The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
From inside the book
Results 1-5 of 6
Page 5
... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or if the multiple of the first bo equal to the multiple of the second , that of the third is also equal to that of ...
... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or if the multiple of the first bo equal to the multiple of the second , that of the third is also equal to that of ...
Page 6
... multiples of the same 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 ...
... multiples of the same 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 ...
Page 25
... multiple the base HC is of the base BC , the same multiple is the triangle AHC of the triangle ABC . For the same reason , whatever multiple the base LC is of the base CD , the same multiple is the triangle ALC of the triangle ADC . But ...
... multiple the base HC is of the base BC , the same multiple is the triangle AHC of the triangle ABC . For the same reason , whatever multiple the base LC is of the base CD , the same multiple is the triangle ALC of the triangle ADC . But ...
Page 27
... multiple of ABC , the first , be less than FC , the multiple of ABF , the second , CE the mul- tiple of ACD , the third is also less than EC the multiple of ADE the fourth , if equal , equal and greater , greater . PROP . XVI ...
... multiple of ABC , the first , be less than FC , the multiple of ABF , the second , CE the mul- tiple of ACD , the third is also less than EC the multiple of ADE the fourth , if equal , equal and greater , greater . PROP . XVI ...
Page 72
... multiple soever the arc BE is of the arc BC , the same multiple is the angle BGE of the angle BGC . For the same reason , whatever multiple the arc EN is of the arc EF , the same multiple is the angle EHN of the angle EHF . If the arc ...
... multiple soever the arc BE is of the arc BC , the same multiple is the angle BGE of the angle BGC . For the same reason , whatever multiple the arc EN is of the arc EF , the same multiple is the angle EHN of the angle EHF . If the arc ...
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.