## A TREATISE ON PROBLEMS OF MAXIMA AND MINIMA SOLVED BY ALGEBRA |

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7%e same solved algebra altitude base Calculus circumference cone consequently constant given quantity constant quantity cubic equation cylinder Delhi diameter Differential Calculus Eamchundra easily be solved Ellipse ellipsoid equa equal equation we find equation x2 Euclid evidently a minimum exactly divide expression find x2 fore frustrum geometry GIVEN CIRCLE GIVEN TRIANGLE greater GREATEST POSSIBLE hence it appears Hindoo impossible roots India INSCRIBE THE GREATEST isosceles least possible Let ABC let the product let x2 mathematics MAXIMA AND MINIMA maximum negative quantity negative roots parabola perimeter perpendicular plane PROB quadratic equation quadratic we find radius rectangle right angle sides similar triangles solved without impossible Solving this quadratic square surface taken so small tion variable

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Page 5 - RULE.* Multiply the base by the perpendicular height, and half the product will be the area.

Page vii - Greece and India stand out, in ancient tunes, as the countries of indigenous speculation. But the intellectual fate of the two nations was very different. Among the Greeks, the power of speculation remained active during their whole existence as a nation, even down to the taking of Constantinople : it declined, indeed, but it was never extinguished. Their latest knowledge was inquisitive, as well as their earliest. They preserved their great writers unabridged and unaltered and EUCLID did not degenerate...

Page vi - Peninsula, and judging even these more by the grosser parts of their mythology than by the state of domestic life and hereditary institutions, they presume that the Indian question resolves itself into an inquiry how to create a mind in the country, and that mind fashioned on the English standard. They forget that at this very moment there still exists among the higher castes of the country — castes which exercise vast influence over the rest — a body of literature and science which might well...

Page ix - That sound judgment which gives men well to know what is best for them, as well as that faculty of invention which leads to development of resources and to the increase of wealth and comfort, are both materially advanced, perhaps cannot rapidly be advanced without, a great taste for pure speculation among the general mass of the people, down to the lowest of those who can read and write.

Page 7 - CD, and the halves of all the sides, or the half perimeter of the polygon. Now, conceive the number of sides of the polygon to be indefinitely increased; then will its perimeter coincide with the circumference of the circle, and consequently the altitude CD will become equal to the radius, and the whole polygon equal to the circle. Consequently, the space of the circle, or of the polygon, in that state, is equal to the rectangle of the radius and half the circumference.

Page x - The history of England, as well as of other countries, having impressed me with a strong conviction that pure speculation is a powerful instrument in the progress of a nation...

Page xiii - RAMCHUNDRA'S problem — and I think it ought to go by that name, for I cannot find that it was ever current* as an exercise of ingenuity in Europe — is to find the value of a variable which will make an algebraical function a maximum or a minimum, under the following conditions. Not only is the differential calculus to be excluded, but even that germ of it which, as given by FERMAT in his treatment of this very problem, made some think that he was entitled to claim the invention. The values of...

Page 161 - TO FIND A POINT WITHIN A TRIANGULAR PYRAMID,, FROM WHICH IF LINES BE DRAWN TO THE ANGULAR POINTS, THE SUM OF THEIR SQUARES IS THE LEAST POSSIBLE.

Page 32 - OF ALL TRIANGLES UPON THE SAME BASE, AND HAVING THE SAME PERIMETER, FIND THAT WHICH HAS THE GREATEST AREA.

Page 4 - ... parallelograms. 42. A sphere is a solid figure, generated by the revolution of a circle on its diameter, which is then called the axis. 43. A cube is a solid formed of six equal and mutually parallel sides, all of which are squares. 44 A tetrahedron is a solid contained under four equal, equilateral triangles. 45. A dodecahedron is a solid contained under twelve equal, equilateral, and...