The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
Inni boken
Resultat 1-5 av 5
Side 59
... arc or part of the circumference BC . The angle BEC is double of the angle BAC . Join AE , and produce it to F. First let the centre of the circle be within the angle BAC . Because EA is equal to EB , the angle EAB is equal ( I. 4 ) to ...
... arc or part of the circumference BC . The angle BEC is double of the angle BAC . Join AE , and produce it to F. First let the centre of the circle be within the angle BAC . Because EA is equal to EB , the angle EAB is equal ( I. 4 ) to ...
Side 66
... BC at G and H. Draw GF and HF at right angles to AB and BC . Join FA , FB ... arc intercepted between AL and CL . Join AD , CD . Because DABC is a ... BC be bisected at G and H and from the points G and H perpendiculars GF and HF be drawn ...
... BC at G and H. Draw GF and HF at right angles to AB and BC . Join FA , FB ... arc intercepted between AL and CL . Join AD , CD . Because DABC is a ... BC be bisected at G and H and from the points G and H perpendiculars GF and HF be drawn ...
Side 71
... arc BC and they are greater or less than Therefore the arcs EF equal . Eor , if not , i.e. if EF would be greater or less than BC , the angle BDC would be BAC . But they are equal ( hyp ) . and BC are equal . In a similar way it might ...
... arc BC and they are greater or less than Therefore the arcs EF equal . Eor , if not , i.e. if EF would be greater or less than BC , the angle BDC would be BAC . But they are equal ( hyp ) . and BC are equal . In a similar way it might ...
Side 72
... arc BC is to the are EF , as the angle BGC is to the angle EHF ; and as the angle BAC is to the angle EDF . Also , the arc BC is to the arc EF , as the sector BGC is to the sector EHF . Take any number of arcs CX and XE , each A equal to BC ...
... arc BC is to the are EF , as the angle BGC is to the angle EHF ; and as the angle BAC is to the angle EDF . Also , the arc BC is to the arc EF , as the sector BGC is to the sector EHF . Take any number of arcs CX and XE , each A equal to BC ...
Side 73
... arc EN , the angle BGE is greater than the angle EHN ; and if less , less . But there are four magnitudes , the two arcs BC and EF , and the two angles BGC and EHF ; and of the arc BC , and the angle BGC , have been taken any equi ...
... arc EN , the angle BGE is greater than the angle EHN ; and if less , less . But there are four magnitudes , the two arcs BC and EF , and the two angles BGC and EHF ; and of the arc BC , and the angle BGC , have been taken any equi ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 10 - If two triangles have two sides of the one equal to two sides of the...
Side 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.
Side 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.
Side 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.
Side 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.
Side 74 - Any two sides of a triangle are together greater than the third side.
Side 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...
Side 53 - ... figures are to one another in the duplicate ratio of their homologous sides.
Side 62 - ... in a segment less than a semicircle, is greater than a right angle...
Side 59 - The angles in the same segment of a circle are equal to one another.