A collection of problems and examples adapted to the 'Elementary course of mathematics'.J. & J.J. Deighton, 1847 - 80 páginas |
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Página 54
... inscribed circle , then A r = 4R sin 2 B C sin sin ― 2 3. In a plane triangle ABC , given the sum of the sides AC , BC ; the perpendicular from the vertex C upon the base AB ; and the difference of the segments of the base made by the ...
... inscribed circle , then A r = 4R sin 2 B C sin sin ― 2 3. In a plane triangle ABC , given the sum of the sides AC , BC ; the perpendicular from the vertex C upon the base AB ; and the difference of the segments of the base made by the ...
Página 55
... inscribed and circumscribed circles is a mean proportional between the greatest and the least ; shew that the sides are in the pro- portion of √5-1 : √5 : √5 + 1 . 14. In a right - angled triangle , if the hypothenuse be divided into ...
... inscribed and circumscribed circles is a mean proportional between the greatest and the least ; shew that the sides are in the pro- portion of √5-1 : √5 : √5 + 1 . 14. In a right - angled triangle , if the hypothenuse be divided into ...
Página 61
... inscribed in a circle in terms of the sides . Prove this 3. The excess of the sine above the versed sine , in angles less than 90o , is greatest when the angle 45o . and find the value of the maximum excess . = 4. In any quadrilateral ...
... inscribed in a circle in terms of the sides . Prove this 3. The excess of the sine above the versed sine , in angles less than 90o , is greatest when the angle 45o . and find the value of the maximum excess . = 4. In any quadrilateral ...
Página 62
... inscribed in , and circumscribed about , a circle . A semicircle is divided into three arcs A , B , C , whose cosecants are in harmonical progression , shew that 11 . A C C sin : sin :: sin A - B 2 B - C : sin 2 12. A regular polygon is ...
... inscribed in , and circumscribed about , a circle . A semicircle is divided into three arcs A , B , C , whose cosecants are in harmonical progression , shew that 11 . A C C sin : sin :: sin A - B 2 B - C : sin 2 12. A regular polygon is ...
Página 63
... inscribed square is an harmonical mean between the sides containing the right angle . 19. Prove that the area of a regular polygon inscribed in a circle is a geometrical mean between the areas of an inscribed and of a circumscribed ...
... inscribed square is an harmonical mean between the sides containing the right angle . 19. Prove that the area of a regular polygon inscribed in a circle is a geometrical mean between the areas of an inscribed and of a circumscribed ...
Términos y frases comunes
a²b a³b ab² ab³ angle of incidence angular arithmetical mean arithmetical series axis base beam body is projected centre of gravity circle coefficient concave convex lens cos² cosec cube cylinder distance Divide double convex lens elastic ball equal equation feet find the angle find the focal find the height Find the number find the value focal length focus force fulcrum geometrical progression given point given weight harmonical mean horizontal plane inches inclined plane inscribed latus rectum luminous point miles mirror Multiply observed parallel perpendicular placed polygon prism Prove pully quantities radii radius ratio ray of light rays diverging reflexion refracted regular polygon respectively right angle shew sin² specific gravity sphere spherical reflector square string passing subtends Subtract tower vertical plane
Pasajes populares
Página 23 - A man travelled 105 miles, and then found that if he had not travelled so fast by 2 miles an hour, he should have been 6 hours longer in performing the journey.
Página 22 - B, can perform a piece of work together in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. In what time would each do it separately ? Ans. A in 24 days, B in 48 days.
Página 22 - There is a cistern, into which water is admitted by three cocks, two of which are of exactly the same dimensions. When they are all open, five-twelfths of the cistern is filled in four hours; and if one of the equal cocks be stopped, seven-ninths of the cistern is filled in ten hours and forty minutes.
Página 52 - A person standing at the edge of a river observes that the top of a tower on the edge of the opposite side subtends an angle of 55° with a line drawn from his eye parallel to the horizon ; receding backwards 30 feet, he then finds it to subtend an angle of 48°. Determine the breadth of the river. log. sin 7° = 9.08589 log.
Página 32 - At a game of cards, 3 being dealt to each person, any one can have 425 times as many hands as there are cards in the pack. How many cards are there 1 12.
Página 89 - A descends alone ; the pressure of the atmosphere is equal to that of a column of water...
Página 21 - Fifteen guineas should weigh four ounces ; but a parcel of light gold having been weighed and counted, was found to contain 9 more guineas than was supposed from the weight ; and a part of the whole, exceeding the half by four guineas and a half, was found to be 1-^ oz.
Página 31 - If the first has to the second the same ratio which the third has to the fourth...
Página 24 - For every yard of the better sort he gave as many shillings as he had yards in all ; and for every yard of the worse as many shillings as there were yards of the better sort more than of the worse. And the whole price of the better sort was to the whole price of the worse as 72 to 7. How many yards had he of each ? Ans.
Página 94 - There are three plane reflectors, two of which are at right angles to each other, and a ray of light is incident upon the third, and reflected successively by each of them...