## 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

Page 37

...

...

**Space**included between the Circumferences of two Circles ; the one being .. contained within the other . TAKE the difference between the areas of the two circles , as found by the last problem , for the area of the ring . - Or , the ... Page 43

...

...

**spaces**included by contiguous surfaces ; and the sum of the measures of these including surfaces , is the whole surface ...**space**, or another of an equal magnitude . The The least solid measure is the cubic inch , other OF SOLIDS . 4.3 ... Page 46

...

...

**spaces**equal to the length of the base of the cube P , namely , here 3 in the length and 2 in the breadth , making 3 times 2 or 6 squares in the base AC , each equal to the base of the cube P. Hence it B H G is manifest that the ... Page 72

...

...

**spaces**between them by letters placed at the top , and bottom , and sides , for readily finding any field or other object mentioned in a table . In mapping counties , and estates that have uneven grounds of hills and valleys , reduce ... Page 114

... which are geometricals . And the reciprocals of geome- tricals are also geometricals , and in the same ratio , but de- creasing , or in converse order . THEOREM . THEOREM XIII . The three following

... which are geometricals . And the reciprocals of geome- tricals are also geometricals , and in the same ratio , but de- creasing , or in converse order . THEOREM . THEOREM XIII . The three following

**Spaces**, between the 114 CONIC SECTIONS .### 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 CAČ CDČ centre of gravity circle circular segment circumference column cone consequently Corol Cosine Sine Cotan Cotang cubic cubic foot curve cycloid cylinder DEČ 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.