The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
Dentro del libro
Resultados 1-5 de 38
Página 8
... Wherefore , if a straight line 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 ...
... Wherefore , if a straight line 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 ...
Página 10
... Wherefore , if two angles , & c . Q.E.D. PROP . III . THEOREM . ( Prop 4. Book I. E. ) If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by these sides ...
... Wherefore , if two angles , & c . Q.E.D. PROP . III . THEOREM . ( Prop 4. Book I. E. ) If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by these sides ...
Página 11
... wherefore the base BC coincides with the base EF and is , therefore , equal to it . Wherefore , also the whole triangle ABC coincides with the whole triangle DEF , and is , therefore equal to it . angles of the one coincide with the the ...
... wherefore the base BC coincides with the base EF and is , therefore , equal to it . Wherefore , also the whole triangle ABC coincides with the whole triangle DEF , and is , therefore equal to it . angles of the one coincide with the the ...
Página 12
... , 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 )
... , 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 13
... Wherefore AB is bisected at F Also the angle AFG is equal to the angle BFG ( p . 3 ) . But when a straight line standing on another straight line , makes the adjacent angles equal to one another , eac of these angles is called a right ...
... Wherefore AB is bisected at F Also the angle AFG is equal to the angle BFG ( p . 3 ) . But when a straight line standing on another straight line , makes the adjacent angles equal to one another , eac of these angles is called a right ...
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.