The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Page ii
... in question . In the manuscript of Dasa Gitica Parisistacam or the Hindoo Geometry in hand , the enunciations are stated in the left part of the page and the figures are given in the iii right . Hints or notes , if any , ii.
... in question . In the manuscript of Dasa Gitica Parisistacam or the Hindoo Geometry in hand , the enunciations are stated in the left part of the page and the figures are given in the iii right . Hints or notes , if any , ii.
Page iii
... figures agree with those of Euclid perfectly and there is internal evidence to suspect that either Euclid has borrowed from the Hindoo Geometry or that the Hindoo Geometry is an abridgment of Euclid . In twelve cases where no figures ...
... figures agree with those of Euclid perfectly and there is internal evidence to suspect that either Euclid has borrowed from the Hindoo Geometry or that the Hindoo Geometry is an abridgment of Euclid . In twelve cases where no figures ...
Page iv
... figure or figures as given in the original and the reader can realize well the difficulties in which the editor was placed in explaining a figure ( for instance the figure : Prop . 47 ) when it presented itself to his eyes as alto ...
... figure or figures as given in the original and the reader can realize well the difficulties in which the editor was placed in explaining a figure ( for instance the figure : Prop . 47 ) when it presented itself to his eyes as alto ...
Page 3
... figures : prop43 ) | कथमित्याह स्प क्ष्यति यदि रेखापरिणाहं यदि वार्त्तिकरेखाश्चापि एकस्मिन्नथ योगा अपरस्मिन् सदृशाः पर्य्यायेण || ( figure42 ) ...
... figures : prop43 ) | कथमित्याह स्प क्ष्यति यदि रेखापरिणाहं यदि वार्त्तिकरेखाश्चापि एकस्मिन्नथ योगा अपरस्मिन् सदृशाः पर्य्यायेण || ( figure42 ) ...
Page 5
... figure is that which is enclosed by one or more boundaries . VI . A circle is a plane figure bounded by one line , which is called the circumference , and is such that all straight lines drawn from a certain point within it to the ...
... figure is that which is enclosed by one or more boundaries . VI . A circle is a plane figure bounded by one line , which is called the circumference , and is such that all straight lines drawn from a certain point within it to the ...
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.