The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by Jasoda Nandan Sircar1878 |
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Página ii
... fourth and sixth books being not progressively founded upon each other , but being inde- pendent books all founded upon the first and having no intermediate connections . Glimpses of connection appear now and then ( for instance between ...
... fourth and sixth books being not progressively founded upon each other , but being inde- pendent books all founded upon the first and having no intermediate connections . Glimpses of connection appear now and then ( for instance between ...
Página 5
... fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth , if the multiple of the first be less than that of the second , the multiple of the third is also ...
... fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth , if the multiple of the first be less than that of the second , the multiple of the third is also ...
Página 6
... fourth . XXXII . In proportionals the anticedent terms are called homo- logous to one another , as also the consequents to one another . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If the same ...
... fourth . XXXII . In proportionals the anticedent terms are called homo- logous to one another , as also the consequents to one another . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If the same ...
Página 26
... fourth , any equimultiples whatever have been taken , viz . , the base CL and the triangle ALC , and it has been shown , that if the base HC be greater than the base CL , the triangle AHC is greater than the triangle ALC ; if equal ...
... fourth , any equimultiples whatever have been taken , viz . , the base CL and the triangle ALC , and it has been shown , that if the base HC be greater than the base CL , the triangle AHC is greater than the triangle ALC ; if equal ...
Página 27
... fourth , if equal , equal and greater , greater . PROP . XVI . COROLLARY . 2. ( E. 5. 18 ) . If four magnitudes are proportionals , by composition , the first and second together are to the second ; as the third and fourth together are ...
... fourth , if equal , equal and greater , greater . PROP . XVI . COROLLARY . 2. ( E. 5. 18 ) . If four magnitudes are proportionals , by composition , the first and second together are to the second ; as the third and fourth together are ...
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.