The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página iii
... Similar triangles are to one another in the duplicate ratio of their homologous sides . The whole matter therefore deserves the best attention of the Geometers . The student will find in this edition all the useful pro- positions of ...
... Similar triangles are to one another in the duplicate ratio of their homologous sides . The whole matter therefore deserves the best attention of the Geometers . The student will find in this edition all the useful pro- positions of ...
Página 12
... similar way , it can be to proved , that no part of AC could be equal to AB . Therefore AB is not unequal to AC ; that is , AB is equal to AC . Wherefore , the angles at the base & c . Q.E.D. PROP . V. THEOREM . ( E. 1. 10 ) ( 12 )
... similar way , it can be to proved , that no part of AC could be equal to AB . Therefore AB is not unequal to AC ; that is , AB is equal to AC . Wherefore , the angles at the base & c . Q.E.D. PROP . V. THEOREM . ( E. 1. 10 ) ( 12 )
Página 22
... similar reason , EF is equal to BC . Therefore AD is equal ( Ax . 1 ) to EF ; and DE is common to both Wherefore the whole , or the remainder AE , is equal to the whole , or the remainder DF ( Ax . 2 or 3 ) ; and AB is equal ( P. 11 ) ...
... similar reason , EF is equal to BC . Therefore AD is equal ( Ax . 1 ) to EF ; and DE is common to both Wherefore the whole , or the remainder AE , is equal to the whole , or the remainder DF ( Ax . 2 or 3 ) ; and AB is equal ( P. 11 ) ...
Página 35
... similar to the whole , and to one another and the complements about the diognal are egual . E A H K D Let BD be a parallelogram , of which the diagonal is AC ; and FG and EH parallelograms about the diagonal . Parallelograms FG and EH ...
... similar to the whole , and to one another and the complements about the diognal are egual . E A H K D Let BD be a parallelogram , of which the diagonal is AC ; and FG and EH parallelograms about the diagonal . Parallelograms FG and EH ...
Página 36
... similar . Next , because FG and HK are similar , therefore FK is to KH as FK is to GK ( hyp . ) and also the angle EKG is equal to the angle HKF ( P. 2 ) , therefore the parallelo- grams EG and KD are equal ( P. 19 ) , wherefore ...
... similar . Next , because FG and HK are similar , therefore FK is to KH as FK is to GK ( hyp . ) and also the angle EKG is equal to the angle HKF ( P. 2 ) , therefore the parallelo- grams EG and KD are equal ( P. 19 ) , wherefore ...
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.