The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página ii
... lines it has given all the useful matter , that is contained in the first six books of Euclid besides it seems to give the trisection and , perhaps , polysection of an angle , and to allude as having found in a previous work , a straight ...
... lines it has given all the useful matter , that is contained in the first six books of Euclid besides it seems to give the trisection and , perhaps , polysection of an angle , and to allude as having found in a previous work , a straight ...
Página iii
... given below the enuncia- tions which they are intended to illustrate . Some ... straight lines by a straight line and circle and which , says Mr. Pott , if ... the Hindoo Geometry . The original in Sanskrit is at present reproduced so far.
... given below the enuncia- tions which they are intended to illustrate . Some ... straight lines by a straight line and circle and which , says Mr. Pott , if ... the Hindoo Geometry . The original in Sanskrit is at present reproduced so far.
Página iv
... the finding of two mean proportionals be- tween two given straight lines , which will serve as a specimen for the rest . There ought to have been three figures for the second proposition , but as there is only one figure in the original ...
... the finding of two mean proportionals be- tween two given straight lines , which will serve as a specimen for the rest . There ought to have been three figures for the second proposition , but as there is only one figure in the original ...
Página 7
... straight line pass through the centre and be terminated both ways by the circumference at the points A and C. AC divides the circle ABCD into two equal parts ABC and ADC . A * Given a circle , the centre and a diameter , to prove that the ...
... straight line pass through the centre and be terminated both ways by the circumference at the points A and C. AC divides the circle ABCD into two equal parts ABC and ADC . A * Given a circle , the centre and a diameter , to prove that the ...
Página 13
... given finite straight line and to draw a perpendi- cular to it from the point of bisection . Let AB be a finite straight line . It is required to bisect AB and to raise a perpendicular from the point of bisec- tion . From the point A ...
... given finite straight line and to draw a perpendi- cular to it from the point of bisection . Let AB be a finite straight line . It is required to bisect AB and to raise a perpendicular from the point of bisec- tion . From the point A ...
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.