A Course of Mathematics in Two Volumes for the Use of Academies as Well as Private TuitionJ. Johnson; W.J. and J. Richardson, 1807 - Mathematics Vol. 1 is the 6th ed. published in 1810. Vol. 2 is the 5th ed. published in 1807. The book contains three signatures of Robert Hoddle, all dated 1812 and mathematical calculations in Hoddle's hand on the front end paper and fly leaf. |
From inside the book
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Page 22
... earth in the horizon , or farthest visible point , be 87 ° 58 ' ; it is required from these to de- termine the magnitude of the whole earth , and the utmost distance that can be seen on its surface from the top of the mountain ...
... earth in the horizon , or farthest visible point , be 87 ° 58 ' ; it is required from these to de- termine the magnitude of the whole earth , and the utmost distance that can be seen on its surface from the top of the mountain ...
Page 34
... circumference , is the side of the in- scribed regular hexagon , and is therefore equal to the radius AE or 1 hence , in the right - angled triangle ACD , it will be DC √ AD2 AC2 Ex . 2. If the circumference of the earth be 34 MENSURATION.
... circumference , is the side of the in- scribed regular hexagon , and is therefore equal to the radius AE or 1 hence , in the right - angled triangle ACD , it will be DC √ AD2 AC2 Ex . 2. If the circumference of the earth be 34 MENSURATION.
Page 35
Charles Hutton. Ex . 2. If the circumference of the earth be 25000 miles , what is its diameter ? By the 2d rule , as 3'1416 : 1 :: 25000 : 7957 nearly the diameter . PROBLEM - √AD2 — A02 = √2o — 16 = √3 = 1.7320508076 , the supple ...
Charles Hutton. Ex . 2. If the circumference of the earth be 25000 miles , what is its diameter ? By the 2d rule , as 3'1416 : 1 :: 25000 : 7957 nearly the diameter . PROBLEM - √AD2 — A02 = √2o — 16 = √3 = 1.7320508076 , the supple ...
Page 50
... earth , its diameter being 79574 miles , and its circumference 25000 miles . Ans . 198943750 sq . miles . Ex . 4. The axis of a sphere being 42 inches , what is the convex superficies of the segment whose height is 9 inches ? Ans ...
... earth , its diameter being 79574 miles , and its circumference 25000 miles . Ans . 198943750 sq . miles . Ex . 4. The axis of a sphere being 42 inches , what is the convex superficies of the segment whose height is 9 inches ? Ans ...
Page 51
... earth , supposing its circumference to be 25000 miles . Ans . 263858149120 miles . PROBLEM IX . To find the Solid Content of a Spherical Segment . RULE I. From 3 times the diameter of the sphere také * For , put d the diameter , c = the ...
... earth , supposing its circumference to be 25000 miles . Ans . 263858149120 miles . PROBLEM IX . To find the Solid Content of a Spherical Segment . RULE I. From 3 times the diameter of the sphere také * For , put d the diameter , c = the ...
Other editions - View all
A Course of Mathematics, Vol. 2 of 2: For the Use of Academies, as Well as ... Charles Hutton No preview available - 2017 |
A Course of Mathematics, Vol. 2 of 2: For the Use of Academies, as Well as ... Charles Hutton No preview available - 2018 |
A Course of Mathematics, Vol. 1 Of 2: For the Use of Academies, As Well As ... Charles Hutton No preview available - 2017 |
Common terms and phrases
absciss altitude angle axis ball base body breadth CA² CD² centre of gravity circle circular segment circumference column cone consequently Corol Cosine Sine Cotan Cotang cubic cubic foot curve cycloid cylinder DE² denote density descending diameter direction distance divided draw drawn ellipse equal equation equilibrio EXAM feet figure find the area find the fluent fluid foot force frustum half Hence hyperbola inches inclined plane length lever measure motion moving multiply nearly ordinate parabola parallel parallelogram pendulum perp perpendicular pressure PROBLEM prop proportional PROPOSITION quantity QUEST quicksilver radius ratio rectangle resistance SCHOLIUM secant side Sine Cosine Tang solid space specific gravity square supposed surface tangent theor THEOREM theref trapezium triangle variable velocity vibration weight whole yards
Popular passages
Page 62 - 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.
Page 1 - The Circumference of every circle is supposed to be divided into 360 equal parts, called Degrees ; and each degree into 60 Minutes, each minute into 60 Seconds, and so on. Hence a semicircle contains 180 degrees, and a quadrant 90 degrees. 58. The Measure of an angle is an arc of any circle contained between the two lines which form that angle, the angular point being the centre ; and it is estimated by the number of degrees contained in that arc.
Page 173 - MECHANICAL POWERS are certain simple instruments employed in raising greater weights, or overcoming greater resistance than could be effected by the direct application of natural strength. They are usually accounted six in number; viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.
Page 44 - How many cubic feet in a block of marble, of which the length is 3 feet 2 inches, breadth 2 feet 8 inches, and height or thickness 2 feet 6 inches ? Ans.
Page 86 - WORK. — Glaziers take their dimensions either in feet, inches, and parts ; or feet, tenths, and hundredths. And they compute their work in square feet. In taking the length and breadth of a window, the cross bars between the squares are included. Also, windows of round or oval forms are measured as square, measuring them to their greatest length and breadth, on account of the waste in cutting the glass.
Page 199 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 213 - In turning a one-horse chaise within a ring of a certain diameter, it was observed that the outer wheel made two turns, while the inner made but one : the wheels were both 4 feet high •, and supposing them fixed at the distance of 5 feet asunder on the axletree, what was the circumference of the track described by the outer wheel ? Ans. 62-33 feet. QUEST. 12. What is the side of that equilateral triangle, whose area cost as much paving at 8d.
Page 221 - Then say, As the weight lost in water, Is to the whole weight, So is the specific gravity of water, To the specific gravity of the body.
Page 298 - ... and the relation between these three quantities being universally expressed by this equation m = qf, it follows that, by means of it, any one of the three may be expelled out of the calculation, or else brought into it. Also, the momentum, or quantity of motion in a moving body, is qv, the product of the velocity and matter. It is also to be observed, that the theorems equally hold good for the destruction of motion and velocity, by means of retarding forces, as for the generation of the same,...
Page 173 - A LEVER is any inflexible rod, bar, or beam, which, serves to raise weights, while it is supported at a point by a fulcrum or prop, which is the centre of motion. The lever is supposed to be void of gravity or weight, to render the demonstrations easier and simpler.