The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página 5
... extremities of a line are points . IV . A straight line is the shortest distance between two points . V. A figure is that which is enclosed by one or more boundaries . VI . A circle is a plane figure bounded by one line , which is ...
... extremities of a line are points . IV . A straight line is the shortest distance between two points . V. A figure is that which is enclosed by one or more boundaries . VI . A circle is a plane figure bounded by one line , which is ...
Página 21
... extremities of two equal parallel straight lines are equal and parallel ( E. 1. 33 ) . PROP . XII . THEOREM . ( E. I. 35 ) . Parallelograms upon the same base , and between the same parallels , are equal to one another . Let the ...
... extremities of two equal parallel straight lines are equal and parallel ( E. 1. 33 ) . PROP . XII . THEOREM . ( E. I. 35 ) . Parallelograms upon the same base , and between the same parallels , are equal to one another . Let the ...
Página 37
... extremities of the sides . The rectangle is said to be contained by its two contiguous sides . Cor . 3. Given a side , to make a square . If the perpendiculars drawn from the extremities of the side are equal to the side and the other ...
... extremities of the sides . The rectangle is said to be contained by its two contiguous sides . Cor . 3. Given a side , to make a square . If the perpendiculars drawn from the extremities of the side are equal to the side and the other ...
Página 41
... extremities of the base , is a right angle ; and conversely , in a right - angled triangle if a straight line be drawn from the right angle bisecting the base , the straight line is equal to half the base . First , Let AB be a straight ...
... extremities of the base , is a right angle ; and conversely , in a right - angled triangle if a straight line be drawn from the right angle bisecting the base , the straight line is equal to half the base . First , Let AB be a straight ...
Página 62
... 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 each of them being ...
... 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 each of them being ...
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.