GAC is equal to the angle CAE , the angle AGC to the angle AEC and the angle ACG to the angle ACE . But it has been shown that the angles GAC , AGC and ACG are respectively equal to the angles ...
Page 35
... equiangular . Because the angle ADC is equal to the angle AHK and the angle DAC common to the two triangles DAC and AHK .. They are equiangular to one another . Therefore AD is to DC , as AH is to HK ( P. 18 ) . Because the opposite ...
... equiangular . Because the angle ADC is equal to the angle AHK and the angle DAC common to the two triangles DAC and AHK .. They are equiangular to one another . Therefore AD is to DC , as AH is to HK ( P. 18 ) . Because the opposite ...
Page 51
... equi- angular and similar ( P. 18 ) . And AB to BH as BD to BC . Wherefore BH and BD are mean proportionals between AB and BC . Q. E. F. Cor . If four straight lines be proportionals and if a or two means be taken between the extremes ...
... equi- angular and similar ( P. 18 ) . And AB to BH as BD to BC . Wherefore BH and BD are mean proportionals between AB and BC . Q. E. F. Cor . If four straight lines be proportionals and if a or two means be taken between the extremes ...
Common terms and phrases
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
Popular passages
Page 10 - If two triangles have two sides of the one equal to two sides of the...
Page 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.
Page 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.
Page 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.
Page 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.
Page 74 - Any two sides of a triangle are together greater than the third side.
Page 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...
Page 53 - ... figures are to one another in the duplicate ratio of their homologous sides.
Page 62 - ... in a segment less than a semicircle, is greater than a right angle...
Page 59 - The angles in the same segment of a circle are equal to one another.