The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
Inni boken
Resultat 1-5 av 7
Side 7
... passes through the centre of a circle and is terminated both ways by the circumference , the straight line divides the circle into two equal parts . Let ABCD be a circle and F its centre . Let AC a straight line pass through the centre ...
... passes through the centre of a circle and is terminated both ways by the circumference , the straight line divides the circle into two equal parts . Let ABCD be a circle and F its centre . Let AC a straight line pass through the centre ...
Side 8
... passes through the centre of a circle , & c . Q.E.D. Corollary . - If one circle touch another internally , they have not the same centre ( Prop . 5 : 3. E. ) . Cor . 2. — If two circles cut one another , they have not the same centre ...
... passes through the centre of a circle , & c . Q.E.D. Corollary . - If one circle touch another internally , they have not the same centre ( Prop . 5 : 3. E. ) . Cor . 2. — If two circles cut one another , they have not the same centre ...
Side 58
... pass- ing through the centre it is bisected . First , let BD be bisected at Let ABCD be a circle . right angles by AC . The centre of the circle ABCD is in AC . For if not , let G be the centre . Join GB , FD , GD . Because FB and FD ...
... pass- ing through the centre it is bisected . First , let BD be bisected at Let ABCD be a circle . right angles by AC . The centre of the circle ABCD is in AC . For if not , let G be the centre . Join GB , FD , GD . Because FB and FD ...
Side 59
... passing through F , the centre , cuts BD at right angles , BD is bisected at E the centre , Join FD , FB . Because FB and FD are equal ( Def . 6 ) , therefore the angle FBE is equal to the angle FDE ( Prop . 4 ) . Because of the two ...
... passing through F , the centre , cuts BD at right angles , BD is bisected at E the centre , Join FD , FB . Because FB and FD are equal ( Def . 6 ) , therefore the angle FBE is equal to the angle FDE ( Prop . 4 ) . Because of the two ...
Side 62
... pass through the extremities of the other two , and be described about the triangle ABC . Q.E.F. 1 Cor . It is manifest , that when the centre of the circle fall , within the triangle , each of its angles is less than a right angles ...
... pass through the extremities of the other two , and be described about the triangle ABC . Q.E.F. 1 Cor . It is manifest , that when the centre of the circle fall , within the triangle , each of its angles is less than a right angles ...
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.